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State complexity of prefixfree regular languages
 IN: PROCEEDINGS OF DCFS’06
, 2006
"... We investigate the state complexities of basic operations for prefixfree 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 (DFA) that accepts ..."
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We investigate the state complexities of basic operations for prefixfree 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 (DFA) that accepts the language obtained from the operation. We know that a regular language is prefixfree if and only if its minimal DFA has only one final state and the final state has no outtransitions whose target state is not a sink state. Based on this observation, we reduce the state complexities for prefixfree regular languages compared with the state complexities for (general) regular languages. For both catenation and Kleene star operations of (general) regular languages, the state complexities are exponential in the size of given minimal DFAs. On the other hand, if both regular languages are prefixfree, then the state complexities are at most linear. We also demonstrate that we can reduce the state complexities of intersection and union operations based on the structural properties of prefixfree minimal DFAs.
Simpleregular expressions and languages
 In Proceedings of DCFS’05, 146–157
, 2005
"... We define simpleregular expressions and languages. Simpleregular languages provide a necessary condition for a language to be outfixfree. We design algorithms that compute simpleregular languages from finitestate automata. Furthermore, we investigate the complexity blowup from a given finitest ..."
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We define simpleregular expressions and languages. Simpleregular languages provide a necessary condition for a language to be outfixfree. We design algorithms that compute simpleregular languages from finitestate automata. Furthermore, we investigate the complexity blowup from a given finitestate automaton to its simpleregular language automaton and show that there is an exponential blowup. In addition, we present a finitestate automata construction for simpleregular expressions based on state expansion. 1
IOS Press Intercode Regular Languages ∗
"... Abstract. Intercodes are a generalization of commafree codes. Using the structural properties of finitestate automata recognizing an intercode we develop a polynomialtime algorithm for determining whether or not a given regular language L is an intercode. If the answer is yes, our algorithm yield ..."
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Abstract. Intercodes are a generalization of commafree codes. Using the structural properties of finitestate automata recognizing an intercode we develop a polynomialtime algorithm for determining whether or not a given regular language L is an intercode. If the answer is yes, our algorithm yields also the smallest index k such that L is a kintercode. Furthermore, we examine the prime intercode decomposition of intercode regular languages and design an algorithm for the intercode primality test of an intercode recognized by a finitestate automaton. We also propose an algorithm that computes the prime intercode decomposition of an intercode regular language in polynomial time. Finally, we demonstrate that the prime intercode decomposition need not be unique.
Regular Languagesusing StatePair Graphs
"... We survey recent results on decision algorithms for subfamilies of regular languages. In particular, we look at the decision algorithms using statepair graphs constructed from finitestate automata. The algorithms rely on the structural property of a finitestate automaton that is preserved in its s ..."
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We survey recent results on decision algorithms for subfamilies of regular languages. In particular, we look at the decision algorithms using statepair graphs constructed from finitestate automata. The algorithms rely on the structural property of a finitestate automaton that is preserved in its statepair graph. We also review applications of statepair graphs in different subfamilies of regular languages. ∗ Han was supported by the KIST Tangible Space Initiative Grants 2E20050 and 2Z03050. The Bulletin of the EATCS 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 ..."
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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.