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15
VCR: A VDMbased software component retrieval tool
, 1994
"... We present a tool which allows implicit VDM specifications to be used as search keys for the retrieval of software components. A preprocessing phase utilizes signature matching to filter promising candidates out of a component library. The actual specification matching phase builds proof obligations ..."
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Cited by 23 (0 self)
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We present a tool which allows implicit VDM specifications to be used as search keys for the retrieval of software components. A preprocessing phase utilizes signature matching to filter promising candidates out of a component library. The actual specification matching phase builds proof obligations from the specifications of key and candidates and feeds them into a theorem prover. Validated obligations denote matching components. First experiments clearly demonstrate the feasibility of this approach. We thus get a highprecision retrieval tool which helps programmers in locating components which exactly match their needs. Keywords: formal methods, software component retrieval, signature matching, specification matching, theorem proving, model searching. 1 Introduction Effective software component retrieval methods play a key role in reuse. Most methods grew out of classical information retrieval (e. g. [13, 10]) but recently semanticbased methods have gained more attention. As oppo...
Adventures in AssociativeCommutative Unification
 Journal of Symbolic Computation
, 1989
"... We have discovered an efficient algorithm for matching and unification in associativecommutative (AC) equational theories. In most cases of AC unification our method obviates the need for solving diophantine equations, and thus avoids one of the bottlenecks of other associativecommutative unificat ..."
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Cited by 22 (0 self)
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We have discovered an efficient algorithm for matching and unification in associativecommutative (AC) equational theories. In most cases of AC unification our method obviates the need for solving diophantine equations, and thus avoids one of the bottlenecks of other associativecommutative unification techniques. The algorithm efficiently utilizes powerful constraints to eliminate much of the search involved in generating valid substitutions. Moreover, it is able to generate solutions lazily, enabling its use in an SLDresolutionbased environment like Prolog. We have found the method to run much faster and use less space than other associativecommutative unification procedures on many commonly encountered AC problems. 1 Introduction Associativecommutative (AC) equational theories surface in a number of computer science applications, including term rewriting, automatic theorem proving, software verification, and database retrieval. As a simple example, consider trying to find a sub...
Bisimulation by unification
 Proc. AMAST 2002, LNCS 2422
, 2002
"... Abstract. We propose a methodology for the analysis of open systems based on process calculi and bisimilarity. Open systems are seen as coordinators (i.e. terms with placeholders), that evolve when suitable components (i.e. closed terms) fill in their placeholders. The distinguishing feature of ou ..."
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Cited by 13 (7 self)
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Abstract. We propose a methodology for the analysis of open systems based on process calculi and bisimilarity. Open systems are seen as coordinators (i.e. terms with placeholders), that evolve when suitable components (i.e. closed terms) fill in their placeholders. The distinguishing feature of our approach is the definition of a symbolic operational semantics for coordinators that exploits spatial/modal formulae as labels of transitions and avoids the universal closure of coordinators w.r.t. all components. Two kinds of bisimilarities are then defined, called strict and large, which differ in the way formulae are compared. Strict bisimilarity implies large bisimilarity which, in turn, implies the one based on universal closure. Moreover, for process calculi in suitable formats, we show how the symbolic semantics can be defined constructively, using unification. Our approach is illustrated on a toy process calculus with ccslike communication within ambients. 1
Complete Solving of Linear Diophantine Equations and Inequations without Adding Variables
 PROC. OF 1ST INTERNATIONAL CONFERENCE ON PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING
, 1995
"... In this paper, we present an algorithm for solving directly linear Diophantine systems of both equations and inequations. Here directly means without adding slack variables for encoding inequalities as equalities. This algorithm is an extension of the algorithm due to Contejean and Devie [9] for so ..."
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Cited by 11 (1 self)
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In this paper, we present an algorithm for solving directly linear Diophantine systems of both equations and inequations. Here directly means without adding slack variables for encoding inequalities as equalities. This algorithm is an extension of the algorithm due to Contejean and Devie [9] for solving linear Diophantine systems of equations, which is itself a generalization of the algorithm of Fortenbacher [6] for solving a single linear Diophantine equation. All the nice properties of the algorithm of Contejean and Devie are still satisfied by the new algorithm: it is complete, i.e. provides a (finite) description of the set of solutions, it can be implemented with a bounded stack, and it admits an incremental version. All of these characteristics enable its easy integration in the CLP paradigm.
