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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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Cited by 6 (4 self)
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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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Cited by 1 (1 self)
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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
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.