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Tight Bounds on the Descriptional Complexity of Regular Expressions
, 2009
"... We improve on some recent results on lower bounds for conversion problems for regular expressions. In particular we consider the conversion of planar deterministic finite
automata to regular expressions, study the effect of the complementation operation on the
descriptional complexity of regular exp ..."
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We improve on some recent results on lower bounds for conversion problems for regular expressions. In particular we consider the conversion of planar deterministic finite
automata to regular expressions, study the effect of the complementation operation on the
descriptional complexity of regular expressions, and the conversion of regular expressions
extended by adding intersection or interleaving to ordinary regular expressions. Almost all
obtained lower bounds are optimal, and the presented examples are over a binary alphabet,
which is best possible.
Short Regular Expressions from Finite Automata: Empirical Results
 CIAA 2009. LNCS
, 2009
"... Abstract. We continue our work [H. Gruber, M. Holzer: Provably shorter regular expressions from deterministic finite automata (extended abstract). In Proc. DLT, LNCS 5257, 2008] on the problem of finding good elimination orderings for the state elimination algorithm, one of the most popular algorith ..."
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Abstract. We continue our work [H. Gruber, M. Holzer: Provably shorter regular expressions from deterministic finite automata (extended abstract). In Proc. DLT, LNCS 5257, 2008] on the problem of finding good elimination orderings for the state elimination algorithm, one of the most popular algorithms for the conversion of finite automata into equivalent regular expressions. Here we tackle this problem both from the theoretical and from the practical side. First we show that the problem of finding optimal elimination orderings can be used to estimate the cycle rank of the underlying automata. This gives good evidence that the problem under consideration is difficult, to a certain extent. Moreover, we conduct experiments on a large set of carefully chosen instances for five different strategies to choose elimination orderings, which are known from the literature. Perhaps the most surprising result is that a simple greedy heuristic by [M. Delgado, J. Morais: Approximation to the smallest regular expression for a given regular language. In Proc. CIAA, LNCS 3317, 2004] almost always outperforms all other strategies, including those with a provable performance guarantee. 1
SeriesParallel Automata and Short Regular Expressions
, 2009
"... Computing short regular expressions equivalent to a given finite automaton is a hard task. In this work we present a class of acyclic automata for which it is possible to obtain in time O(n² log n) an equivalent regular expression of size O(n). A characterisation of this class is made using propert ..."
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Cited by 4 (1 self)
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Computing short regular expressions equivalent to a given finite automaton is a hard task. In this work we present a class of acyclic automata for which it is possible to obtain in time O(n² log n) an equivalent regular expression of size O(n). A characterisation of this class is made using properties of the underlying digraphs that correspond to the seriesparallel digraphs class. Using this characterisation we present an algorithm for the generation of automata of this class and an enumerative formula for the underlying digraphs with a given number of vertices.
Implementation of state elimination using heuristics
 CIAA 2009, 14th International Conference on Implementation and Application of Automata, volume 5642 of LNCS
, 2009
"... Abstract. State elimination is an intuitive and easytoimplement algorithm that computes a regular expression from a finitestate automaton (FA). The size of a regular expression from state elimination depends on the state removal sequence. Note that it is very hard to compute the shortest regular ..."
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Abstract. State elimination is an intuitive and easytoimplement algorithm that computes a regular expression from a finitestate automaton (FA). The size of a regular expression from state elimination depends on the state removal sequence. Note that it is very hard to compute the shortest regular expression for a given FA in general and we cannot avoid the exponential blowup from state elimination. Nevertheless, we notice that we may have a shorter regular expression if we choose a good removal sequence. This observation motivates us to examine heuristics based on the structural properties of an FA and implement state elimination using the heuristics that run in polynomial time. We demonstrate the effectiveness of our algorithm by experiments.
A Provenance Framework for DataDependent Process Analysis ∗
"... A datadependent process (DDP) models an application whose control flow is guided by a finite state machine, as well as by the state of an underlying database. DDPs are commonly found e.g., in ecommerce. In this paper we develop a framework supporting the use of provenance in static (temporal) anal ..."
