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The generalization of generalized automata: Expression automata
 International Journal of Foundations of Computer Science
, 2005
"... Abstract. We explore expression automata with respect to determinism, minimization and primeness. We define determinism of expression automata using prefixfreeness. This approach is, to some extent, similar to that of Giammarresi and Montalbano’s definition of deterministic generalized automata. We ..."
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Abstract. We explore expression automata with respect to determinism, minimization and primeness. We define determinism of expression automata using prefixfreeness. This approach is, to some extent, similar to that of Giammarresi and Montalbano’s definition of deterministic generalized automata. We prove that deterministic expression automata languages are a proper subfamily of the regular languages. We define the minimization of deterministic expression automata. Lastly, we discuss prime prefixfree regular languages. Note that we have omitted almost all proofs in this preliminary version. 1
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.
Nondeterministic State Complexity of Basic Operations for PrefixFree Regular Languages
, 2009
"... We investigate the nondeterministic state complexity of basic operations for prefixfree regular languages. The nondeterministic state complexity of an operation is the number of states that are necessary and sufficient in the worstcase for a minimal nondeterministic finitestate automaton that ac ..."
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Cited by 7 (2 self)
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We investigate the nondeterministic state complexity of basic operations for prefixfree regular languages. The nondeterministic state complexity of an operation is the number of states that are necessary and sufficient in the worstcase for a minimal nondeterministic finitestate automaton that accepts the language obtained from the operation. We establish the precise state complexity of catenation, union, intersection, Kleene star, reversal and complementation for prefixfree regular languages.
Prefixfree regularexpression matching
 In Proceedings of CPM’05
, 2005
"... Abstract. We explore the regularexpression matching problem with respect to prefixfreeness of the pattern. We show that the prefixfree regular expression gives only linear number of matching substrings in the size of a given text. Based on this observation, we propose an efficient algorithm for t ..."
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Cited by 6 (6 self)
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Abstract. We explore the regularexpression matching problem with respect to prefixfreeness of the pattern. We show that the prefixfree regular expression gives only linear number of matching substrings in the size of a given text. Based on this observation, we propose an efficient algorithm for the prefixfree regularexpression matching problem. Furthermore, we suggest an algorithm to determine whether or not a given regular language is prefixfree. 1
Outfixfree regular languages and prime outfixfree decomposition
 PROCEEDINGS OF ICTAC’05, LNCS 3722
, 2005
"... A string x is an outfix of a string y if there is a string w such that x1wx2 = y, wherex = x1x2 and a set X of strings is outfixfree if no string in X is an outfix of any other string in X. We examine the outfixfree regular languages. Based on the properties of outfix strings, we develop a polyno ..."
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Cited by 5 (4 self)
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A string x is an outfix of a string y if there is a string w such that x1wx2 = y, wherex = x1x2 and a set X of strings is outfixfree if no string in X is an outfix of any other string in X. We examine the outfixfree regular languages. Based on the properties of outfix strings, we develop a polynomialtime algorithm that determines the outfixfreeness of regular languages. We consider two cases: A language is given as a set of strings and a language is given by an acyclic deterministic finitestate automaton. Furthermore, we investigate the prime outfixfree decomposition of outfixfree regular languages and design a lineartime prime outfixfree decomposition algorithm for outfixfree regular languages. We demonstrate the uniqueness of prime outfixfree decomposition.
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
PDL over Accelerated Labeled Transition Systems
"... We present a thorough study of Propositional Dynamic Logic over a variation of labeled transition systems, called accelerated labelled transition systems, which are transition systems labeled with regular expressions over action labels. We study the model checking and satisfiability decision probl ..."
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We present a thorough study of Propositional Dynamic Logic over a variation of labeled transition systems, called accelerated labelled transition systems, which are transition systems labeled with regular expressions over action labels. We study the model checking and satisfiability decision problems. Through a notion of regular expression rewriting, we reduce these two problems to the corresponding ones of PDL in the traditional semantics (w.r.t. LTS). As for the complexity, both of problems are proved to be EXPSPACEcomplete. Moreover, the program complexity of model checking problem turns out to be NLOGSPACEcomplete. Furthermore, we provide an axiomatization for PDL which involves Kleene Algebra as an Oracle. The soundness and completeness are shown. 1
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