Relating the Degree of Ambiguity of Finite Automata to the Succinctness of their Representation

We consider the problem of how the size of a nondeterministic finite automaton (nfa) representing a regular language depends on the degree of ambiguity of the nfa. We obtain results for the unary and bounded inputs, and partial results for the unrestricted inputs. One of the main results of this paper shows that for unrestricted inputs, deterministic, unambiguous and nondeterministic machines form a hierarchy with respect to the number of states, solving an open problem of Stearns and Hunt. We also propose a new approach to the study of the succinctness of representation through regularity preserving closure properties and obtain some results in this direction.

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