The state complexities of some basic operations on regular languages
Theoretical Computer Science
Derivatives of Regular Expressions
Journal of the ACM (JACM)
State complexity of regular languages
Journal of Automata, Languages and Combinatorics
On the state complexity of k-entry deterministic finite automata
Journal of Automata, Languages and Combinatorics - Special issue: selected papers of the second internaional workshop on Descriptional Complexity of Automata, Grammars and Related Structures (London, Ontario, Canada, July 27-29, 2000)
On the state complexity of reversals of regular languages
Theoretical Computer Science
Decision Problems for Convex Languages
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
State complexity of basic operations on suffix-free regular languages
Theoretical Computer Science
Theoretical Computer Science
Closures in Formal Languages and Kuratowski's Theorem
DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
On NFAs where all states are final, initial, or both
Theoretical Computer Science
Multiple-entry finite automata
Journal of Computer and System Sciences
A note on multiple-entry finite automata
Journal of Computer and System Sciences
Quotient complexity of ideal languages
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Complexity of operations on cofinite languages
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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
Note on reversal of binary regular languages
DCFS'11 Proceedings of the 13th international conference on Descriptional complexity of formal systems
Complexity in convex languages
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
Basic operations on binary suffix-free languages
MEMICS'11 Proceedings of the 7th international conference on Mathematical and Engineering Methods in Computer Science
Reversal of binary regular languages
Theoretical Computer Science
Nondeterministic state complexity of star-free languages
Theoretical Computer Science
Quotient complexity of ideal languages
Theoretical Computer Science
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A language L is prefix-closed if, whenever a word w is in L, then every prefix of w is also in L. We define suffix-, factor-, and subword-closed languages in an analogous way, where by subword we mean subsequence. We study the quotient complexity (usually called state complexity) of operations on prefix-, suffix-, factor-, and subword-closed languages. We find tight upper bounds on the complexity of the subword-closure of arbitrary languages, and on the complexity of boolean operations, concatenation, star, and reversal in each of the four classes of closed languages. We show that repeated application of positive closure and complement to a closed language results in at most four distinct languages, while Kleene closure and complement gives at most eight.