Abstract
We show that, on inputs of length exceeding 5n 2, any n-state unary 2nfa (two-way nondeterministic finite automaton) can be simulated by a (2n+2)-state quasi sweeping 2nfa. Such a result, besides providing a “normal form” for 2nfa’s, enables us to get a subexponential simulation of unary 2nfa’s by 2dfa’s (two-way deterministic finite automata). In fact, we prove that any n-state unary 2nfa can be simulated by a 2dfa with O(n logn+4) states.
Supported by the Slovak Grant Agency for Science (VEGA) under contract #1/7465/20 “Combinatorial Structures and Complexity of Algorithms.”
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Geffert, V., Mereghetti, C., Pighizzini, G. (2001). Converting Two—Way Nondeterministic Unary Automata into Simpler Automata. In: Sgall, J., Pultr, A., Kolman, P. (eds) Mathematical Foundations of Computer Science 2001. MFCS 2001. Lecture Notes in Computer Science, vol 2136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44683-4_35
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DOI: https://doi.org/10.1007/3-540-44683-4_35
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