the following description is presented to enable any person skilled in the art to make and use the invention , and is provided in the context of particular applications and their requirements . various modifications to the preferred embodiments will be readily apparent to those skilled in the art , and the generic principles defined herein may be applied to other embodiments and applications without departing from the spirit and scope of the invention . moreover , in the following description , numerous details are set forth for the purpose of explanation . however , one of ordinary skill in the art will realize that the invention might be practiced without the use of these specific details . in other instances , well - known structures and devices are shown in block diagram form in order not to obscure the description of the invention with unnecessary detail . thus , the present invention is not intended to be limited to the embodiments shown , but is to be accorded the widest scope consistent with the principles and features disclosed herein . in one embodiment of the invention , a bottom - up preprocessing process seeks to identify groups of ports that have dc paths between them . the dc paths may be within a leaf circuit , within a branch circuit , or within a root circuit , for example . dc paths within a branch circuit may encompass dc paths within a call within the branch circuit ; such a call may comprise a leaf circuit or another branch circuit , for example . similarly , dc paths within a root circuit may encompass dc paths within a call within the root circuit ; such call may comprise a branch circuit or a leaf circuit , for example . the term call is used to designate an instruction used to retrieve a called circuit module such as a branch or leaf circuit . more specifically , the term call in the computer software context generally signifies a computer program instruction to get or to access some specified information from computer program memory . the term call , as used herein , also signifies the called information , such as a branch circuit or leaf circuit that such computer program call instructs the program to get or to access . thus , the term call is used interchangeably to signify the computer instruction and to signify the called module . a person skilled in the art will understand from the discussion herein that a root circuit , branch circuit and leaf circuit each represent different levels of a circuit design hierarchy . the root circuit is at a higher level of the hierarchy than either the root circuit or the leaf circuit . the branch circuit is at a higher level of the circuit hierarchy than the leaf circuit . there may be many different kinds of root circuits , many different kinds of branch circuits and many different kinds of leaf circuits . a multi - level circuit design hierarchy may have many levels of branch circuits , for example . more generally , a branch circuit may be described as being a first lower level circuit relative to a higher level ( root ) circuit or as being a second lower level circuit relative to a first lower level ( branch ) circuit . similarly , a leaf circuit may be described as being a first lower level circuit relative to a root circuit or as being a second lower level circuit relative to a first lower level ( branch ) circuit , for example . the preprocessing process records groups of ports that have dc paths between them . more particularly , the preprocessing process identifies and records dc path port groups in which group members have dc paths between them . for example , two ports that are members of different dc path port groups , or that are not members of any port groups , do not have dc paths between them . preprocessing proceeds within a circuit hierarchy in a bottom - up direction starting at a port of a given circuit and traversing through nodes within the circuit . preprocessing starts at a leaf circuit level of the hierarchy and progresses up through branch circuit levels . there may be multiple types of leaf circuits , and there may be multiple types and levels of branch circuits . each type of leaf circuit and each type of branch circuit is preprocessed . if there are multiple levels of branch circuits , then preprocessing proceeds level - by - level up through the branch levels . preprocessing also may progress from the branch circuit level to a root circuit level . a circuit iterator structure , which forms no part of the present invention and which will be readily understood by persons skilled in the art , provides a map of the hierarchy levels of a hierarchical circuit design structure . this map guides traversals between circuit hierarchy levels . preprocessing , level - by - level , involves evaluation of circuit components , e . g ., leaf circuits and branch circuits , to identify dc paths within circuit components of a circuit hierarchy . in general , for a dc path to exist between two given ports , there should be no circuit element that blocks a dc signal . a dc path evaluation process in accordance with one embodiment of the invention , involves attempts at dc traversal across circuit elements from port - to - port within a circuit component in order to identify dc paths between such ports . a dc path between ports of an element is identified when there is a successful traversal along a dc path between such ports within a circuit element , e . g ., leaf circuit or branch circuit . if all circuit elements along a given circuit path from one port to another port permit passage of a dc signal , then dc traversal is successful , and the given path is determined to be a dc path between the ports . however , if there is a circuit element that blocks passage of a dc signal , then dc traversal is unsuccessful , and the given path is determined not to be a dc path between the ports . the following chart sets forth the dc path properties of several example circuit elements that may be present in a circuit path between nodes . the following chart provides a set of examples and is not intended to be a comprehensive list . hierarchical circuit components lower in a circuit hierarchy are evaluated first so that preprocessing results for circuit components lower in the hierarchy can be used during preprocessing of circuit components higher up in the hierarchy . that is , for example , a circuit component that is called by another circuit component higher up in the circuit hierarchy is preprocessed before the preprocessing of the higher level calling circuit component . thus , as the preprocessing process progresses from the bottom toward the top of a circuit hierarchy , dc path port groups identified for circuit components lower in the hierarchy can be used to more efficiently evaluate possible dc paths within circuit