Solving Linear Diophantine Constraints Incrementally
 PROC. OF 10TH INTERNATIONAL CONFERENCE ON LOGIC PROGRAMMING
, 1993
"... In this paper, we show how to handle linear Diophantine constraints incrementally by using several variations of the algorithm by Contejean and Devie (hereafter called ABCD) for solving linear Diophantine systems [4, 5]. The basic algorithm is based on a certain enumeration of the potential solution ..."
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Cited by 11 (0 self)
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In this paper, we show how to handle linear Diophantine constraints incrementally by using several variations of the algorithm by Contejean and Devie (hereafter called ABCD) for solving linear Diophantine systems [4, 5]. The basic algorithm is based on a certain enumeration of the potential solutions of a system, and termination is ensured by an adequate restriction on the search. This algorithm generalizes a previous algorithm due to Fortenbacher [2], which was restricted to the case of a single equation. Note that using Fortenbacher's algorithm for solving systems of Diophantine equations by repeatedly applying it to the successive equations is completely unrealistic: the tuple of variables in the solved equation must then be substituted in the rest of the system by a linear combination of the minimal solutions found in which the coefficients stand for new variables. Unfortunately, the number of these minimal solutions is actually exponential in both the number of variables and the v...
Theorem Proving in Cancellative Abelian Monoids
, 1996
"... We describe a refined superposition calculus for cancellative abelian monoids. They encompass not only abelian groups, but also such ubiquitous structures as the natural numbers or multisets. Both the AC axioms and the cancellation law are difficult for a general purpose superposition theorem prover ..."
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Cited by 8 (1 self)
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We describe a refined superposition calculus for cancellative abelian monoids. They encompass not only abelian groups, but also such ubiquitous structures as the natural numbers or multisets. Both the AC axioms and the cancellation law are difficult for a general purpose superposition theorem prover, as they create many variants of clauses which contain sums. Our calculus requires neither explicit inferences with the theory clauses for cancellative abelian monoids nor extended equations or clauses. Improved ordering constraints allow us to restrict to inferences that involve the maximal term of the maximal sum in the maximal literal. Furthermore, the search space is reduced drastically by certain variable elimination techniques. Keywords Automated Theorem Proving, FirstOrder Logic, Superposition, Cancellative Abelian Monoids, Associativity, Commutativity, Variable Elimination, Term Rewriting. 1 Introduction To be useful in applications such as program verification and synthesis, a...
Combining Constraint Solving
, 2001
"... this paper. On the one hand, dening a semantics for the combined system may depend on methods and results from formal logic and universal algebra. On the other hand, an ecient combination of the actual constraint solvers often requires the possibility of communication and cooperation between the sol ..."
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Cited by 5 (0 self)
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this paper. On the one hand, dening a semantics for the combined system may depend on methods and results from formal logic and universal algebra. On the other hand, an ecient combination of the actual constraint solvers often requires the possibility of communication and cooperation between the solvers.
Unification Algorithms Cannot be Combined in Polynomial Time
 in Proceedings of the 13th International Conference on Automated Deduction, M.A. McRobbie and J.K. Slaney (Eds.), Springer LNAI 1104
, 1996
"... . We establish that there is no polynomialtime general combination algorithm for unification in finitary equational theories, unless the complexity class #P of counting problems is contained in the class FP of function problems solvable in polynomialtime. The prevalent view in complexity theory is ..."
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Cited by 4 (0 self)
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. We establish that there is no polynomialtime general combination algorithm for unification in finitary equational theories, unless the complexity class #P of counting problems is contained in the class FP of function problems solvable in polynomialtime. The prevalent view in complexity theory is that such a collapse is extremely unlikely for a number of reasons, including the fact that the containment of #P in FP implies that P = NP. Our main result is obtained by establishing the intractrability of the counting problem for general AGunification, where AG is the equational theory of Abelian groups. Specifically, we show that computing the cardinality of a minimal complete set of unifiers for general AGunification is a #Phard problem. In contrast, AGunification with constants is solvable in polynomial time. Since an algorithm for general AGunification can be obtained as a combination of a polynomialtime algorithm for AGunification with constants and a polynomialtime algorithm...