Global constraints for integer and set value precedence

2009 21st IEEE International Conference on Tools with Artificial Intelligence, 2009

In this paper, we propose to automatically detect variable symmetries of CSP instances by computing for each constraint scope a partition exhibiting locally symmetric variables. From this local information obtained in polynomial time, we can build a so-called lsv-graph whose automorphisms correspond to (global) variable symmetries. Interestingly enough, our approach allows us to disregard the representation (extension, intension, global) of constraints. Besides, the size of the lsv-graph is linear with respect to the number of constraints (and their arity).

Journal of Symbolic Computation, 1994

Imperative programming languages for computing on intervals stand in contrast to systems of relational interval arithmetic that are seamlessly integrated into a logic programming language like CLP# BNR#. The combined power of a symbolic, logic programming language on the one hand and a mathematically correct, logically sound and computationally e# cient programming system# constraint arithmetic on intervals# on the other, is considerably more powerful than either taken separately. Boolean, integer and ...

2011

Mathematical programs whose formulation is symmetric often take a long time to solve using Branch-and-Bound type algorithms, because of the several symmetric optima. One of the techniques used to decrease the adverse effects of symmetry is adjoining symmetry breaking constraints to the formulation before solving the problem. These constraints aim to make some of the symmetric optima infeasible but guarantee that at least one optimum is feasible. Such constraints are usually associated to the different orbits of the action of the formulation group on the set of variable indices. In general, one cannot adjoin symmetry breaking constraints from more than one orbit. In previous work [14] we discussed some (restrictive) sufficient conditions for adjoining such constraints from several orbits. In this paper we present a new method for generating symmetry breaking constraints from several orbits. We show it is less restrictive than the existing method, and discuss some computational experi...

Lecture Notes in Computer Science, 2016

Over the years the constraint-based method has been successfully applied to a wide range of problems in program analysis, from invariant generation to termination and non-termination proving. Quite often the semantics of the program under study as well as the properties to be generated belong to difference logic, i.e., the fragment of linear arithmetic where atoms are inequalities of the form u − v ≤ k. However, so far constraint-based techniques have not exploited this fact: in general, Farkas' Lemma is used to produce the constraints over template unknowns, which leads to non-linear SMT problems. Based on classical results of graph theory, in this paper we propose new encodings for generating these constraints when program semantics and templates belong to difference logic. Thanks to this approach, instead of a heavyweight non-linear arithmetic solver, a much cheaper SMT solver for difference logic or linear integer arithmetic can be employed for solving the resulting constraints. We present encouraging experimental results that show the high impact of the proposed techniques on the performance of the VeryMax verification system.

Lecture Notes in Computer Science, 1995

This paper introduces a finite-automata based representation of Presburger arithmetic definable sets of integer vectors. The representation consists of concurrent automata operating on the binary encodings of the elements of the represented sets. This representation has several advantages. First, being automata-based it is operational in nature and hence leads directly to algorithms, for instance all usual operations on sets of integer vectors translate naturally to operations on automata. Second, the use of concurrent automata makes it compact. Third, it is insensitive to the representation size of integers. Our representation can be used whenever arithmetic constraints are needed. To illustrate its possibilities we show that it can handle integer programming optimally, and that it leads to a new original algorithm for the satisfiability of arithmetic inequalities.

Artificial Intelligence and Mathematics, 2002

Two methods performing Symmetry Breaking During Search (SBDS) are presented, as described in [1] and [2]. The first was also the the one that defined SBDS, under the name Symmetry Excluding Search, being the first attempt to use it for symmetries of arbitrary type, in contrast to previous attempts that could only handle certain symmetry types. The basic characteristic is that SBDS does not affect the search procedure, meaning that it does not force it to use paths with a certain order. The method was refined later in [2]. While in [1] mathematical proofs were given in order to obtain the final results, in [2], the use of group theory and the known properties of symmetric groups make the method more compact. Moreover, in the first case the authors had to implement their method by writing explicit code for everything, while in the second case, a combination of two systems, ECL i PS e and GAP, is used, which results in formalizing the use of symmetries, making the separation between the search procedure and symmetry breaking more clear. In addition, the method becomes now easier to use, since the programmer no longer needs to keep in mind how symmetries work. GAP provides all the information needed, leaving the programmer with the need only to implement the search procedure, using directly the results for symmetry exclusion given by GAP. Examples and experimental results are provided for both cases, indicating the significant profit in reducing the search space, and thus search time in solving Constraint Satisfaction Problems.

This paper advances the state of the art in abstract interpretation of machine code. It tackles two of the biggest challenges in machine-code analysis: (1) holding onto invariants about values in memory, and (2) identifying affine-inequality invariants while handling overflow in arithmetic operations over bit-vector data-types. Most current approaches either capture relations only among registers (and ignore memory entirely), or make potentially unsound assumptions when handling memory. Furthermore, existing bit-vector domains are able to represent either relational affine equalities or non-relational inequalities (e.g., intervals). The key insight to tackling both challenges is to define a new domain combinator (denoted by V), called the view-product combinator. V constructs a reduced product of two domains in which shared view-variables are used to communicate information among the domains. V applied to a non-relational memory domain and a relational bit-vector affine-equality domain constructs the Bit-Vector Memory-Equality Domain (BVME), a domain of bit-vector affine-equalities over memory and registers. V applied to the BVME domain and a bit-vector interval domain constructs the Bit-Vector Memory-Inequality Domain, a domain of relational bitvector affine-inequalities over memory and registers.

Proceedings of the 2007 workshop on Declarative aspects of multicore architectures - DAMP '07, 2007

Constraint Handling Rules (CHR) is a concurrent committedchoice constraint logic programming language to describe transformations (rewritings) among multi-sets of constraints (atomic formulae). CHR is widely used in a range of applications spanning from type system design to artificial intelligence. However, none of the existing CHR implementations we are aware of exploits concurrency or parallelism explicitly. We give a concurrent CHR implementation using GHC (Glasgow Haskell Compiler) with support for Software Transactional Memory. We achieve some significant performance improvements compared to a single-threaded CHR implementation. We obtain a further speed-up, in some cases nearly close to the optimum of 100%, when running programs under under a dual-core processor architecture. Our results show that CHR can be implemented efficiently on a multi-core architecture.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2011

Symmetry-breaking constraints in the form of inequalities between variables have been proposed for a few kind of solution symmetries in numeric CSPs. We show that, for the variable symmetries among those, the proposed inequalities are but a specific case of a relaxation of the well-known LEX constraints extensively used for discrete CSPs. We discuss the merits of this relaxation and present experimental evidences of its practical interest. 6 Note there are only 2 different solutions when n is even, n solutions when it is odd.