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Syntactic Complexity of Suffix-Free Languages

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syntactic_suffix-free7-s.pdf (253.86 KB)

Date

2017-09-05

Authors

Brzozowski, Janusz
Szykuła, Marek

Journal Title

Journal ISSN

Volume Title

Publisher

Elsevier

Abstract

We solve an open problem concerning syntactic complexity: We prove that the cardinality of the syntactic semigroup of a suffix-free language with n left quotients (that is, with state complexity n) is at most (n−1)n−2+n−2 for n⩾6. Since this bound is known to be reachable, this settles the problem. We also reduce the alphabet of the witness languages reaching this bound to five letters instead of n+2, and show that it cannot be any smaller. Finally, we prove that the transition semigroup of a minimal deterministic automaton accepting a witness language is unique for each n.

Description

The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.ic.2017.08.014 © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

Regular language, Suffix-free, Syntactic complexity, Transition semigroup, Upper bound

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Citation

URI

http://dx.doi.org/10.1016/j.ic.2017.08.014
 http://hdl.handle.net/10012/12500

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Waterloo Research
Computer Science