Miquel Bofill

The Barcelogic SMT Solver

This is the first system description of the Barcelogic SMT solver, which implements all techniques that our group has been developing over the last four years as well as state-of-the-art features developed by other research groups. We pay special attention to the theory solvers and to functionalities that are not common in SMT solvers.

A Write-Based Solver for SAT Modulo the Theory of Arrays

The extensional theory of arrays is one of the most important ones for applications of SAT modulo theories (SMT) to hardware and software verification. Here we present a new T-solver for arrays in the context of the DPLL(T) approach to SMT. The main characteristics of our solver are: (i) no translation of writes into reads is needed, (ii) there is no axiom instantiation, and (iii) the T-solver interacts with the Boolean engine by asking to split on equality literals between indices. Unlike most state-of-the-art array solvers, it is not based on a lazy instantiation of the array axioms. This novelty might make it more convenient to apply this solver in some particular environments. Moreover, it is very competitive in practice, specially on problems that require heavy reasoning on array literals.

Building Automated Theorem Provers for Infinitely-Valued Logics with Satisfiability Modulo Theory Solvers

There is a relatively large number of papers dealing with complexity and proof theory issues of infinitely-valued logics. Nevertheless, little attention has been paid so far to the development of efficient solvers for such logics. In this paper we show how the technology of Satisfiability Modulo Theories (SMT) can be used to build efficient automated theorem provers for relevant infinitely-valued logics, including Lukasiewicz, Gödel and Product logics. Moreover, we define a test suite for those logics, and report on an experimental investigation that evaluates the practical complexity of Lukasiewicz and Gödel logics, and provides empirical evidence of the good performance of SMT technology for automated theorem proving on infinitely-valued logics.

A system for solving constraint satisfaction problems with SMT

SAT Modulo Theories (SMT) consists of deciding the satisfiability of a formula with respect to a decidable background theory, such as linear integer arithmetic, bit-vectors, etc, in first-order logic with equality. SMT has its roots in the field of verification. It is known that the SAT technology offers an interesting, efficient and scalable method for constraint solving, as many experimentations have shown. Although there already exist some results pointing out the adequacy of SMT techniques for constraint solving, there are no available tools to extensively explore such adequacy. In this paper we introduce a tool for translating FlatZinc (MiniZinc intermediate code) instances of constraint satisfaction problems to the standard SMT-LIB language. It can be used for deciding satisfiability as well as for optimization. The tool determines the required logic for solving each instance. The obtained results suggest that SMT can be effectively used to solve CSPs.

Paramodulation with non-monotonic orderings

All current completeness results for ordered paramodulation require the term ordering > to be well-founded, monotonic and total(izable) on ground terms. Here we introduce a new proof technique where the only properties required for > are well foundedness and the subterm property: The technique is a relatively simple and elegant application of some fundamental results on the termination and confluence of ground term rewrite systems (TRS). By a careful further analysis of our technique, we obtain the first Knuth-Bendix completion procedure that finds a convergent TRS for a given set of equations E and a (possibly non-totalizable) reduction ordering p whenever it exists. Note that being a reduction ordering is the minimal possible requirement on >, since a TRS terminates if, and only if, it is contained in a reduction ordering.

Solving constraint satisfaction problems with SAT modulo theories

Due to significant advances in SAT technology in the last years, its use for solving constraint satisfaction problems has been gaining wide acceptance. Solvers for satisfiability modulo theories (SMT) generalize SAT solving by adding the ability to handle arithmetic and other theories. Although there are results pointing out the adequacy of SMT solvers for solving CSPs, there are no available tools to extensively explore such adequacy. For this reason, in this paper we introduce a tool for translating FLATZINC (MINIZINC intermediate code) instances of CSPs to the standard SMT-LIB language. We provide extensive performance comparisons between state-of-the-art SMT solvers and most of the available FLATZINC solvers on standard FLATZINC problems. The obtained results suggest that state-of-the-art SMT solvers can be effectively used to solve CSPs.

Finding Hard Instances of Satisfiability in Lukasiewicz Logics

One aspect that has been poorly studied in multiple-valued logics, and in particular in Lukasiewicz logics, is the generation of instances of varying difficulty for evaluating, comparing and improving satisfiability solvers. In this paper we present a new class of clausal forms, called Lukasiewicz (L-)clausal forms, motivate their usefulness, study their complexity, and report on an empirical investigation that shows an easy-hard-easy pattern and a phase transition phenomenon when testing the satisfiability of L-clausal forms.

Fuzzy XPath for the automatic search of fuzzy formulae models

In this paper we deal with propositional fuzzy formulae containing several propositional symbols linked with connectives defined in a lattice of truth degrees more complex than Bool. Instead of focusing on satisfiability (i.e., proving the existence of at least one model) as usually done in a SAT/SMT setting, our interest moves to the problem of finding the whole set of models (with a finite domain) for a given fuzzy formula. We reuse a previous method based on fuzzy logic programming where the formula is conceived as a goal whose derivation tree, provided by our FLOPER tool, contains on its leaves all the models of the original formula, together with other interpretations. Next, we use the ability of the FuzzyXPath tool (developed in our research group with FLOPER) for exploring these derivation trees once exported in XML format, in order to discover whether the formula is a tautology, satisfiable, or a contradiction, thus reinforcing the bi-lateral synergies between FuzzyXPath and FLOPER.

A declarative approach to robust weighted Max-SAT

The presence of uncertainty in the real world makes robustness to be a desired property of solutions to constraint satisfaction problems. Roughly speaking, a solution is robust if it can be easily repaired when unexpected events happen. This issue has already been addressed in the frameworks of Boolean satisfiability (SAT) and Constraint Programming (CP). Most works on robustness implement search algorithms to look for such solutions instead of taking the declarative approach of reformulation, since reformulation tends to generate prohibitively large formulas, especially in the CP setting. On the other hand, recent works suggest the use of SAT and Max-SAT encodings for solving CP instances. In this paper we present how robust solutions to weighted Max-SAT problems can be effectively obtained via reformulation into pseudo-Boolean formulae, thus providing a much flexible approach to robustness. We illustrate the use of our approach in the robust combinatorial auctions setting and provide some promising experimental results.

The recursive path and polynomial ordering for first-order and higher-order terms

In most termination tools two ingredients, namely recursive path orderings (RPOs) and polynomial interpretation orderings (POLOs), are used in a consecutive disjoint way to solve the final constraints generated from the termination problem. In this article we present a simple ordering that combines both RPO and POLO and defines a family of orderings that includes both, and extend them with the possibility of having, at the same time, an RPO-like treatment for some symbols and a POLO-like treatment for the others. The ordering is extended to higher-order terms, providing a new fully automatable use of polynomial interpretations in combination with beta-reduction.