Claudio Castellini

SAT-Based Procedures for Temporal Reasoning

In this paper we study the consistency problem for a set of disjunctive temporal constraints [Stergiou and Koubarakis, 1998]. We propose two SAT-based procedures, and show that—on sets of binary randomly generated disjunctive constraints—they perform up to 2 orders of magnitude less consistency checks than the best procedure presented in [Stergiou and Koubarakis, 1998]. On these tests, our experimental analysis confirms Stergiou and Koubarakis’s result about the existence of an easy-hard-easy pattern whose peak corresponds to a value in between 6 and 7 of the ratio of clauses to variables.

SAT-based planning in complex domains: concurrency, constraints and nondeterminism

Planning as satisfiability is a very efficient technique for classical planning, i.e., for planning domains in which both the effects of actions and the initial state are completely specified. In this paper we present C-SAT, a SAT-based procedure capable of dealing with planning domains having incomplete information about the initial state, and whose underlying transition system is specified using the highly expressive action language C. Thus, C-SAT allows for planning in domains involving (i) actions which can be executed concurrently; (ii) (ramification and qualification) constraints affecting the effects of actions; and (iii) nondeterminism in the initial state and in the effects of actions. We first prove the correctness and the completeness of C-SAT, discuss some optimizations, and then we present C-PLAN, a system based on C-SAT. C-PLAN works on any C planning problem, but some optimizations have not been fully implemented yet. Nevertheless, the experimental analysis shows that SAT-based approaches to planning with incomplete information are viable, at least in the case of problems with a high degree of parallelism.

A SAT-based decision procedure for the boolean combination of difference constraints

The problem of deciding satisfiability of Boolean combinations of difference constraints is at the core of many important techniques such as planning, scheduling and bounded model checking of real-time systems. Efficient decision procedures for this class of formulas are, therefore, strongly needed. In this paper we present TSAT++, a system implementing a SAT-based decision procedure for this problem, and the techniques implemented in it; in particular, TSAT++ takes full advantage of recent SAT techniques. Comparative experimental results indicate that TSAT++ outperforms its competitors both on randomly generated, hand-made and real world problems.

SAT-Based Decision Procedures for Automated Reasoning: A Unifying Perspective

Propositional reasoning (SAT) is an essential part of many reasoning tasks. Many problems in computer science can be compiled to SAT and then effectively decided using state-of-the-art solvers. Alternatively, if reduction to SAT is not feasible, the ideas and technology of state-of-the-art SAT solvers can be useful in deciding the propositional component of the reasoning task being considered. This last approach has been used in different contexts by different authors, many times by authors of this paper. Because of the essential role played by the SAT solver, these decision procedures have been called “SAT-based”. SAT-based decision procedures have been proposed for various logics, but also in other areas such as planning. In this paper we present a unifying perspective on the various SAT-based approaches to these different reasoning tasks.

TSAT++: an Open Platform for Satisfiability Modulo Theories

Abstract This paper describes TSAT++ , an open platform which realizes the lazy SAT-based approach to Satisfiability Modulo Theories (SMT). SMT is the problem of determining satisfiability of a propositional combination of T-literals, where T is a first-order theory for which a satisfiability procedure for a set of ground atoms is known. TSAT++ enjoys a modular design in which an enumerator and a theory-specific satisfiability checker cooperate in order to solve SMT. Modularity allows both different enumerators, and satisfiability checkers for different theories (or combinations of theories), to be plugged in, as far as they comply to a simple and well-defined interface. A number of optimization techniques are also implemented in TSAT++ , which are independent of the modules used (and of the corresponding theory). Some experimental results are presented, showing that TSAT++ , instantiated for Separation Logic, is competitive with, or faster than, state-of-the-art solvers for that very logic.

A Systematic Presentation of Quantified Modal Logics

This paper provides a systematic presentation of Quantified Modal Logics (with constant domains and rigid designators). We therefore present a set of modular, uniform, normalising, sound and complete labelled sequent calculi for all QMLs whose frame properties can be expressed as a finite set of first-order sentences with equality. We first present C-QK, a calculus for the logic QK, and then we extend it to any such logic QL. Each calculus, called C-QL, is modular (obtained by adding rules to C-QK), uniform (each added rule clearly relates to a property of the frame), normalising (frame reasoning only happens at the top of the proof tree) and Kripke-sound and complete for QL. We improve on the existing literature on the subject (mainly, Vigano‘, ”Labelled non-classical logics”, 2000) by extending the class of logics for which such a presentation is given, and by giving a new proof of soundness and completeness.

The SAT-based Approach to Separation Logic

The SAT-based approach to the decision problem for expressive, decidable, quantifier-free first-order theories has been investigated with remarkable results at least since 1993. One such theory, successfully employed in the formal verification of complex, infinite state systems, is Separation Logic (SL), which combines Boolean logic with arithmetic constraints of the form x − y ⋈ c, where ⋈ is ≤, <, >, ≥, =, or ≠. The SAT-based approach to SL was first proposed and implemented in 1999: the results in terms of performance were good, and since then a number of other systems for SL have appeared. In this paper we focus on the problem of building efficient SAT-based decision procedures for SL. We present the basic procedure and four optimizations that improve dramatically its effectiveness in most cases: (a) IS2 preprocessing, (b) early pruning, (c) model reduction, and (d) best reason detection. For each technique we give an example of how it might improve the performance. Furthermore, for the first three techniques, we give a pseudo-code representation and formally state the soundness and completeness of the resulting optimized procedure. We also show how it is possible to check the satisfiability of valuations involving constraints of the form x − y < c using the Bellman–Ford algorithm. Lastly, we present an extensive comparative experimental analysis, showing that our solver TSAT++, built along the lines described in this paper, is currently the state of the art on various classes of problems, including randomly generated, hand-made, and real-world instances.

Proof Planning for Feature Interactions: A Preliminary Report

We report on an initial success obtained in investigating the Feature Interaction problem (FI) via proof planning. FIs arise as an unwanted/ unexpected behaviour in large telephone networks and have recently attracted interest not only from the Computer Science community but also from the industrial world. So far, FIs have been solved mainly via approximation plus finite-state methods (model checking being the most popular); in our work we attack the problem via proof planning in First-Order Linear Temporal Logic (FOLTL), therefore making use of no finite-state approximation or restricting assumption about quantification. We have integrated the proof planner λCLAM with an object-level FOLTL theorem prover called FTL, and have so far re-discovered a feature interaction in a basic (but far from trivial) example.