Consistency and the quantified constraint satisfaction problem

Abstract

Constraint satisfaction is a very well studied and fundamental artificial intelligence technique. Various forms of knowledge can be represented with constraints, and reasoning techniques from disparate fields can be encapsulated within constraint reasoning algorithms. However, problems involving uncertainty, or which have an adversarial nature (for example, games), are difficult to express and solve in the classical constraint satisfaction problem. This thesis is concerned with an extension to the classical problem: the Quantified Constraint Satisfaction Problem (QCSP). QCSP has recently attracted interest. In QCSP, quantifiers are allowed, facilitating the expression of uncertainty.

I examine whether QCSP is a useful formalism. This divides into two questions: whether QCSP can be solved efficiently; and whether realistic problems can be represented in QCSP. In attempting to answer these questions, the main contributions of this thesis are the following:

- the definition of two new notions of consistency;

- four new constraint propagation algorithms (with eight variants in total), along with empirical evaluations;

- two novel schemes to implement the pure value rule, which is able to simplify QCSP instances;

- a new optimization algorithm for QCSP;

- the integration of these algorithms and techniques into a solver named Queso;

- and the modelling of the Connect 4 game, and of faulty job shop scheduling, in QCSP.

These are set in context by a thorough review of the QCSP literature.