Bit-Vector Model Counting using Statistical Estimation

Approximate model counting for bit-vector SMT formulas (generalizing \#SAT) has many applications such as probabilistic inference and quantitative information-flow security, but it is computationally difficult. Adding random parity constraints (XOR streamlining) and then checking satisfiability is an effective approximation technique, but it requires a prior hypothesis about the model count to produce useful results. We propose an approach inspired by statistical estimation to continually refine a probabilistic estimate of the model count for a formula, so that each XOR-streamlined query yields as much information as possible. We implement this approach, with an approximate probability model, as a wrapper around an off-the-shelf SMT solver or SAT solver. Experimental results show that the implementation is faster than the most similar previous approaches which used simpler refinement strategies. The technique also lets us model count formulas over floating-point constraints, which we demonstrate with an application to a vulnerability in differential privacy mechanisms

Modern Coding Theory: The Statistical Mechanics and Computer Science Point of View

These are the notes for a set of lectures delivered by the two authors at the Les Houches Summer School on `Complex Systems' in July 2006. They provide an introduction to the basic concepts in modern (probabilistic) coding theory, highlighting connections with statistical mechanics. We also stress common concepts with other disciplines dealing with similar problems that can be generically referred to as `large graphical models'. While most of the lectures are devoted to the classical channel coding problem over simple memoryless channels, we present a discussion of more complex channel models. We conclude with an overview of the main open challenges in the field.Comment: Lectures at Les Houches Summer School on `Complex Systems', July 2006, 44 pages, 25 ps figure

Rational Deployment of CSP Heuristics

Heuristics are crucial tools in decreasing search effort in varied fields of AI. In order to be effective, a heuristic must be efficient to compute, as well as provide useful information to the search algorithm. However, some well-known heuristics which do well in reducing backtracking are so heavy that the gain of deploying them in a search algorithm might be outweighed by their overhead. We propose a rational metareasoning approach to decide when to deploy heuristics, using CSP backtracking search as a case study. In particular, a value of information approach is taken to adaptive deployment of solution-count estimation heuristics for value ordering. Empirical results show that indeed the proposed mechanism successfully balances the tradeoff between decreasing backtracking and heuristic computational overhead, resulting in a significant overall search time reduction.Comment: 7 pages, 2 figures, to appear in IJCAI-2011, http://www.ijcai.org