components higher up in the hierarchy . during preprocessing higher level circuit components , the use of dc port group information developed previously during preprocessing of lower level circuit components , can obviate the need to step down into the lower level circuit component to glean dc path information . preprocessing of a higher level circuit component that calls a previously preprocessed lower level circuit component , may effect a dc traversal of such lower level circuit element as if it was a ‘ black box ’. that is , the traversal may proceed by jumping automatically from port - to - port across the lower level circuit component for those ports of the lower level circuit component identified as members of the same dc port group . conversely , during preprocessing of such higher level circuit element , it may be determined that there can be no dc traversal of such lower level circuit between ports of that lower level circuit element that are members of different port groups , or that are not members of any dc port group . thus , dc path traversal information gleaned during preprocessing of lower level circuit elements is used to more efficiently preprocess higher level circuit elements that call such lower level circuit elements . more particularly , for example , assume that dc traversal of circuit paths within a leaf circuit during preprocessing determines which ports of a given leaf circuit are interconnected by a dc path and which are not . dc traversal preprocessing assigns ports of the given leaf circuit to the same dc port group if they have a dc path between . further , assume that a branch circuit includes a circuit path with a call to the given leaf circuit . dc traversal preprocessing of a circuit path within the branch circuit that includes a all to the given leaf circuit may be expedited by reference to previously determined dc port group information . specifically , for example , dc traversal preprocessing automatically determines that there is a dc path across a call to the given leaf circuit if the leaf circuit ports associated with a given branch circuit path are members of the same dc port group . conversely , the dc traversal preprocessing automatically determines that there is not a dc path across a call to the given leaf circuit if the leaf circuit ports associated with a given branch circuit path are not members of the same dc port group . as used herein , ‘ automatically determines ’ means that a dc path determination is made based upon dc port group information without the need to step down in the circuit hierarchy to ( again ) traverse a given lower level ( e . g ., leaf ) circuit to ascertain its internal dc paths . fig6 a - 6b are an illustrative flow diagram representing computer program controlled preprocessing of a hierarchical circuit representation in accordance with one embodiment of the invention . it will be appreciated that the flow of fig6 a - 6b represents a computer program controlled process that can be used to program a general purpose computer to implement the preprocessing process . preprocessing begins at the lowest level of the circuit of a circuit hierarchy as indicated by step 612 . in step 614 , a determination is made as to whether or not there are unprocessed circuit components at a level of the hierarchy that currently is the focus of preprocessing . if there are no unprocessed circuit components at this current level of the circuit hierarchy , then in step 616 a determination is made as to whether this current level of the hierarchy is the top level of the hierarchy . if the current level is the top level of the hierarchy then the preprocessing ends . however , if the level of the circuit hierarchy currently undergoing preprocessing is not the top level of the hierarchy , then in step 618 preprocessing moves up in the circuit hierarchy to a next level up in the hierarchy and returns again to decision step 614 . if in decision step 614 a determination is made that there remain unprocessed circuits at this current level of the hierarchy , then in step 620 , one of the remaining unprocessed circuits at the current level of the hierarchy is selected for preprocessing . in decision step 622 , a determination is made as to whether or not there are unprocessed ports associated with the currently selected circuit at this current level of the circuit hierarchy . if a determination is made that there are no further unprocessed ports associated with the selected circuit , then preprocessing returns to decision step 614 , which determines whether there are additional unprocessed circuits at this current level of the hierarchy . if , on the other hand , decision step 622 determines that there are unprocessed ports associated with the currently selected circuit at the current level of the circuit hierarchy , then in step 624 an unprocessed port of the selected circuit is chosen for preprocessing . in decision step 626 a determination is made as to whether the chosen port already is a member of a previously identified port group . if so , then preprocessing returns to decision step 622 , which determines whether there is another unprocessed port associated with the selected circuit . if the decision step 626 determines that the selected port is not already a member of a port group , then step 628 attempts a dc circuit path traversal starting at the currently selected port . circuit path traversal during preprocessing involves a computer program controlled process that follows a circuit path within the circuit design . the circuit path may be within a root circuit , a branch circuit or a leaf circuit . dc circuit path traversal starts at the currently selected port and proceeds until it arrives at another port or until it arrives at a circuit element , such as a capacitor , that blocks dc signals . only if the dc path traversal successfully proceeds from a selected port of a circuit to another port of a circuit , is a determination made that there is a dc path between those ports . in decision step 630 , there , is a determination as to whether the attempted dc path traversal starting with the currently selected port has been successful . if the traversal has been successful , then in decision step 632 a determination is made as to whether the currently selected port and one or more other ports at the other end of the traversal path which has just been traversed , already are members of a port group . if decision step 632 determines that the beginning or any ending ports on the path just successfully traversed already is a member of a port group , then the other beginning or ending ports on the successfully traversed path are added as members of that existing port group in step 634 . on the other hand , if decision step 632 determines