Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6873875 | Information and Computation | 2018 | 17 Pages |
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 (nâ1)nâ2+nâ2 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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Janusz A. Brzozowski, Marek SzykuÅa,