Intersection and union of regular languages and state complexity
Information Processing Letters
The state complexities of some basic operations on regular languages
Theoretical Computer Science
A lower bound technique for the size of nondeterministic finite automata
Information Processing Letters
Handbook of formal languages, vol. 1
Journal of the ACM (JACM)
State complexity of regular languages
Journal of Automata, Languages and Combinatorics
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Parallel Composition of Words with Re-entrant Symbols
Parallel Composition of Words with Re-entrant Symbols
The size of Higman-Haines sets
Theoretical Computer Science
Descriptional and Computational Complexity of Finite Automata
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
More on the Size of Higman-Haines Sets: Effective Constructions
Fundamenta Informaticae - Machines, Computations and Universality, Part I
On the State Complexity of Scattered Substrings and Superstrings
Fundamenta Informaticae
Inverse star, borders, and palstars
Information Processing Letters
Chop operations and expressions: descriptional complexity considerations
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Quotient complexity of ideal languages
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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We investigate the descriptional complexity of some inverse language operations applied to languages accepted by finite automata. For instance, the inverse Kleene star operation for a language L asks for the smallest language S such that S* is equal to L, if it exists [J. Brzozowski. Roots of star events. J. ACM 14, 1967]. Other inverse operations based on the chop operation or on insertion/deletion operations can be defined appropriately. We present a general framework, that allows us to give an easy characterization of inverse operations, whenever simple conditions on the originally considered language operation are fulfilled. It turns out, that in most cases we obtain exponential upper and lower bounds that are asymptotically close, for the investigated inverse language operation problems.