that neither the port at the beginning nor any port at another end of the path just traversed currently is a member of an existing port group , then in step 636 a new port group is established with the beginning and all end ports included as members of a new port group . if decision step 630 determines that the attempted traversal of the path beginning with the currently selected port has been unsuccessful , then in step 638 the currently selected port is added to a list of uncorrelated ports . following step 634 or 636 or 638 , whichever one occurs at this juncture , preprocessing returns to decision step 622 , where a determination is made as to whether there remain unprocessed ports associated with the currently selected circuit component . in one embodiment , a dc path traversal process uses preprocessing results during a search to identify dc paths to ground in a hierarchical circuit design representation . the dc path to ground traversal process proceeds in a direction from higher levels of a circuit design hierarchy to lower levels of the circuit design hierarchy . in the course of the top - down dc traversal , a circuit splitting process may dynamically modify representations of circuit components ( e . g ., leaf circuits or branch circuits ) stored in a database . dc path port group information developed during preprocessing makes the traversal more efficient since it can obviate the need to repeatedly traverse preprocessed circuit components , e . g ., leaf circuits or branch circuits . basically , dc path port group information indicates correlations among ports , which can obviate the need to actually traverse paths within a called circuit component to identify a dc path during the dc path to ground traversal . modification of the database through circuit splitting can subdivide a given call , e . g ., a leaf circuit or branch circuit , into separate instances , such as a call instance that is not floating relative to ground potential and at least one other call instance that is floating relative to ground potential , for example . generally speaking , the dc path to ground traversal proceeds in a breadth first fashion in a top to bottom direction within a circuit hierarchy . for example , if there is a node that is connected to a ground ( or reference ) potential at a higher level of a circuit hierarchy , then the traversal process proceeds from that node . the dc path to ground traversal process traverses all nodes at that higher level of the circuit design hierarchy to ascertain which nodes are connected to ground and which nodes are not connected to ground . for a call within the higher level circuit , a determination is made as to whether a port of such call is associated ( i . e ., is connected on the same circuit path ) with a node of the higher level circuit determined to be dc connected to ground . if the call is associated with a higher level circuit node determined to be dc path connected to ground , then the dc path to ground traversal process proceeds downward through the hierarchy to the called lower level circuit , starting with the port of that call associated with the node that is dc connected to ground . at a next level down in the circuit design hierarchy , the dc path to ground traversal process traverses a circuit path within the next lower level circuit to determine whether at least a portion of that circuit path is dc path connected to the port of the called next lower level down circuit determined to be dc connected to ground . that portion may include one or both of a node of such next lower level down circuit or a port of call to an even lower down in the hierarchy circuit called by such next level down circuit , for example . the dc path to ground traversal process references dc port groups to expedite the circuit path traversal within a call . for example , if a given port of a call is determined to be associated with a higher level circuit node that is connected to a dc path to ground , then all other ports of that instance of the call that are in the same dc port group as that given port are automatically determined to be dc connected to ground . by ‘ automatically determined ’ it is meant that a dc path connection to ground determination is made for certain ports of the call based upon dc port group information without the need to ( again ) traverse the internal circuit paths of the called circuit . a circuit hierarchy can be split in the course of a traversal to account for a given call having at least one instance determined to be floating and another instance determined to be not floating within a circuit hierarchy . for example , one call to a given circuit component , e . g ., a branch circuit or a leaf circuit , may be identified in the course of a circuit hierarchy traversal as being not floating , i . e ., as having a connection to a dc path to ground , and another call to that same given circuit component may be identified as being floating , i . e ., as not having a connection to a dc path to ground . in such a case , the circuit hierarchy can be split so as to include separate instances of the given call , one instance that is marked as not floating and another instance that is marked as not floating . in one embodiment , a new instance of a call is produced for each different dc port signature identified for the call in the course of the dc path to ground traversal . thus , multiple instances of a single call may be produced , each corresponding to a different dc port signature . a call &# 39 ; s dc port signature indicates which ports of a call are dc connected to ground and which are not . basically , a given call may occur multiple times in a hierarchical circuit design . for example , the dc path to ground traversal process may determine that one occurrence of the call has a dc port signature that does not include a dc connection to ground . the dc path to ground traversal process also may determine that another occurrence of the same call has a dc port signature that does include a dc connection to ground . by creating a new call instance for each of these two call occurrences , each can be separately traversed without the need to disrupting the circuit hierarchy . thus , the circuit design hierarchy is maintained , despite different occurrences of a call having different dc path to ground relationships within the hierarchy . in this overall manner , the dc path to ground process proceeds to identify nodes within a given level of a circuit design hierarchy that are connected to ground ; and to then progress downward within the circuit design hierarchy from respective nodes determined to be dc connected to ground at the given level of the hierarchy , to respective ports of calls associated with such nodes . in order to avoid