2011/09/15 by Janusz Brzozowski, Brzozowski, Janusz, Baiyu Li +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #Advanced Algebra and Logic #Chemical Synthesis and Analysis #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1109.3381
openalex publication_date 2011/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 syntactic 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.