Abstract
An automaton is monotonic if its states can be arranged in a linear order that is preserved by the action of every letter. We prove that the problem of deciding whether a given automaton is monotonic is NP-complete. The same result is obtained for oriented automata, whose states can be arranged in a cyclic order. Moreover, both problems remain hard under the restriction to binary input alphabets.
M. Szykuła—Supported in part by Polish NCN grant DEC-2013/09/N/ST6/01194.
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Szykuła, M. (2015). Checking Whether an Automaton Is Monotonic Is NP-complete. In: Drewes, F. (eds) Implementation and Application of Automata. CIAA 2015. Lecture Notes in Computer Science(), vol 9223. Springer, Cham. https://doi.org/10.1007/978-3-319-22360-5_23
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