disruption of the hierarchy , in one embodiment , a new instance of a given call is created for each different port signature identified for the given call within the hierarchy . also , in order to expedite processing in one embodiment , dc port group information is used to automatically identify all other ports that are dc connected to a given port determined to be dc connected to ground . fig7 a - 7b provide an illustrative flow diagram representing a computer program controlled dc path to ground traversal process through a hierarchical circuit representation in accordance with an embodiment of the invention . it will be appreciated that the flow of fig7 a - 7b represents a computer program controlled process that can be used to program a general purpose computer to implement the dc path to ground traversal process . dc path to ground traversal starts at step 712 by going to the top level of the circuit hierarchy . in decision step 714 , a determination is made as to whether there are untraversed nodes connected to a ground node or connected to a node that is connected to a higher level circuit component that itself is connected to a dc path to ground . if there are no unprocessed nodes at this current circuit hierarchy level , then in decision step 716 a determination is made as to whether there are still lower levels of the circuit hierarchy that have not yet been traversed . if there are not , then the dc patbto ground traversal process ends . if there are , then in step 718 the traversal process goes down one level in the circuit hierarchy and proceeds back to step 714 and continues the dc path to ground traversal at this next lower level . if in step 714 a determination is made that there do exist nodes that have not been traversed to determine whether there they are connected to a dc path to ground , then in step 720 an untraversed node from the current level is selected for a traversal attempt . in decision step 722 a determination is made as to whether there is a dc blocking element on the currently selected attempted traversal path . a blocking element may be a capacitor , for example . if in decision step 723 a determination is made that the traversal is unsuccessful due to the presence of a blocking element , then in step 724 , all other circuit elements located on the blocked traversal path opposite the blocking circuit element are marked as floating . for example , a circuit component disposed on an opposite side of a capacitor from the currently selected node will be marked as floating . circuit elements marked as floating are not part of a circuit path that has a dc connected to ground . if , on the other hand , in decision 722 a determination is made that there is no dc blocking element in the attempted traversal path , then in decision step 730 , a determination is made as to whether there is a call connected in the attempted traversal path . if decision step 730 determines that there is a call in the circuit path , then in decision step 732 , a determination is made as to whether the port of the call that is connected to the path being traversed is a member of a dc port group for the call . if in decision step 732 it is determined that the port of the call connected to the path is correlated to other ports of the call through membership in a dc port group , then in step 734 the traversal process automatically jumps to each other port of the call that is a member of the dc port group . thus , all such other ports are marked as connected to a circuit path that has dc connection to ground . if in decision step 732 , a determination is made that the selected node of the call incident upon the path under attempted traversal is not correlated to any other port through a dc port group , then in step 736 , the currently selected node is marked as not being connected to a dc path to ground . in the course of step 734 or 736 , assuming that one of these steps occurs , step 740 splits the circuit hierarchy database , to create in the circuit hierarchy a new instance of the call identified in the most recent iteration of step 730 . the new call instance is associated with a dc port signature that indicates dc port connection to ground for at least one port of the new call instance . in one embodiment , the dc port signature serves as an identifier or reference to the new instance . for any given call , only one new instance is created for each dc port signature . the following table provides an example of a port signature for a hypothetical call having four ports . thus , the port signature for the above hypothetical new call instance is ( 1010 ), indicating that two ports are dc connected to ground and two ports are not dc connected to ground . if in decision step 730 , a determination is made that there is not a call in the attempted traversal path , then in step 738 , the next nodes ( s ) in the path under attempted traversal are added to a dc path to ground with the currently selected node . following step 724 or 738 or 740 , whichever occurs , the traversal process returns to step 714 . fig8 is an illustrative drawing of a spice - like model of a hypothetical first leaf circuit 810 used to explain an embodiment of the invention . the first leaf circuit model 810 represents a pair of cascaded inverters 812 , 814 . a first inverter 812 includes mosfets m 1 , m 2 . a second inverter includes mosfets m 3 , m 4 . each respective mosfet includes a dc channel path between its respective source and drain . however , no dc channel path exists between any of the respective mosfet gates and their respective source / drain channels . a first node n 2 is disposed at the source / drain connection between m 1 and m 2 . a second node n 2 is disposed at the source / drain connection between m 3 and m 4 . a conductive path 816 interconnects the first and second nodes , n 1 and n 2 . the first leaf circuit model also includes four ports p 1 - p 4 and two nodes n 1 - n 2 . as used herein , a port signifies a terminal or a pin . as set explained above , a node signifies a point of interconnection between branch paths among circuit elements . during computer program controlled preprocessing , a dc path is identified between the first leaf circuit &# 39 ; s ports p 1 and p 2 due to the dc channel paths of mosfets m 1 and m 2 . specifically , through dc path traversal attempts , a determination is made that there exists a dc path between p 1 and node n 1 , via the m 1 channel , and that there exists a dc path between n 1 and p 2 , via the m 2 channel . it will be appreciated that the dc path is bidirectional . similarly , during preprocessing , a dc path is identified between port p 1 and p 2 due to the dc channel paths of mosfets m 3 and m 4 . specifically , there exists a dc path between p 1 and node