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A datadependent process (DDP) models an application whose control flow is guided by a finite state machine, as well as by the state of an underlying database. DDPs are commonly found e.g., in ecommerce. In this paper we develop a framework supporting the use of provenance in static (temporal) analysis of possible DDP executions. Using provenance support, analysts can interactively test and explore the effect of hypothetical modifications to a DDP’s state machine and/or to the underlying database. They can also extend the analysis to incorporate the propagation of annotations from metadomains of interest, e.g., cost or access privileges. Toward this goal we note that the framework of semiringbased provenance was proven highly effective in fulfilling similar needs in the context of database queries. In this paper we consider novel constructions that generalize the semiring approach to the context of DDP analysis. These constructions address two interacting new challenges: (1) to combine provenance annotations for both information that resides in the database and information about external inputs (e.g., user choices), and (2) to finitely capture infinite process executions. We analyze our solution from theoretical and experimental perspectives, proving its effectiveness. 1.
2010): State Elimination Ordering Strategies: Some Experimental Results
 Proceedings of the 12th Workshop on Descriptional Complexity of Formal Systems, EPTCS 31
"... Abstract. Recently, the problem of obtaining a short regular expression equivalent to a given finite automaton has been intensively investigated. Algorithms for converting finite automata to regular expressions have an exponential blowup in the worstcase. To overcome this, simple heuristic method ..."
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Abstract. Recently, the problem of obtaining a short regular expression equivalent to a given finite automaton has been intensively investigated. Algorithms for converting finite automata to regular expressions have an exponential blowup in the worstcase. To overcome this, simple heuristic methods have been proposed. In this paper we analyse some of the heuristics presented in the literature and propose new ones. We also present some experimental comparative results based on uniform random generated deterministic finite automata.
From finite automata to regular expressions and back–a summary on descriptional complexity
 EPTCS: AFL14
"... The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956. In the present paper we tour a fragment of the literature and summarize results on upper and lower bounds on the conversion of finite automata t ..."
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The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956. In the present paper we tour a fragment of the literature and summarize results on upper and lower bounds on the conversion of finite automata to regular expressions and vice versa. We also briefly recall the known bounds for the removal of spontaneous transitions (εtransitions) on nonεfree nondeterministic devices. Moreover, we report on recent results on the average case descriptional complexity bounds for the conversion of regular expressions to finite automata and brand new developments on the state elimination algorithm that converts finite automata to regular expressions. 1
Technique to Remove Indistinguishable State with Unreachable State and Dead State from Deterministic Finite Automata
"... This paper presents a new technique for efficiently calculating and remove indistinguishable states in finitestate automata. A central problem in automata theory is to minimize a given Deterministic Finite Automaton (DFA). DFA minimization is an important topic because it can be applied both theore ..."
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This paper presents a new technique for efficiently calculating and remove indistinguishable states in finitestate automata. A central problem in automata theory is to minimize a given Deterministic Finite Automaton (DFA). DFA minimization is an important topic because it can be applied both theoretically and practically, in for instance compilers. Minimizing a DFA increases its efficiency by reducing its amount of states and it also enables us to determine if two DFAs are equivalent. A DFA(deterministic finite automata) have some redundant state that means this type of state doesn‟t participant for generating useful strings. And these types of state are called dead state, unreachable state or indistinguishable state. In deterministic finite automata, it is not easy to determine dead state, unreachable state or inaccessible state and it is necessary for removing unreachable state and dead state from DFA(deterministic finite automata).And removing unreachable state and dead state from deterministic finite automata is very necessary to generating useful string. We can generate minimize deterministic finite automata after removing unreachable state, dead state and indistinguishable state. But it is very difficult to removing these type of state from DFA. Then first we will choose useful state. This paper also explaining about how useful automata package simulator and java formal languages for new technique.