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29
A Fast Bisimulation Algorithm
 PROC. OF INT. CONFERENCE ON COMPUTER AIDED VERIFICATION (CAV’01), VOLUME 2102 OF LNCS
, 2000
"... In this paper we propose an efficient algorithmic solution to the problem of determining a Bisimulation Relation on a finite structure. ..."
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Cited by 29 (15 self)
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In this paper we propose an efficient algorithmic solution to the problem of determining a Bisimulation Relation on a finite structure.
From Bisimulation to Simulation  Coarsest Partition Problems
 J. Automated Reasoning
, 2002
"... The notions of bisimulation and simulation are used for graph reduction and are widely employed in many areas: Modal Logic, Concurrency Theory, Set Theory, Formal Verification, etc. In particular, in the context of Formal Verification they are used to tackle the socalled stateexplosion problem. ..."
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Cited by 19 (1 self)
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The notions of bisimulation and simulation are used for graph reduction and are widely employed in many areas: Modal Logic, Concurrency Theory, Set Theory, Formal Verification, etc. In particular, in the context of Formal Verification they are used to tackle the socalled stateexplosion problem.
Taming the complexity of biochemical models through bisimulation and collapsing: Theory and practice
 Theor. Comput. Sci
, 2004
"... Abstract. Many biological systems can be modeled using systems of ordinary differential algebraic equations (e.g., Ssystems), thus allowing the study of their solutions and behavior automatically with suitable software tools (e.g., PLAS, Octave/Matlab tm). Usually, numerical solutions (traces or tr ..."
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Cited by 18 (2 self)
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Abstract. Many biological systems can be modeled using systems of ordinary differential algebraic equations (e.g., Ssystems), thus allowing the study of their solutions and behavior automatically with suitable software tools (e.g., PLAS, Octave/Matlab tm). Usually, numerical solutions (traces or trajectories) for appropriate initial conditions are analyzed in order to infer significant properties of the biological systems under study. When several variables are involved and the traces span over a long interval of time, the analysis phase necessitates automation in a scalable and efficient manner. Earlier, we have advocated and experimented with the use of automata and temporal logics for this purpose (XSsystems and Simpathica) and here we continue our investigation more deeply. We propose the use of hybrid automata and we discuss the use of the notions of bisimulation and collapsing for a “qualitative ” analysis of the temporal evolution of biological systems. As compared with our previous approach, hybrid automata allow maintenance of more information about the differential equations (Ssystem) than standard automata. The use of the notion of bisimulation in the definition of the projection operation (restrictions to a subset of “interesting ” variables) makes it possible to work with reduced automata satisfying the same formulae as the initial ones. Finally, the notion of collapsing is introduced to move toward still simpler and equivalent automaton taming the complexity in terms of states whose number depends on the attained level of approximation.
On the complexity of Hopcroft’s state minimization algorithm
 of Lecture Notes in Computer Science
, 2004
"... Abstract. Hopcroft’s algorithm for minimizing a deterministic automaton has complexity O(n log n). We show that this complexity bound is tight. More precisely, we provide a family of automata of size n =2 k on which the algorithm runs in time k2 k. These automata have a very simple structure and are ..."
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Cited by 13 (1 self)
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Abstract. Hopcroft’s algorithm for minimizing a deterministic automaton has complexity O(n log n). We show that this complexity bound is tight. More precisely, we provide a family of automata of size n =2 k on which the algorithm runs in time k2 k. These automata have a very simple structure and are built over a oneletter alphabet. Their sets of final states are defined by de Bruijn words. 1
Universal regular path queries
 HigherOrder and Symbolic Computation
, 2003
"... Given are a directed edgelabelled graph G with a distinguished node n0, and a regular expression P which may contain variables. We wish to compute all substitutions φ (of symbols for variables), together with all nodes n such that all paths n0 → n are in φ(P). We derive an algorithm for this proble ..."
