Given an initial memory state mem0 and an input stream ins, the machine executes in a step-wise fashion, consuming one input at a time, and generating one output at a time. Provided that (at least) one recognised path path = φ1 ... φn exists leading to a state in which the input has been consumed, the machine yields a final memory state memn and an output stream outs.
Given an initial memory state mem0 and an input sequence ins, the machine processes each input in turn, producing corresponding outputs. If there is at least one recognized path φ1 ... φn that results in all inputs being processed, the machine will produce a final memory state memn and an output stream outs.