2014/12/06 by Brzozowski, Janusz, Szykuła, Marek
#FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL)
paper · doi:10.48550/arxiv.1412.2281
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.