Handbook of theoretical computer science (vol. B)
The state complexities of some basic operations on regular languages
Theoretical Computer Science
Handbook of formal languages, vol. 1
Derivatives of Regular Expressions
Journal of the ACM (JACM)
Ultimate-Definite and Symmetric-Definite Events and Automata
Journal of the ACM (JACM)
Efficient string matching: an aid to bibliographic search
Communications of the ACM
State complexity of regular languages
Journal of Automata, Languages and Combinatorics
Finiteness and Regularity in Semigroups and Formal Languages
Finiteness and Regularity in Semigroups and Formal Languages
State Complexity of Basic Operations on Finite Languages
WIA '99 Revised Papers from the 4th International Workshop on Automata Implementation
State complexity of some operations on binary regular languages
Theoretical Computer Science - Descriptional complexity of formal systems
Fast and memory-efficient regular expression matching for deep packet inspection
Proceedings of the 2006 ACM/IEEE symposium on Architecture for networking and communications systems
Algorithms on Strings
State complexity of basic operations on suffix-free regular languages
Theoretical Computer Science
More on the Size of Higman-Haines Sets: Effective Constructions
Fundamenta Informaticae - Machines, Computations and Universality, Part I
Determination of finite automata accepting subregular languages
Theoretical Computer Science
Finite automata and their decision problems
IBM Journal of Research and Development
Decision problems for convex languages
Information and Computation
Syntactic complexity of ideal and closed languages
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Nondeterministic state complexity of star-free languages
CIAA'11 Proceedings of the 16th international conference on Implementation and application of automata
Quotient complexity of ideal languages
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Quotient complexity of closed languages
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Reversal of binary regular languages
Theoretical Computer Science
Quotient Complexity of Closed Languages
Theory of Computing Systems
Hi-index | 5.23 |
A language L over an alphabet @S is a right (left) ideal if it satisfies L=L@S^* (L=@S^*L). It is a two-sided ideal if L=@S^*L@S^*, and an all-sided ideal if L=@S^*L, the shuffle of @S^* with L. Ideal languages are not only of interest from the theoretical point of view, but also have applications to pattern matching. We study the state complexity of common operations in the class of regular ideal languages, but prefer to use the equivalent term ''quotient complexity'', which is the number of distinct left quotients of a language. We find tight upper bounds on the complexity of each type of ideal language in terms of the complexity of an arbitrary generator and of the minimal generator, and also on the complexity of the minimal generator in terms of the complexity of the language. Moreover, tight upper bounds on the complexity of union, intersection, set difference, symmetric difference, concatenation, star, and reversal of ideal languages are derived.