Abstract
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 (2n − 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.
This work is the result of the project implementation: Research and Education at UPJŠ—Heading towards Excellent European Universities, ITMS project code: 26110230056, supported by the Operational Program Education funded by the European Social Fund (ESF).
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Geffert, V., Okhotin, A. (2014). Transforming Two-Way Alternating Finite Automata to One-Way Nondeterministic Automata. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44522-8_25
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