Abstract
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(n 8)–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(n 8) states.
This work was partially supported by the Science and Technology Assistance Agency under contract APVT-20-004104, by the Slovak Grant Agency for Science (VEGA) under contract “Combinatorial Structures and Complexity of Algorithms”, and by MIUR under the projects FIRB “Descriptional complexity of automata and related structures” and COFIN “Linguaggi formali e automi: metodi, modelli e applicazioni”
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Geffert, V., Mereghetti, C., Pighizzini, G. (2005). Complementing Two-Way Finite Automata. In: De Felice, C., Restivo, A. (eds) Developments in Language Theory. DLT 2005. Lecture Notes in Computer Science, vol 3572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11505877_23
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DOI: https://doi.org/10.1007/11505877_23
Publisher Name: Springer, Berlin, Heidelberg
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