LOGPROG  Lògica i Programació
La recerca del nostre grup "Lògica i Programació" s'emmarca en el desenvolupament de tècniques i eines per a l'aplicació de la lògica a la resolució de sistemes de restriccions. Més concretament, les principals línies de la nostra investigació es basen per una banda en (a) l'estudi de mètodes de resolució de problemes mitjançant resolvedors de satisfactibilitat proposicional (SAT), de satisfactibilitat mòdul teories (SMT), de programació amb restriccions (CP), i d'extensions d'aquests a optimització (MaxSAT, MaxSMT); i (b) per una altra en l'aplicació d'aquests mètodes per atacar problemes complexos d'interès pràctic, com ara de planificació industrial o d'anàlisis de programes. Mentre que la recerca de tipus més teòric és presentada a les conferències i revistes internacionals de més prestigi de les respectives àrees, els resultats en la vessant més pràctica es materialitzen en transferència de tecnologia en empreses tant de dins com de fora de Catalunya.
The group carries out research in basic computer science. In particular, it has internationallyrecognised expertise in the (closely related) fields of logic in computer science, computational complexity and constraintsolving problems, and in the use of advanced programming techniques (e.g. constraint programming, automated deduction, etc.) for the development of practical software tools.
In what follows, we give a brief overview of these research lines. Logic has been called "the calculus of computer science", because its role in computer science is similar to that of mathematics in the physical sciences (see, for example, www.cs.rice.edu/~vardi/logic).
Similarly to the way in which architects and engineers analyse their designs mathematically, computer scientists use logic to analyse systems¿ properties (e.g. correctness, safety and security), during all the phases of their life cycles (e.g. specification, development, verification and maintenance). Also, for systems whose efficiency is critical, logicbased analysis can be very helpful, and in all kinds of systems, logicbased techniques help to reduce costs (see, for example, the section on software productivity tools at research.microsoft.com). Hence, it is not surprising that there is an increasing tendency to use logicbased formalisms in all kinds of hardware and software systems and their components, such as databases or programming languages, among others.
Computational complexity involves the study of the resources required during computation to solve a given problem. The most common resources are time (number of computation steps) and space (amount of memory). Other resources can also be considered, such as randomness (how randomness can increase efficiency) and parallelism (how the use of parallel processors can help). Today, the connections between logic and complexity are well established. For example, the field of proof complexity involves the study of the mathematical relationships between complexity classes (i.e. classes of problems that are solvable using the same amount of resources) and the length of proofs in certain logical systems. This field arose as an approach to the wellknown problem of whether the P class of problems equals the NP class or not (see the milliondollar prizes at www.claymath.org): if one could show that, for every propositional proof system, there is a class of tautologies with no short proofs, then the answer is negative. The study of the limitations of proof systems has also led to the discovery of important new algorithms.
Constraint programming is the study of computational systems based on constraints. It has recently emerged as an area of research that engages researchers from a variety of fields. The idea is to solve problems by stating constraints (i.e. conditions, properties) that must be satisfied by the solution. Constraint programming consists of the generation of requirements (constraints) and the solution of these requirements by specialised constraint solvers. It has been successfully applied in numerous domains, including computer graphics (to express geometric coherence), natural language processing (to construct efficient parsers), database systems (to ensure and/or restore the consistency of the data), operations research (optimisation problems), molecular biology (DNA sequencing), business applications (option trading), electrical engineering (to locate faults), circuit design (to compute layouts), etc. Most, if not all, of these practical problems fall into the complexity class of NPcomplete problems, for which proof complexity results give insight into classes of deterministic algorithms.
The research group will continue to carry out research in logicbased methods in the areas of automated deduction, rewriting, constraint/logic programming, hardware and software verification, and symbolic computation. For constraintsatisfaction problems and algorithms for combinatorial optimisation problems, the group will also continue to work on aspects such as heuristics, symmetries, and valued constraints, and carry out research in the field of proof and circuit complexity and its close relationship with automated theoremproving and the satisfiability problem.
