An analysis is described that can automatically find models of first-order formulas with relational operators and scalar quantifiers. The formula is translated to a quantifier-free boolean formula that has a model exactly when the original formula has a model within a given scope (that is, involving no more than some finite number of atoms). The paper presents a simple logic and gives a compositional translation scheme. It reports on the use of Alcoa, a tool based on the scheme, to analyze a variety of specifications expressed in Alloy, an object modelling notation based on the logic.

Abstract. The key design challenges in the construction of a SAT-based relational model finder are described, and novel techniques are proposed to address them. An efficient model finder must have a mechanism for specifying partial solutions, an effective symmetry detection and breaking scheme, and an economical translation from relational to boolean logic. These desiderata are addressed with three new techniques: a symmetry detection algorithm that works in the presence of partial solutions, a sparse-matrix representation of relations, and a compact representation of boolean formulas inspired by boolean expression diagrams and reduced boolean circuits. The presented techniques have been implemented and evaluated, with promising results. 1

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This article describes a technique for analyzing relational specifications. The underlying idea is very simple. Both simulation and checking amount to finding models of a relational formula, i.e., assignments for which the formula is true. For simulation the formula is the description of the operation; for checking, the formula is the negation of an assertion about an operation. Models are found by a generate-and-test strategy: the formula is repeatedly evaluated for a series of assignments until one is found for which the formula is true

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The Design of a Relational Engine The key design challenges in the construction of a SAT-based relational engine are described, and novel techniques are proposed to address them. An efficient engine must have a mechanism for specifying partial solutions, an effective symmetry detection and breaking scheme, and an economical translation from relational to boolean logic. These desiderata are addressed with three new techniques: a symmetry detection algorithm that works in the presence of partial solutions, a sparse-matrix representation of relations, and a compact representation of boolean formulas inspired by boolean expression diagrams and reduced boolean circuits. The presented techniques have been implemented and evaluated, with promising results.

This paper describes two communication formalisms for Automated Theorem Proving (ATP) tools. First, a problem and solution language has been designed. The language will be used for writing problems to be input to ATP systems, and for writing solutions output by ATP systems. Second, a hierarchy of result statuses, which adequately express the range of results output by ATP systems, has been established. These formalisms will support application and research in ATP, and will facilitate direct communication between ATP tools when they are used as embedded components in larger systems.

Introduction This chapter discusses how to specify various Latin squares so that their existence can be efficiently decided by computer programs. The computer programs considered here are so-called general-purpose model generation programs (or simply model generators) that are used to solve constraint satisfaction problems in AI, to prove theorems in finite domains, or to produce counterexamples to false conjectures. For instance, any example of finite structures in Larry Wos's book [16] can be easily solved using these model generators. In the recent years, model generators have been used to solve the existence problem of Latin squares with specified properties. Numerous previously open cases of Latin squares were first solved by these model generators. These Latin square problems are attacked along the two lines: (a) develop efficient model generation programs; (b) provide efficient specifications of the same problem. This chapter will focus on the latter as we realize throu

Introduction SCOTT is an ATP formed by augmenting OTTER [1] (a resolution-style ATP) with FINDER [2] (a finite model generator) as a subsystem. By providing semantic information about the search as it unfolds, the FINDER subsystem allows us to explore two new strategies [4]. The first, semantic resolution, generalises the set of support strategy throughout the whole search [5]. This has the potential to substantially reduce the number of proof fragments that need to be explored at any level in a systematic search. Although semantic resolution has been a theoretical possibility for a long time, it had not been implemented in any sophisticated fashion before the formation of SCOTT [4]. The second strategy, semantic guidance, uses semantic information to guide the prover towards developing the most promising proof fragments. This strategy is more interesting because it presents a serious challenge to the "inevitable" combinatorial e

this paper we report one line of attack on the focus problem for saturation methods of first order theorem proving, by injecting semantic information into heuristics for ordering the possible inferences. Preliminary work on this idea, 1 in collaboration with Lusk, McCune and others, resulted in the system Scott [5, 1, 7] which showed some modest e#ciency gains relative to its parent Otter. However, the main technique used in that prover was model resolution; the work on false preference (see below) remained unsystematic and lacked a theoretical basis. The new generation of Scott rests on a new understanding of semantic guidance and shows remarkably stable behaviour over a wide range of problems. We present results on problems from the TPTP library and performance under fair conditions in CASC as compelling evidence that the e#ects exploited by our technique are real and useful