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Thompson Digraphs: A Characterization
"... . A finitestate machine is called a Thompson machine if it can be constructed from a regular expression using Thompson's construction. We call the underlying digraph of a Thompson machine a Thompson digraph. We establish and prove a characterization of Thompson digraphs. As one application ..."
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. A finitestate machine is called a Thompson machine if it can be constructed from a regular expression using Thompson's construction. We call the underlying digraph of a Thompson machine a Thompson digraph. We establish and prove a characterization of Thompson digraphs. As one application of the characterization, we give an algorithm that generates an equivalent regular expression from a Thompson machine in time linear in the number of states. 1 Introduction In 1968, Thompson [8] gave an inductive construction of finitestate machines from regular expressions that was motivated by grep. The resulting finitestate machines have sizes linear in the sizes of the original expressions. A resurge of interest in the implementation of machines has resulted in some new discoveries about the Thompson construction [2, 4]. We characterize the underlying digraphs of the machines resulting from the Thompson construction on emptyfree regular expressions (they do not include the emptyset ...
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
DRAFT—Do not distribute RAPID Programming of PatternRecognition Processors
"... We present RAPID, a highlevel programming language and combined imperative and declarative model for programming patternrecognition processors, such as Micron’s Automata Processor (AP). The AP is a novel, nonVon Neumann architecture for direct execution of nondeterministic finite automata (NF ..."
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We present RAPID, a highlevel programming language and combined imperative and declarative model for programming patternrecognition processors, such as Micron’s Automata Processor (AP). The AP is a novel, nonVon Neumann architecture for direct execution of nondeterministic finite automata (NFAs), and has been demonstrated to provide substantial speedup for a variety of dataprocessing applications. RAPID is clear, maintainable, concise, and efficient both at compile and run time. Language features, such as code abstraction and parallel control structures, map well to patternmatching problems, providing clarity and maintainability. For generation of efficient runtime code, we present algorithms to convert RAPID programs into finite automata. Further, we introduce a tessellation technique for configuring the AP, which significantly reduces compile time, increases programmer productivity, and improves maintainability. We evaluate five RAPID programs against custom, baseline implementations previously demonstrated to be significantly accelerated by the AP. We find that RAPID programs are much shorter in length, are expressible at a higher level of abstraction than their handcrafted counterparts, and yield generated code that is often more compact. In addition, our tessellation technique for configuring the AP has comparable device utilization to, and results in compilation that is up to four orders of magnitude faster than, current solutions. 1.
Algorithms for Glushkov Kgraphs
, 2009
"... The automata arising from the well known conversion of regular expression to non deterministic automata have rather particular transition graphs. We refer to them as the Glushkov graphs, to honour his nice expressiontoautomaton algorithmic short cut [10]. The Glushkov graphs have been characterize ..."
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The automata arising from the well known conversion of regular expression to non deterministic automata have rather particular transition graphs. We refer to them as the Glushkov graphs, to honour his nice expressiontoautomaton algorithmic short cut [10]. The Glushkov graphs have been characterized [6] in terms of simple graph theoretical properties and certain reduction rules. We show how to carry, under certain restrictions, this characterization over to the weighted Glushkov graphs. With the weights in a semiring K, they are defined as the transition Glushkov Kgraphs of the Weighted Finite Automata (WFA) obtained by the generalized Glushkov construction [4] from the Kexpressions. It works provided that the semiring K is factorial and the Kexpressions are in the so called star normal form (SNF) of BrüggemanKlein [2]. The restriction to the factorial semiring ensures to obtain algorithms. The restriction to the SNF would not be necessary if every Kexpressions were equivalent to some with the same litteral length, as it is the case for the boolean semiring B but remains an open question for a general K.
Weak Inclusion for XML Types ⋆
"... Abstract. Considering that the unranked tree languages L(G) and L(G ′ ) are those defined by given nonrecursive XML types G and G ′,this paper proposes a simple and intuitive method to verify whether L(G) is “approximatively ” included in L(G ′). Our approximative criterion consists in weakening th ..."
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Abstract. Considering that the unranked tree languages L(G) and L(G ′ ) are those defined by given nonrecursive XML types G and G ′,this paper proposes a simple and intuitive method to verify whether L(G) is “approximatively ” included in L(G ′). Our approximative criterion consists in weakening the fatherchildren relationships. Experimental results are discussed, showing the efficiency of our method in many situations. 1
A Synthesis \Lambda
, 1998
"... Abstract We reexamine the relationship between the two most popular methods for transforming a regular expression into a finitestate machine: the Glushkov and Thompson constructions. These methods have received more attention recently because of the Standard Generalized Markup Language (SGML) and a ..."
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Abstract We reexamine the relationship between the two most popular methods for transforming a regular expression into a finitestate machine: the Glushkov and Thompson constructions. These methods have received more attention recently because of the Standard Generalized Markup Language (SGML) and a revival of interest in symbolic toolkits for regular and contextfree expressions, grammars, and machines. We establish that:
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.
Running Time Complexity of Printing an Acyclic Automaton
"... Abstract. This article estimates the worstcase running time complexity for traversing and printing all successful paths of a normalized trim acyclic automaton. First, we show that the worstcase structure is a festoon with distribution of arcs on states as uniform as possible. Then, we prove that t ..."
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Abstract. This article estimates the worstcase running time complexity for traversing and printing all successful paths of a normalized trim acyclic automaton. First, we show that the worstcase structure is a festoon with distribution of arcs on states as uniform as possible. Then, we prove that the complexity is maximum when we have a distribution of e (Napier constant) outgoing arcs per state on average, and that it can be exponential in the number of arcs. 1