Complementing Two-Way Finite Automata [chapter]

Viliam Geffert, Carlo Mereghetti, Giovanni Pighizzini
2005 Lecture Notes in Computer Science  
We study the relationship between the sizes of two-way finite automata accepting a language and its complement. In the deterministic case, 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
more » ... f 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 2nfa's halting. This allows the simulation of unary 2nfa's by probabilistic Las Vegas two-way automata with O(n 8 ) states.
doi:10.1007/11505877_23 fatcat:2drvedou2ff5rpljrhya44dtri