Syntactic Complexity of Star-Free Languages [article]

Janusz Brzozowski, Baiyu Li
2011 arXiv   pre-print
The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of regular languages is the maximal syntactic complexity of languages in that subclass, taken as a function of the state complexity of these languages. We study the syntactic complexity of star-free regular languages, that is, languages that can be constructed from finite languages using union, complement and concatenation. We find tight upper bounds on the
more » ... ic complexity of languages accepted by monotonic and partially monotonic automata. We introduce "nearly monotonic" automata, which accept star-free languages, and find a tight upper bound on the syntactic complexity of languages accepted by such automata. We conjecture that this bound is also an upper bound on the syntactic complexity of star-free languages.
arXiv:1109.3381v1 fatcat:xdoe2qmlpjcq5j4y7s3jc7dhnm