Results 1 
4 of
4
Quotient complexity of regular languages
 J. Autom. Lang. Comb
, 2010
"... The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is appropriate to define it in formallanguage terms as the nu ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is appropriate to define it in formallanguage terms as the number of distinct quotients of the language, and to call it “quotient complexity”. The problem of finding the quotient complexity of a language f(K,L) is considered, where K and L are regular languages and f is a regular operation, for example, union or concatenation. Since quotients can be represented by derivatives, one can find a formula for the typical quotient of f(K,L) in terms of the quotients of K and L. To obtain an upper bound on the number of quotients of f(K,L) all one has to do is count how many such quotients are possible, and this makes automaton constructions unnecessary. The advantages of this point of view are illustrated by many examples. Moreover, new general observations are presented to help in the estimation of the upper bounds on quotient complexity of regular operations. 1
State complexity of basic operations on suffixfree regular languages
, 2007
"... We investigate the state complexity of basic operations for suffixfree regular languages. The state complexity of an operation for regular languages is the number of states that are necessary and sufficient in the worstcase for the minimal deterministic finitestate automaton that accepts the lan ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
We investigate the state complexity of basic operations for suffixfree regular languages. The state complexity of an operation for regular languages is the number of states that are necessary and sufficient in the worstcase for the minimal deterministic finitestate automaton that accepts the language obtained from the operation. We establish the precise state complexity of catenation, Kleene star, reversal and the Boolean operations for suffixfree regular languages.
State complexity of union and intersection of finite languages
 In Proceedings of DLT’07, Lecture Notes in Computer Science 4588
, 2007
"... Abstract. We investigate the state complexity of union and intersection for finite languages. Note that the problem of obtaining the tight bounds for both operations was open. We compute the upper bounds based on the structural properties of minimal deterministic finitestate automata (DFAs) for fin ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
Abstract. We investigate the state complexity of union and intersection for finite languages. Note that the problem of obtaining the tight bounds for both operations was open. We compute the upper bounds based on the structural properties of minimal deterministic finitestate automata (DFAs) for finite languages. Then, we show that the upper bounds are tight if we have a variable sized alphabet that can depend on the size of input DFAs. In addition, we prove that the upper bounds are unreachable for any fixed sized alphabet. 1
Ajay Kumar
"... Regular languages are closed under union, intersection, complementation, Kleeneclosure and reversal operations. Regular languages can be classified into infixfree, prefixfree and suffixfree. In this paper various closure properties of prefixfree regular languages are investigated and result show ..."
Abstract
 Add to MetaCart
Regular languages are closed under union, intersection, complementation, Kleeneclosure and reversal operations. Regular languages can be classified into infixfree, prefixfree and suffixfree. In this paper various closure properties of prefixfree regular languages are investigated and result shows that prefixfree regular languages are closed under union and concatenation. Under complementation, reverse, Kleeneclosure and intersection operations prefixfree regular languages are not closed.