n 2 , via the m 3 channel , and there exists a dc path between n 2 and p 2 , via the m 4 channel . thus , a determination is made that the first leaf circuit &# 39 ; s ports p 1 and p 2 are correlated ports . moreover , during computer program controlled preprocessing , a dc path is identified between the first leaf circuit &# 39 ; s p 1 and p 4 and between the first leaf circuit &# 39 ; s p 2 and p 4 . more particularly , through dc path traversal attempts , a determination is made that there exists a dc path between the first leaf circuit &# 39 ; s p 1 and its node n 2 and between n 2 and p 4 . likewise , a determination is made that there exists a dc path between the first leaf circuit &# 39 ; s p 2 and its node n 2 and between n 2 and p 4 . thus , a determination is made that the first leaf circuit &# 39 ; s ports p 1 and p 4 are correlated , and the first leaf circuit &# 39 ; s ports p 2 and p 4 are correlated . as mentioned above , a port group is a collection of ports that are correlated , such that there is a dc path between any two members of the group . for example , for the first leaf circuit 810 , there are dc paths between ports p 1 and p 2 and between p 1 and p 4 and between p 2 and p 4 . therefore , the first leaf circuit &# 39 ; s ports p 1 , p 2 and p 4 are correlated . preprocessing identifies and records these three ports as members of the same port group relative to the first leaf circuit 810 . the first leaf circuit &# 39 ; s port p 3 is not correlated , which means that there is no dc path from that port to any other port in the first leaf circuit 810 . basically , p 3 is connected to the gates of mosfets m 1 and m 2 , and there is no dc path from either of those two gates to any other port of the first leaf circuit 810 . as will be apparent from the illustrative description below , grouping correlated ports of the first leaf circuit 810 into port groups can speed and simplify dc path to ground identification by obviating the need to repeatedly traverse instances of the first leaf circuit 810 to identify dc paths during the dc path to ground traversal process . fig9 is an illustrative spice - like model of a hypothetical second leaf circuit 910 used to explain an embodiment of the invention . in the example , the second leaf circuit model 910 is at the same lower level of the overall circuit hierarchy as the first leaf circuit model 810 . the second leaf circuit model 910 represents a pair of resistors 912 , 914 and a pair of capacitors 916 , 918 . the second leaf circuit includes a four ports p 1 - p 4 and two nodes n 1 , n 2 . a first resistor 912 is connected between port p 1 and node n 1 . a second resistor 914 is connected between port p 2 and n 1 . a first capacitor 916 is connected between port p 3 and node n 2 . a second capacitor 918 is connected between port p 4 and n 2 . during computer program controlled preprocessing , a dc path is identified between the second leaf circuit &# 39 ; s p 1 and p 2 . that is , there is a dc path between ports p 1 and p 2 via resistors 912 and 914 . thus , the second leaf circuit &# 39 ; s ports p 1 , p 2 are correlated . during preprocessing , a dc path is identified between p 3 and p 4 . the capacitors 916 , 918 preclude a dc path between p 3 and p 4 . thus , the second leaf circuit &# 39 ; s ports p 3 , p 4 are uncorrelated . therefore , preprocessing identifies and records p 1 and p 2 as members of the same dc port group relative to the second leaf circuit 910 . fig1 is an illustrative spice - like model of a hypothetical branch circuit 1010 used to explain an embodiment of the invention . in this example , branch circuit 1010 is at a next higher level in the circuit hierarchy above the first and second leaf circuits 810 , 910 . thus , in accordance with one embodiment , branch circuit 1010 is preprocessed after the preprocessing of the first and second leaf circuits 810 , 910 . also , port group membership determinations derived during preprocessing of the first and second leaf circuits 810 , 910 are used during preprocessing of the branch circuit 1010 . the branch circuit model 1010 includes two calls 1012 , 1014 . a first call 1012 is to an instance of the first leaf circuit model 810 illustrated in fig8 . a second call 1014 is to an instance of the second leaf circuit model 910 illustrated in fig9 . the branch circuit model 1010 also includes a resistor 1016 and a capacitor 1018 as shown . the branch circuit model 1010 also includes four ports p 1 - p 4 and two nodes n 1 - n 3 as shown . components of the branch circuit model 1010 are interconnected as follows . branch circuit model port p 1 is connected to port p 1 of the call 1012 to the first leaf circuit 810 . branch circuit capacitor 1018 is connected between port p 2 of the branch circuit model 1010 and p 4 of the call 1014 to the first leaf circuit model 810 . branch circuit node n 3 is on a conductor path between port p 4 of the call 1012 to the first leaf circuit model 810 and branch circuit capacitor 1018 . branch circuit model p 3 is connected to p 3 of the call 1012 to the first leaf circuit model 810 . branch circuit resistor 1016 is connected between p 4 of the branch circuit model and port p 3 of the call 1014 to the second leaf circuit 910 . branch circuit node n 2 is on a branch path between the p 3 of the call 1014 to the second leaf circuit 910 and resistor 1016 of the branch circuit 1010 . branch circuit port p 5 is connected to p 2 of the call 1014 to the second leaf circuit 910 . branch circuit port p 6 is connected to p 4 of the call 1014 to the second leaf circuit 910 . also , p 1 of the call 1014 to the second leaf circuit 910 is connected to p 2 of the call 1012 to the first leaf circuit 810 . during preprocessing , a determination is made that branch circuit ports p 1 and p 5 of the branch circuit 1010 are correlated , and therefore , are members of the same dc port group relative to the branch circuit 1010 . more specifically , through traversal of branch path 1020 within the branch circuit model 1010 , a determination is made that there is a dc path between p 1 of the branch circuit 1010 and p 1 of the call 1012 to the first leaf circuit model 810 . since , ports of p 1 and p 2 of the first leaf circuit model 810 were identified during preprocessing as being correlated , i . e ., members of the same port group , an automatic determination is made that there is a dc path between p 1 and p 2 of the call 1014 to the first leaf circuit 810 . the use of port group information derived during the preprocessing stage to make this determination obviates the need to step down to a lower level of the hierarchy during this preprocessing stage to evaluate dc paths within the first leaf circuit model 810 . based on a branch path through n 1 of the