Upper Bound on Syntactic Complexity of Suffix-Free Languages

  • Janusz Brzozowski
  • Marek Szykuła
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9118)


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 \(n\geqslant 7\). 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 such a witness language is unique for each \(n\geqslant 7\).


Regular language Suffix-free Syntactic complexity Transition semigroup Upper bound 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Institute of Computer ScienceUniversity of WrocławWrocławPoland

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