For both deterministic and non-deterministic FSMs, it is conventional to allow formula_6 to be a partial function, i.e. formula_13 does not have to be defined for every combination of formula_14 and formula_15. If an FSM formula_16 is in a state formula_17, the next symbol is formula_18 and formula_13 is not defined, then formula_16 can announce an error (i.e. reject the input). This is useful in definitions of general state machines, but less useful when transforming the machine. Some algorithms in their default form may require total functions.