branch circuit 1010 , a determination is made that there is a dc path between p 2 of the call 1012 to the first leaf circuit model 810 and p 1 of the call 1014 to the second leaf circuit model 910 . based upon the correlation between p 1 and p 2 of the call 1014 to the second leaf circuit model 910 , a further determination is made automatically that there is a dc path between p 1 and p 2 of the call 1014 to the second leaf circuit model 910 . again , note that this determination is made based upon preprocessing information without the need to step down in the hierarchy during this traversal stage to evaluate dc paths within the second leaf circuit model 910 . based upon path 1022 in the branch circuit model 1010 , a determination is made that there is a dc path between p 2 of the call 1014 to the second leaf circuit model 910 and port p 5 of the branch circuit model 1010 . thus , there is a dc path between p 1 and p 5 of the branch circuit model 1010 . it happens that in this example , a dc path traverses two different calls , the call 1012 to the first leaf circuit 810 and call 1014 to the second leaf circuit 910 . accordingly , ports p 1 and p 5 of the branch circuit are correlated , and are members of the same dc port group relative to the branch circuit 1010 . also during computer program controlled preprocessing , a determination is made that branch circuit ports p 2 , p 3 , p 4 and p 6 of branch circuit 1010 are uncorrelated . as to port p 2 of the branch circuit 1010 , capacitor 1018 of the branch circuit 1010 precludes a dc path between that p 2 and any other port of the branch circuit 1010 . as to port p 3 of the branch circuit 1010 , a lack of correlation of port p 3 of the call 1012 to the first leaf circuit 810 with any other port of the first leaf circuit 810 indicates that p 3 of the branch circuit 1010 is uncorrelated . this determination is made automatically based upon dc port group information developed about the first leaf circuit 810 during preprocessing , which obviates the need to step down into the hierarchy during this traversal stage to ascertain whether port p 3 of the first leaf circuit 810 is correlated to any other port of the first leaf circuit 810 . as to port p 4 , of the branch circuit 1010 , a lack of correlation of port p 3 of the call 1014 to the second leaf circuit 910 with any other port of the call 1014 to the second leaf circuit 910 indicates that p 4 of the branch circuit 1010 is uncorrelated . as to port p 6 , of the branch circuit 1010 , a lack of correlation of port p 4 of the call 1014 to the second leaf circuit 910 with any other port of the call 1014 to the second leaf circuit 910 indicates that p 6 of the branch circuit 1010 is uncorrelated . the determinations about p 4 and p 6 of the branch circuit 1010 are made automatically based upon dc port group information developed about the second leaf circuit 910 during preprocessing , which obviates the need to step down into the hierarchy during this traversal stage to ascertain whether ports p 3 or p 4 of the second leaf circuit 910 are correlated to any other port of the second leaf circuit 910 . fig1 is an illustrative drawing of a spice - like model of a hypothetical root circuit 1110 used to explain an embodiment of the invention . the root circuit model 1110 includes a call 1112 to an instance of the branch circuit 1010 of fig1 and includes calls 1014 , 1016 to two instances of the second leaf circuit 910 of fig9 . the root circuit model 1110 also includes multiple capacitors 1118 , 1120 , a plurality of resistors 1122 - 1136 , a plurality of nodes n 1 - n 18 and a ground node 1142 , connected as shown . more specifically , nodes n 1 - n 6 of the root circuit model 1110 are respectively connected to ports p 1 - p 5 of the call 1112 to the branch circuit model 1010 . nodes n 11 - n 14 of the root circuit model are respectively connected to ports p 1 - p 4 of a first call 1114 to the second leaf circuit model 910 . nodes n 15 - n 18 of the root circuit model 1110 are respectively connected to ports p 1 - p 4 of a second call 1116 to the second leaf circuit model 910 . in accordance with one embodiment of the invention , a computer program controlled dc path to ground traversal downward through the circuit hierarchy in search of dc paths to ground is performed once preprocessing has been completed . in one embodiment , the traversal proceeds downward from the top of the hierarchy and progresses level - by - level through the hierarchy in a breadth first manner , at each level . moreover , at each level of a circuit hierarchy , the traversal in search of dc paths to ground may begin at each port at that level determined to be connected to a dc path to a designated reference value , which typically is ground potential . thus , a top down traversal may spawn multiple parallel top down traversals , each starting , or branching , from different starting locations within one or more levels of a circuit hierarchy . in this example , the dc path traversal starts at ground node 1142 . a dc path to ground is identified between ground node 1142 and node n 1 of the root circuit model 1110 . the dc traversal process , also traverses a dc circuit path from ground node 1142 across resistor 1124 to node n 6 . due to the presence of capacitor 1118 , the dc traversal process is unable to traverse a dc path from ground node 1142 to node n 3 . nodes n 5 , n 6 and n 1 of root circuit 1110 are associated with ports p 1 , p 5 and p 6 of call 1112 to branch circuit 1010 . the dc traversal path uses the dc port group information developed for root circuit 1010 to determine that ports p 1 and p 5 of branch circuit 1010 are correlated and that ports p 2 , p 3 , p 4 and p 6 are not correlated . based on this information , the dc path traversal process determines that nodes n 1 , n 5 and n 6 of the root circuit 1110 are dc path connected to ground , and that nodes n 2 , n 3 and n 4 of the branch circuit 1110 are not dc path connected to ground . the dc path traversal process also determines that ports p 1 , p 5 and p 6 of call 1112 to root circuit 1010 are connected to a dc path to ground , and that ports p 2 , p 3 and p 4 are not connected to a dc path to ground . the dc path to ground traversal process marks ports p 1 , p 5 and p 6 of call 1112 to branch circuit 1010 as connected to a dc path to ground , and marks ports p 2 , p 3 and p 4 of the call as not connected to a dc path to ground . there is no need to step down again into the branch circuit model 1010 to ascertain this internal dc path , since a determination was made during preprocessing . an absence of dc paths to ground is identified during the top down dc path to ground traversal with respect to nodes n 2 , n 3 , n 4 and n 6 of the root circuit 1110 . specifically , for example , during the traversal at this same level , a determination is made that there is no dc path between ground node 1142 and n 3 of the root circuit due to the presence of capacitor 1118 . a determination also is made that there is no dc path between ground node 1142 and either n 2 or n 4 of the root circuit 1110 . these two nodes n 2 and n 4 are respectively connected to nodes uncorrelated ports p 2 and p 4 of the call 1112 to the branch circuit 1010 . these two nodes , n 2 and n 4 , also are connected to each other through resistors 1128 and 1130 . however , neither nodes n 2 nor n 4 has a dc path connection to the ground terminal 1142 . moreover , node n 6 of the root circuit 1110 has no associated dc path . although this node n 6 is connected with the ground terminal 1142 , it also is connected to uncorrelated port p 6 of the call 1112 to the branch circuit 1010 . thus , n 6 of the root circuit 1110 is not part of a dc path . note that the dc path determinations as to n 2 , n 4 and n 6 were made , at least in part , based upon information about uncorrelated ports developed during preprocessing . thus , there was no need to step down into the branch circuit 1010 to determine whether or not there were internal dc paths between these ports . during the dc path to ground traversal , a determination is made that nodes n 11 and n 12 of the root circuit 1110 are part of a dc path to ground , but nodes n 13 and n 14 of the root circuit 1110 are not part of a dc path . also , during the dc path to ground traversal , a determination is made that none of nodes n 15 - n 18 of the root circuit 1110 is part of a dc path to ground . basically , capacitor 1120 isolates nodes n 15 - n 18 from node n 1 of the root circuit 1110 , which itself , is on a dc path . however , nodes n 11 and n 13 of the root circuit 1110 are connected with n 1 of the root circuit 1110 via resistors . in particular , nodes n 11 and n 13 of the root circuit 1110 are on a dc path to ground because they are connected to n 1 of the root circuit 1110 via resistors 1132 , 1134 and 1132 , 1136 , respectively . hence , these nodes n 11 and n 13 are determined to be on a dc path to ground . nodes n 11 and n 13 of the root circuit 1110 are respectively connected to ports p 1 and p 3 of a first call 1112 to of the second leaf circuit 910 . nodes n 12 and n 14 of the root circuit 1110 are respectively connected to ports p 2 and p 4 of the first call to the second leaf circuit 910 . as explained above , p 1 and p 2 of the second leaf circuit 910 are correlated ; they are members of the same dc port group . thus , nodes n 11 , n 12 and n 13 of the root circuit are determined to be on a dc path to ground and are marked as such . ports p 3 and p 4 of the second leaf circuit 910 are uncorrelated . thus , node n 14 of the root circuit is determined to not be on a dc path to ground and is marked as such . fig1 is an illustrative drawing showing in conceptual terms , a splitting of the circuit hierarchy structure to include additional instances of the second leaf circuit 910 . more particularly , based on the traversal of nodes n 11 , n 12 , n 13 and n 14 , of root circuit 1110 , which are associated with ports p 1 , p 2 , p 3 and p 4 of call dd 14 to the second leaf circuit 910 , the dc path traversal process determines that call 1114 has the following dc port signature : ( 1 , 1 , 1 , 0 ,), where 1 signifies a dc path connected to ground , and 0 signifies that there is no dc path connected to ground . furthermore , based on the traversal of nodes n 15 , n 16 , n 17 and n 18 of root circuit 1110 , which are associated with ports p 1 , p 2 , p 3 and p 4 of call dd 16 to the second leaf circuit 910 , the dc path traversal process determines that call 1116 has the following dc port signature : ( 0 , 0 , 0 , 0 ,). consequently , the dc traversal process splits the portion of the circuit hierarchy representing leaf circuit 910 , to include a first new instance of the second leaf circuit 910 - 1 corresponding to port signature ( 1 , 1 , 1 , 0 ) and to include a second new instance of the second leaf circuit 910 - 2 corresponding to port signature ( 0 , 0 , 0 , 0 ). these two corresponding port signatures are used subsequently by the dc traversal process to reference these two new instances of the second leaf circuit 910 - 1 and 910 - 2 in the circuit design hierarchy . fig1 is an illustrative drawing showing in conceptual terms , a splitting of the circuit hierarchy structure to include additional instances of the branch circuit 1010 . as explained above , based on the traversal of nodes n 1 , n 2 , n 3 , n 4 , n 5 and n 6 , of root circuit 1110 , which are associated with ports p 1 , p 2 , p 3 , p 4 , p 5 and p 6 of call 1112 to the branch circuit 1010 , the dc path traversal process determines that call 1112 has the following dc port signature : ( 1 , 0 , 0 , 0 , 1 , 1 ). consequently , the dc traversal process splits the portion of the circuit hierarchy representing branch circuit 1010 , to include a first new instance of the branch leaf circuit 1010 - 1 corresponding to port signature ( 1 , 0 , 0 , 0 , 1 , 1 ). this corresponding port signature is used subsequently by the dc traversal process to reference this new instance of the root circuit 1010 - 1 in the circuit design hierarchy . when the nodes of the root level of the hierarchy have been traversed , the dc path to ground circuit traversal process , there is a step down into a next lower level of the circuit hierarchy , the branch circuit level in this example . in a current embodiment , the dc path to ground traversal progresses within each level in a breadth first manner . thus , at this next level , the traversal starts from each ground node at that next level , if there are any , and from each circuit element marked as being connected to a dc path to ground within a previously traversed higher level circuit element . in this example , the next level traversal would proceed by pushing inside of branch circuit call 1112 , since ports p 1 , p 5 and p 6 of call 1112 were identified and marked by the dc path to ground traversal process as being part of a dc path to ground . specifically , the dc path traversal process continues the dc path traversal at each of these marked ports p 1 , p 5 and p 6 within the first instance of the branch circuit 1010 - 1 corresponding to port signature ( 1 , 0 , 0 , 0 , 1 , 1 ). in pushing in to the branch level circuit instance 1010 - 1 , the dc traversal process visits nodes n 1 , n 2 and n 3 to determine which , if any , are connected to a dc path to ground . in the course of the branch level traversal , the process determines that port p 1 of branch 1010 is connected to port p 1 of call 1012 to first leaf circuit 810 . the dc path