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Cited by 12 (1 self)
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Given are a directed edgelabelled graph G with a distinguished node n0, and a regular expression P which may contain variables. We wish to compute all substitutions φ (of symbols for variables), together with all nodes n such that all paths n0 → n are in φ(P). We derive an algorithm for this problem using relational algebra, and show how it may be implemented in Prolog. The motivation for the problem derives from a declarative framework for specifying compiler optimisations. 1 Bob Paige and IFIP WG 2.1 Bob Paige was a longstanding member of IFIP Working Group 2.1 on Algorithmic Languages and Calculi. In recent years, the main aim of this group has been to investigate the derivation of algorithms from specifications by program transformation. Already in the mideighties, Bob was way ahead of the pack: instead of applying transformational techniques to wellworn examples, he was applying his theories of program transformation to new problems, and discovering new algorithms [16, 48, 52]. The secret of his success lay partly in his insistence on the study of general algorithm design strategies (in particular
Efficient Type Matching
, 2001
"... Palsberg and Zhao [14] presented an O(n²) time algorithm for matching two recursive types. In this paper, we present an O(n log n) algorithm for the same problem. Our algorithm works by reducing the type matching problem to the wellunderstood problem of finding a sizestable partition of a graph. ..."
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Cited by 10 (3 self)
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Palsberg and Zhao [14] presented an O(n²) time algorithm for matching two recursive types. In this paper, we present an O(n log n) algorithm for the same problem. Our algorithm works by reducing the type matching problem to the wellunderstood problem of finding a sizestable partition of a graph. Our result may help improve systems, such as Polyspin and Mockingbird, that are designed to facilitate interoperability of software components. We also discuss possible applications of our algorithm to Java. Issues related to subtyping of recursive types are also discussed.
Time granularities and ultimately periodic automata
 In Proc. of the 9th European Conference on Logics in Artificial Intelligence (JELIA) volume 3229 of Lecture Notes in Computer Science
, 2004
"... Abstract. The relevance of the problem of managing periodic phenomena is widely recognized in the area of knowledge representation and reasoning. One of the most effective attempts at dealing with this problem has been the addition of a notion of time granularity to knowledge representation systems. ..."
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Cited by 7 (1 self)
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Abstract. The relevance of the problem of managing periodic phenomena is widely recognized in the area of knowledge representation and reasoning. One of the most effective attempts at dealing with this problem has been the addition of a notion of time granularity to knowledge representation systems. Different formalizations of such a notion have been proposed in the literature, following algebraic, logical, stringbased, and automatonbased approaches. In this paper, we focus our attention on the automatonbased one, which allows one to represent a large class of granularities in a compact and suitable to algorithmic manipulation form. We further develop such an approach to make it possible to deal with (possibly infinite) sets of granularities instead of single ones. We define a new class of automata, called Ultimately Periodic Automata, we give a characterization of their expressiveness, and we show how they can be used to encode and to solve a number of fundamental problems, such as the membership problem, the equivalence problem, and the problem of granularity comparison. Moreover, we give an example of their application to a concrete problem taken from clinical medicine. 1
Simulation as Coarsest Partition Problem
, 2002
"... The problem of determining the coarsest partition stable with respect to a given binary relation, is known to be equivalent to the problem of finding the maximal bisimulation on a given structure. Such an equivalence has suggested efficient algorithms for the computation of the maximal bisimulation ..."
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Cited by 4 (1 self)
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The problem of determining the coarsest partition stable with respect to a given binary relation, is known to be equivalent to the problem of finding the maximal bisimulation on a given structure. Such an equivalence has suggested efficient algorithms for the computation of the maximal bisimulation relation. In this paper the simulation problem is rewritten in terms of coarsest stable partition problem and, on this ground, a new algorithm for its solution is proposed. The proposed algorithm consists of a calculation of the simulation relation as fixpoint of suitable operators and improves on either time or space complexity with respect to previously proposed algorithms.