Constraint Satisfaction Problems over Numeric Domains
نویسندگان
چکیده
We present a survey of complexity results for constraint satisfaction problems (CSPs) over the integers, the rationals, the reals, and the complex numbers. Examples of such problems are feasibility of linear programs, integer linear programming, the max-atoms problem, Hilbert’s tenth problem, and many more. Our particular focus is to identify those CSPs that can be solved in polynomial time, and to distinguish them from CSPs that are NP-hard. A very helpful tool for obtaining complexity classifications in this context is the concept of a polymorphism from universal algebra. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems
منابع مشابه
Consistency Techniques for Numeric CSPs
Many problems can be expressed in terms of a numeric constraint satisfaction problem over finite or continuous domains (numeric CSP). The purpose of this paper is to show that the consistency techniques that have been developed for CSPs can be adapted to numeric CSPs. Since the numeric domains are ordered the underlying idea is to handle domains only by their bounds. The semantics that have bee...
متن کاملAccelerating filtering techniques for numeric CSPs
Search algorithms for solving Numeric CSPs (Constraint Satisfaction Problems) make an extensive use of filtering techniques. In this paper1 we show how those filtering techniques can be accelerated by discovering and exploiting some regularities during the filtering process. Two kinds of regularities are discussed, cyclic phenomena in the propagation queue and numeric regularities of the domain...
متن کاملRewriting Numeric Constraint Satisfaction Problems for Consistency Algorithms
Reformulating constraint satisfaction problems (CSPs) in lower arity is a common procedure when computing consistency. Lower arity CSPs are simpler to treat than high arity CSPs. Several consistency algorithms have exponential complexity in the CSP’s arity, others only work on low
متن کاملAn Algorithm Inspired by Constraint Solvers to Infer Inductive Invariants in Numeric Programs
This paper addresses the problem of proving a given invariance property φ of a loop in a numeric program, by inferring automatically a stronger inductive invariant ψ. The algorithm we present is based on both abstract interpretation and constraint solving. As in abstract interpretation, it computes the effect of a loop using a numeric abstract domain. As in constraint satisfaction, it works fro...
متن کاملCSP(M): Constraint Satisfaction Problem over Models
Constraint satisfaction programming (CSP) has been successfully used in model-driven development (MDD) for solving a wide range of (combinatorial) problems. In CSP, declarative constraints capture restrictions over variables with finite domains where both the number of variables and their domains are required to be a priori finite. However, the existing formulation of constraint satisfaction pr...
متن کامل