traversal process uses dc port group information developed during preprocessing , to determine that ports p 1 and p 2 of the call 1012 to the first leaf circuit 810 are correlated and that ports p 3 and p 4 of that call 1012 are not correlated . hence , the dc path to ground traversal process marks ports p 1 and p 2 of the call 1012 as dc path connected to ground and marks ports p 3 and p 4 of that call as not dc path connected to ground . the call 1012 to the first leaf circuit 810 , therefore , is determined to have a port signature ( 1 , 1 , 0 , 0 ), and as shown in fig1 , a new first instance of the first leaf circuit 810 - 1 is produced that corresponds to port signature ( 1 , 1 , 0 , 0 ). also , in pushing in to the branch level circuit instance 1010 - 1 , the dc traversal process determines that ports p 5 and p 6 of branch circuit 1010 are connected to port p 2 and p 4 of call 1014 to second leaf circuit 910 . the dc path traversal process uses dc port group information developed during preprocessing , to determine that port p 2 of the call 1014 to the second leaf circuit 910 is correlated to port p 1 of the second leaf circuit 910 . the dc path traversal process also uses dc port group information developed during preprocessing , to determine that port p 4 of the call 1014 to the second leaf circuit 910 is not correlated to port p 3 of the second leaf circuit 910 . thus , the dc path to ground traversal process marks ports p 1 , p 2 and p 4 of the call 1014 , as dc path connected to ground and marks port p 3 as not dc path connected to ground . the call 1014 to the second leaf circuit 910 , therefore , is determined to have a port signature ( 1 , 1 , 0 , 1 ), and as shown in fig1 . when the nodes at the branch level of the hierarchy have been traversed , the dc path to ground circuit traversal process , there is a step down into a next lower level of the circuit hierarchy , the leaf circuit level in this example . as mentioned above , in a current embodiment , the dc path to ground traversal progresses within each level in a breadth first manner . thus , at this next level , the traversal starts from each ground node at that next level , if there are any , and from each circuit element marked as being connected to a dc path to ground within a previously traversed higher level circuit element . in this example , the dc path to ground traversal process needs to traverse each of the three new instances of the second leaf circuit 910 - 1 , 910 - 2 and 910 - 3 having respective port signatures , ( 1 , 1 , 1 , 0 ), ( 0 , 0 , 0 , 0 ) and ( 1 , 1 , 0 , 1 ), and the single new instance of the first leaf circuit 810 - 1 having a port signature ( 1 , 1 , 0 , 0 ). the dc path traversal process traverses the nodes of each of these four leaf level circuit instances . for each respective leaf circuit instance , a respective traversal progresses from each port of the respective instance determined to be connected to a dc path to ground . more specifically , for example , for the first instance of the second leaf circuit 910 - 1 , the traversal begins at ports p 1 , p 2 and p 3 . for the second instance of the second leaf circuit 910 - 2 , there is no need for a traversal since no port is connected to a dc path to ground . thus , all nodes of the second instance of the second leaf circuit 910 - 1 are determined to be not dc path connected to ground . for the third instance of the second leaf circuit 910 - 3 , the dc path traversal proceeds from ports p 1 , p 2 and p 4 . for the first instance of the first leaf circuit , the dc path traversal proceeds from ports p 1 and p 2 . thus , each different new instance of each leaf circuit can be separately traversed without the need to disrupt the circuit design hierarchy . specifically , each new instance is disposed in the hierarchy at the same location in the hierarchy where its original instantiation was located . referring to fig1 , for example , each of the first , second and third new instances of the second leaf circuit , 910 - 1 , 910 - 2 and 910 - 3 is disposed in the hierarchy where the original instantiation of the second leaf circuit 910 was disposed . however , each separate respective new instance can be referenced separately and can be traversed separately using its respective dc port signature . furthermore , the dc path to ground traversal process is made more efficient through the use of dc port group information , which can obviate the need to step down into a call to a lower level of the hierarchy and traverse dc path connections within the call . the dc port group information readily provides dc path connection information for the ports of the call thereby avoiding the need to actually traverse the call to determine the dc path connectivity among ports within the call . fig1 is a schematic drawing of an illustrative computer system 1500 that can be programmed to run a preprocessing process and / or to run a dc path to ground traversal process in accordance with embodiments of the invention . the computer system 1500 includes one or more central processing units ( cpu &# 39 ; s ) 1502 , a user interface 1504 , computer readable storage media 1506 , a system bus 1508 , and one or more bus interfaces for connecting the cpu , user interface , memory and system bus together . the illustrative computer system also includes a network interface 1510 for communicating with other devices 1512 on a computer network . a computer readable hierarchical representation of a circuit design , such as that explained with reference to fig8 - 14 , may be stored in the storage media 1506 . the computer system 1500 may be programmed to preprocess of the hierarchical circuit design representation in accordance with an aspect of the invention . the computer system 1500 also may be programmed to conduct a dc path traversal of the hierarchical circuit design representation in accordance with another aspect of the invention . specifically , for example , the computer readable hierarchical models of circuit design representations may be accessible , via bus 1508 , from interface 1504 , storage media 1508 or other devices 1512 , to a preprocessing program of the embodiment of fig6 a - 6b and / or to a dc path traversal program of the embodiment of fig7 a - 7b that runs on the cpu 1502 . while the invention has been described herein with reference to various illustrative features , aspects and embodiments , it will be appreciated that the invention is susceptible of variations , modifications and other embodiments , other than those specifically shown and described . the invention is therefore to be broadly interpreted and construed as including all such alternative variations , modifications and other embodiments within its spirit and scope as hereinafter claimed .