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)2n − 2 + 1. Since these bounds are known to be reachable, this settles the problems.
This work was supported by the Natural Sciences and Engineering Research Council of Canada grant No. OGP000087, and by Polish NCN grant DEC-2013/09/N/ST6/01194.
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Brzozowski, J., Szykuła, M. (2014). Upper Bounds on Syntactic Complexity of Left and Two-Sided Ideals. In: Shur, A.M., Volkov, M.V. (eds) Developments in Language Theory. DLT 2014. Lecture Notes in Computer Science, vol 8633. Springer, Cham. https://doi.org/10.1007/978-3-319-09698-8_2
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DOI: https://doi.org/10.1007/978-3-319-09698-8_2
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