2010/12/17 by Janusz Brzozowski, Bo Liu, Brzozowski, Janusz +1 · 1 citation
Computer Science · #Advanced Algebra and Logic #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Logic, programming, and type systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1012.3962
openalex publication_date 2010/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The quotient complexity, also known as state complexity, of a regular language is the number of distinct left quotients of the language. The quotient complexity of an operation is the maximal quotient complexity of the language resulting from the operation, as a function of the quotient complexities of the operands. The class of star-free languages is the smallest class containing the finite languages and closed under boolean operations and concatenation. We prove that the tight bounds on the quotient complexities of union, intersection, difference, symmetric difference, concatenation, and star for star-free languages are the same as those for regular languages, with some small exceptions, whereas the bound for reversal is 2n-1.