Specific tools that are being developed and maintained include automated deduction systems for firstorder logic, efficient decision procedures for decidable logics of interest, environments for automated termination proofs, and environments for program verification. Moreover, the research group will continue to apply such tools to circuit verification, industrial planning/scheduling, the Semantic Web, and education, and to pursue their free distribution throughout the Internet.
New research lines of particular interest include the forthcoming Semantic World Wide Web and its associated description logics for semantic search criteria, consistency/integrity restrictions, etc. Another example is the crucial need for logicbased techniques for the verification of cryptographic protocols, in applications such as secrecy, electronic signatures, and electronic money (since testing is useless against malicious attackers). From a more theoretical point of view, we intend to open new lines of research in quantum computing, cryptography, data compression, and applications of game theory to computer science.
All the members of the group have international experience, some as researchers, lecturers and guest lecturers at international institutions. This facilitates close relationships with prestigious institutions, such as the Institute for Advanced Study in Princeton (USA), the DIMACS Research Centre at Rutgers University (USA), the University of Toronto (Canada), the University of California at San Diego (USA), the MaxPlanckInstitut for Computer Science (Germany), the École Normale Superieure (France), the École Polytechnique (France), etc.
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Recent Submissions

The scaling of the minimum sum of edge lengths in uniformly random trees
(Institute of Physics (IOP), 20160621)
Article
Restricted access  publisher's policyThe minimum linear arrangement problem on a network consists of finding the minimum sum of edge lengths that can be achieved when the vertices are arranged linearly. Although there are algorithms to solve this problem on ... 
Resolvedor SAT, basado en procedimientos DavisPutnamLongemannLoveland
(200701)
External research report
Open AccessEl problema de satisfación de fórmulas lógicas (SAT), es un problema NPHard. Una forma de resolverlo es por medio de procedimientos DavisPutnamLongemannLoveland (DPLL), ahora presentamos una implementación de un ... 
Compositional safety verification with MaxSMT
(2015)
Conference report
Open AccessWe present an automated compositional program verification technique for safety properties based on conditional inductive invariants. For a given program part (e.g., a single loop) and a postcondition, we show how to, using ... 
Termination competition (termCOMP 2015)
(Springer, 2015)
Conference report
Restricted access  publisher's policyThe termination competition focuses on automated termination analysis for all kinds of programming paradigms, including categories for term rewriting, imperative programming, logic programming, and functional programming. ... 
The computability path ordering
(20151026)
Article
Open AccessThis paper aims at carrying out termination proofs for simply typed higherorder calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation ... 
Exponential separation between treelike and daglike Cutting Planes proof systems
(199712)
External research report
Open AccessWe prove an exponential lower bound for treelike Cutting Planes refutations of a set of clauses which has polynomial size resolution refutations. This implies an exponential separation between treelike and daglike ... 
Normal higherorder termination
(20150301)
Article
Open AccessWe extend the termination proof methods based on reduction orderings to higherorder rewriting systems based on higherorder pattern matching. We accommodate, on the one hand, a weakly polymorphic, algebraic extension of ... 
The fractal dimension of SAT formulas
(Springer, 2014)
Conference report
Restricted access  publisher's policyModern SAT solvers have experienced a remarkable progress on solving industrial instances. Most of the techniques have been developed after an intensive experimental process. It is believed that these techniques exploit ... 
Decomposing utility functions in Bounded MaxSum for distributed constraint optimization
(Springer, 2014)
Conference report
Open AccessBounded MaxSum is a messagepassing algorithm for solving distributed Constraint Optimization Problems (DCOP) able to compute solutions with a guaranteed approximation ratio. In this paper we show that the introduction ... 
The IntSat method for integer linear programming
(Springer, 2014)
Conference report
Open AccessConflictDriven ClauseLearning (CDCL) SAT solvers can automatically solve very large realworld problems. To go beyond, and in particular in order to solve and optimize problems involving linear arithmetic constraints, ...