2017/08/04 by Janusz Brzozowski, Marek Szykuła, Yuli Ye · 1 citation
Computer Science · Biochemistry, Genetics and Molecular Biology · Mathematics · #semigroups and automata theory #Algorithms and Data Compression #DNA and Biological Computing #Regular language #Cardinality (data modeling) #Suffix #Mathematics #Prefix #Discrete mathematics #Nondeterministic finite automaton #Descriptive complexity theory #Combinatorics #Computer science #Time complexity #Automaton #Automata theory #Linguistics #Theoretical computer science
paper · pdf · doi:10.1007/s00224-017-9803-8
openalex publication_date 2017/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
The state complexity of a regular language is the number of states in a minimal deterministic finite automaton accepting the language. 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 worst-case syntactic complexity taken as a function of the state complexity n of languages in that class. We prove that n n−1, n n−1 + n − 1, and n n−2 + (n − 2)2 n−2 + 1 are tight upper bounds on the syntactic complexities of right ideals and prefix-closed languages, left ideals and suffix-closed languages, and two-sided ideals and factor-closed languages, respectively. Moreover, we show that the transition semigroups meeting the upper bounds for all three types of ideals are unique, and the numbers of generators (4, 5, and 6, respectively) cannot be reduced.