Abstract
We investigate the state complexity of the square operation on languages represented by deterministic, alternating, and Boolean automata. For each k such that \(1 \le k \le n-2\), we describe a binary language accepted by an n-state DFA with k final states meeting the upper bound \(n2^n - k2^{n-1}\) on the state complexity of its square. We show that in the case of \(k=n-1\), the corresponding upper bound cannot be met. Using the DFA witness for square with \(2^n\) states where half of them are final, we get the tight upper bounds on the complexity of the square operation on alternating and Boolean automata.
Research supported by grant VEGA 2/0084/15 and grant APVV-15-0091. This work was conducted as a part of PhD study of the first author at Comenius University in Bratislava.
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Krajňáková, I., Jirásková, G. (2017). Square on Deterministic, Alternating, and Boolean Finite Automata. In: Pighizzini, G., Câmpeanu, C. (eds) Descriptional Complexity of Formal Systems. DCFS 2017. Lecture Notes in Computer Science(), vol 10316. Springer, Cham. https://doi.org/10.1007/978-3-319-60252-3_17
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DOI: https://doi.org/10.1007/978-3-319-60252-3_17
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