Complementing Two-Way Finite Automata
We study the relationship between the sizes of two-way finite automata accepting a language and its complement. In the deterministic case, by adapting Sipser’s method, for a given automaton (2dfa) with n states we build an automaton accepting the complement with at most 4n states, independently of the size of the input alphabet. Actually, we show a stronger result, by presenting an equivalent 4n–state 2dfa that always halts.
For the nondeterministic case, using a variant of inductive counting, we show that the complement of a unary language, accepted by an n–state two-way automaton (2nfa), can be accepted by an O(n8)–state 2nfa. Here we also make the 2nfa halting. This allows the simulation of unary 2nfa’s by probabilistic Las Vegas two-way automata with O(n8) states.
Keywordsautomata and formal languages descriptional complexity
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- 12.Meyer, A., Fischer, M.: Economy of description by automata, grammars, and formal systems. In: Proc. 12th Ann. IEEE Symp. on Switching and Automata Theory, pp. 188–191 (1971)Google Scholar
- 16.Sakoda, W., Sipser, M.: Nondeterminism and the size of two-way finite automata. In: Proc. 10th ACM Symp. Theory of Computing, pp. 275–86 (1978)Google Scholar