Constraint Propagation as Information Maximization

TL;DR

This paper presents a unified framework for constraint satisfaction problems using information maximization, generalizing optimization, relations, and logic, with applications to numerical analysis and nonlinear equations.

Contribution

It introduces a novel unified view of constraint satisfaction based on information theory and logic, extending existing models and applying to real-valued problems.

Findings

Chaotic algorithm combines efficiency and correctness guarantees.

Framework generalizes optimization and relations for constraint problems.

Application to nonlinear equations over reals demonstrates practical relevance.

Abstract

This paper draws on diverse areas of computer science to develop a unified view of computation: (1) Optimization in operations research, where a numerical objective function is maximized under constraints, is generalized from the numerical total order to a non-numerical partial order that can be interpreted in terms of information. (2) Relations are generalized so that there are relations of which the constituent tuples have numerical indexes, whereas in other relations these indexes are variables. The distinction is essential in our definition of constraint satisfaction problems. (3) Constraint satisfaction problems are formulated in terms of semantics of conjunctions of atomic formulas of predicate logic. (4) Approximation structures, which are available for several important domains, are applied to solutions of constraint satisfaction problems. As application we treat constraint satisfaction problems over reals. These cover a large part of numerical analysis, most significantly nonlinear equations and inequalities. The chaotic algorithm analyzed in the paper combines the efficiency of floating-point computation with the correctness guarantees of arising from our logico-mathematical model of constraint-satisfaction problems.