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arXiv · 1403.2090

Upper Bounds on Syntactic Complexity of Left and Two-Sided Ideals

Janusz Brzozowski·Marek Szykuła
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Abstract

We solve two open problems concerning syntactic complexity: We prove that the cardinality of the syntactic semigroup of a left ideal or a suffix-closed language with $n$ left quotients (that is, with state complexity $n$) is at most $n^{n-1}+n-1$, and that of a two-sided ideal or a factor-closed language is at most $n^{n-2}+(n-2)2^{n-2}+1$. Since these bounds are known to be reachable, this settles the problems.

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Janusz Brzozowski, Marek Szykuła. 2014-03-09. Upper Bounds on Syntactic Complexity of Left and Two-Sided Ideals. https://arxiv.org/abs/1403.2090

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