Structurally Unambiguous Finite Automata
We define a structurally unambiguous finite automaton (SUFA) to be a nondeterministic finite automaton (NFA) with one starting state q 0 such that for all input strings w and for any state q, there is at most one path from q 0 to q that consumes w. The definition of SUFA differs from the usual definition of an unambiguous finite automaton (UFA) in that the new definition is defined in terms of the transition logic of the finite automaton, and is independent of the choice of final states. We show that SUFA can be exponentially more succinct in the number of states than UFA and MDFA (deterministic finite automata with multiple initial states). Some interesting examples of SUFA are given. We argue that SUFA is a meaningful concept, and can have practical importance as it can implemented efficiently on synchronous models of parallel computation.
KeywordsTransition Logic Starting State Equivalence Problem Regular Language Input String
Unable to display preview. Download preview PDF.
- 6.Ibarra, O., Ravikumar, B.: On sparseness, ambiguity and other decision problems for acceptors and transducers. In: Monien, B., Vidal-Naquet, G. (eds.) STACS 1986. LNCS, vol. 210, pp. 171–179. Springer, Heidelberg (1985)Google Scholar
- 9.Meyer, A.R., Fischer, M.: Economy of description by automata, grammars, and formal systems. In: IEEE Twelfth Annual Symposium on Switching and Automata Theory, pp. 188–191 (1971)Google Scholar
- 11.Schmidt, E.M.: Succinctness of descriptions of context-free, regular and finite languages, PhD Thesis, Cornell University, Ithaca, NY (1978)Google Scholar