Finite Domain Solver Research Articles

Invariants and other structural properties of biochemical models as a constraint satisfaction problem.

BackgroundWe present a way to compute the minimal semi-positive invariants of a Petri net representing a biological reaction system, as resolution of a Constraint Satisfaction Problem. The use of Petri nets to manipulate Systems Biology models and make available a variety of tools is quite old, and recently analyses based on invariant computation for biological models have become more and more frequent, for instance in the context of module decomposition.ResultsIn our case, this analysis brings both qualitative and quantitative information on the models, in the form of conservation laws, consistency checking, etc. thanks to finite domain constraint programming. It is noticeable that some of the most recent optimizations of standard invariant computation techniques in Petri nets correspond to well-known techniques in constraint solving, like symmetry-breaking. Moreover, we show that the simple and natural encoding proposed is not only efficient but also flexible enough to encompass sub/sur-invariants, siphons/traps, etc., i.e., other Petri net structural properties that lead to supplementary insight on the dynamics of the biochemical system under study.ConclusionsA simple implementation based on GNU-Prolog's finite domain solver, and including symmetry detection and breaking, was incorporated into the BIOCHAM modelling environment and in the independent tool Nicotine. Some illustrative examples and benchmarks are provided.

A Proposal for the Cooperation of Solvers in Constraint Functional Logic Programming

This paper presents a proposal for the cooperation of solvers in constraint functional logic programming, a quite expressive programming paradigm which combines functional, logic and constraint programming using constraint lazy narrowing as goal solving mechanism. Cooperation of solvers for different constraint domains can improve the efficiency of implementations since solvers can take advantage of other solvers' deductions. We restrict our attention to the cooperation of three solvers, dealing with syntactic equality and disequality constraints, real arithmetic constraints, and finite domain (FD) constraints, respectively. As cooperation mechanism, we consider to propagate to the real solver the constraints which have been submitted to the FD solver (and viceversa), imposing special communication constraints to ensure that both solvers will allow the same integer values for all the variables involved in the cooperation.

A Proposal for Disequality Constraints in Curry

We describe the introduction of disequality constraints over algebraic data terms in the functional logic language Curry, and their implementation in Sloth, our Curry compiler. This addition extends the standard definition of Curry in several ways. On one hand, we provide a disequality counterpart to the constraint equality operator (=:=). Secondly, boolean equality operators are also redefined to cope with constructive disequality information, which leads to a more symmetric design w.r.t. the existing one. Semantically speaking, our implementation is very similar to previous proposals, although there are some novel aspects. One of them is that the implementation is partly based on an existing finite domain (FD) constraint solver, which provides a more efficient execution in some examples and, more important, the first complete implementation of disequality constraints over finite types. A detailed description of the finite type case is provided, including: i) the use of the FD solver; ii) an algorithm for analysing cardinality of types, and iii) how to deal with cardinality information at run time. Some benchmarks, an operational semantics minimally extending the one in the Curry draft, and a moderately detailed description of the implementation complete the paper.

University course timetabling using constraint handling rules

Timetabling the courses offered at the Computer Science Department of the University of Munich requires the processing of hard and soft constraints. Hard constraints are conditions that must be satisfied soft constraints, however, may be violated, but should be satisfied as much as possible. This paper shows how to model the timetabling problem as partial constraint satisfaction problem and gives a concise finite domain solver implemented with constraint handling rules that, by performing soft constraint propagation, allows for making soft constraints an active part of the problem-solving process. Furthermore, efficiency is improved by reusing parts of the timetable of the previous year. This prototype needs only a few minutes to create a timetable while manual timetabling usually takes a few days. This was presented at the Systems'98 Computer Fair in Munich and several universities have inquired about it.