It is proved that a two-way alternating finite automaton (2AFA) with n states can be transformed to an equivalent one-way nondeterministic finite automaton (1NFA) with f(n)=2Θ(n logn) states, and that this number of states is necessary in the worst case already for the transformation of a two-way automaton with universal nondeterminism (2Π1FA) to a 1NFA. At the same time, an n-state 2AFA is transformed to a 1NFA with (2 n -1)2+1 states recognizing the complement of the original language, and this number of states is again necessary in the worst case. The difference between these two trade-offs is used to show that complementing a 2AFA requires at least Ω(n logn) states. © 2014 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Geffert, V., & Okhotin, A. (2014). Transforming two-way alternating finite automata to one-way nondeterministic automata. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8634 LNCS, pp. 291–302). Springer Verlag. https://doi.org/10.1007/978-3-662-44522-8_25
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