We introduce an efficient message passing scheme for solving Constraint Satisfaction Problems (CSPs), which uses stochastic perturbation of Belief Propagation (BP) and Survey Propagation (SP) messages to bypass decimation and directly produce a single satisfying assignment. Our first CSP solver, called Perturbed Blief Propagation, smoothly interpolates two well-known inference procedures; it starts as BP and ends as a Gibbs sampler, which produces a single sample from the set of solutions. Moreover we apply a similar perturbation scheme to SP to produce another CSP solver, Perturbed Survey Propagation. Experimental results on random and real-world CSPs show that Perturbed BP is often more successful and at the same time tens to hundreds of times more efficient than standard BP guided decimation. Perturbed BP also compares favorably with state-of-the-art SP-guided decimation, which has a computational complexity that generally scales exponentially worse than our method (wrt the cardinality of variable domains and constraints). Furthermore, our experiments with random satisfiability and coloring problems demonstrate that Perturbed SP can outperform SP-guided decimation, making it the best incomplete random CSP-solver in difficult regimes.

Not all NP-complete problems share the same practical hardness with respect to exact computation. Whereas some NP-complete problems are amenable to efficient computational methods, others are yet to show any such sign. It becomes a major challenge to develop a theoretical framework that is more fine-grained than the theory of NP-completeness, and that can explain the distinction between the exact complexities of various NP-complete problems. This distinction is highly relevant for constraint satisfaction problems under natural restrictions, where various shades of hardness can be observed in practice. Acknowledging the NP-hardness of such problems, one has to look beyond polynomial time computation. The theory of subexponential-time complexity provides such a framework, and has been enjoying increasing popularity in complexity theory. An instance of the constraint satisfaction problem with n variables over a domain of d values can be solved by brute-force in dn steps (omitting a polynomial factor). In this paper we study the existence of subexponential-time algorithms, that is, algorithms running in do(n) steps, for various natural restrictions of the constraint satisfaction problem. We consider both the constraint satisfaction problem in which all the constraints are given extensionally as tables, and that in which all the constraints are given intensionally in the form of global constraints. We provide tight characterizations of the subexponential-time complexity of the aforementioned problems with respect to several natural structural parameters, which allows us to draw a detailed landscape of the subexponential-time complexity of the constraint satisfaction problem. Our analysis provides fundamental results indicating whether and when one can significantly improve on the brute-force search approach for solving the constraint satisfaction problem.

Artificial intelligence tasks which can be formulated as constraint satisfaction problems, with which this paper is for the most part concerned, are usually solved by backtracking.

In this paper we will be concerned with such reasoning in its most general form, that is, in inferences that are defeasible: given more information, we may retract them. The purpose of this paper is to introduce a form of non-monotonic inference based on the notion of a partial model of the world. We take partial models to reflect our partial knowledge of the true state of affairs. We then define non-monotonic inference as the process of filling in unknown parts of the model with conjectures: statements that could turn out to be false, given more complete knowledge. To take a standard example from default reasoning: since most birds can fly, if Tweety is a bird it is reasonable to assume that she can fly, at least in the absence of any information to the contrary. We thus have some justification for filling in our partial picture of the world with this conjecture. If our knowledge includes the fact that Tweety is an ostrich, then no such justification exists, and the conjecture must be retracted.

A problem simplification approach that generates heuristics for constraint-satisfaction problems ' 125 R. DECHTER and J. PEARL 7. The relation between programming and specification languages with particular reference to Anna 157 A. D. MCGETTRICK and J. G. STELL LOGIC PROGRAMMING TOOLS AND APPLICATIONS 8. YAPES: yet another PROLOG expert system Decision trees and multi-valued attributes 305 J. R. QUINLAN 14. RuleFactory: a new inductive learning shell 319 S. RENNER 15.

Recognition of three-dimensional objects, puzzle solving, electronic circuit analysis and truth-maintenance systems are examples of such problems, and these are normally solved by various versions of backtrack search. In this work we show how advice can be automatically generated to guide the order in which the search algorithm assigns values to the variables, so as to reduce the amount of backtracking. The advice is generated by consulting relaxed models of the subproblems created by each value-assignment candidate. The relaxed problems are chosen to yield backtrack-free solutions, and the information retrieved from these models induces a preference order among the choices pending in the original problem.

Problem solvers need more than just the facts and logic of a problem domain. To work effectively, they also aced meta-knowledge, that is, knowledge about how to use the facts. For example, hierarchical planning uses meta-knowledge to distinguish between the important considerations and the details of a problem. This knowledge is added to the facts and logic of a domain and used to focus the generation of inferences. It relieves a hierarchical planner from trying to deal with everything at once.

The cutting plane method is an augmentative constrained optimization procedure that is often used with continuous-domain optimization techniques such as linear and convex programs. We investigate the viability of a similar idea within message passing -- for integral solutions -- in the context of two combinatorial problems: 1) For Traveling Salesman Problem (TSP), we propose a factor-graph based on Held-Karp formulation, with an exponential number of constraint factors, each of which has an exponential but sparse tabular form. 2) For graph-partitioning (a.k.a. community mining) using modularity optimization, we introduce a binary variable model with a large number of constraints that enforce formation of cliques. In both cases we are able to derive surprisingly simple message updates that lead to competitive solutions on benchmark instances. In particular for TSP we are able to find near-optimal solutions in the time that empirically grows with $N^3$, demonstrating that augmentation is practical and efficient.

We consider the quantified constraint satisfaction problem (QCSP) which is to decide, given a structure and a first-order sentence (not assumed here to be in prenex form) built from conjunction and quantification, whether or not the sentence is true on the structure. We present a proof system for certifying the falsity of QCSP instances and develop its basic theory; for instance, we provide an algorithmic interpretation of its behavior. Our proof system places the established Q-resolution proof system in a broader context, and also allows us to derive QCSP tractability results.