A Logical Approach to Efficient Max-SAT solving

Weighted Max-SAT is the optimization version of SAT and many important problems can be naturally encoded as such. Solving weighted Max-SAT is an important problem from both a theoretical and a practical point of view. In recent years, there has been considerable interest in finding efficient solving techniques. Most of this work focus on the computation of good quality lower bounds to be used within a branch and bound DPLL-like algorithm. Most often, these lower bounds are described in a procedural way. Because of that, it is difficult to realize the {\em logic} that is behind. In this paper we introduce an original framework for Max-SAT that stresses the parallelism with classical SAT. Then, we extend the two basic SAT solving techniques: {\em search} and {\em inference}. We show that many algorithmic {\em tricks} used in state-of-the-art Max-SAT solvers are easily expressable in {\em logic} terms with our framework in a unified manner. Besides, we introduce an original search algorithm that performs a restricted amount of {\em weighted resolution} at each visited node. We empirically compare our algorithm with a variety of solving alternatives on several benchmarks. Our experiments, which constitute to the best of our knowledge the most comprehensive Max-sat evaluation ever reported, show that our algorithm is generally orders of magnitude faster than any competitor

Sur l'UP-résilience des k-UCSs binaires

International audienceAbstract Branch and Bound (BnB) solvers for Max-SAT exploit max-resolution, the inference rule for Max-SAT, to ensure that every computed Inconsistent Subset (IS) is counted only once. However, learning max-resolution transformations can be detrimental to their performance so they are usually selectively learned if they respect certain patterns. In this paper, we focus on particular patterns called binary k-UCSs. We prove that these patterns verify a recent characterization of max-resolution transformations called UP-resilience and we show how this result can help extend the current patterns. Finally, this work is part of a global approach to characterize the relevance of transformations by max-resolution.Les solveurs basés sur la méthode séparation et évaluation (BnB) pour Max-SAT exploitent la max-résolution, la règle d'inférence pour Max-SAT, pour s'as-surer que chaque sous-ensemble inconsistant (IS) détecté n'est compté qu'une seule fois. Cependant, les transformations par max-résolution peuvent affecter négative-ment leurs performances. Elles sont alors généralement apprises de manière sélective : quand elles respectent cer-tains motifs. Dans ce papier, on s'intéresse à des motifs particuliers appelés k-UCSs binaires. On prouve que ces motifs vérifient une caractérisation récente des transformations par max-résolution appelée UP-résilience et on décrit comment ce résultat peut aider à étendre les motifs actuels. Enfin, ce travail s'inscrit d'une démarche globale de caractérisation de la pertinence des transformations par max-résolution

Une vision trivaluée pour les problèmes SAT et MAX-SAT

The aim of this paper is to propose a new resolution framework for the SAT and MAX-SAT problems which introduces a third truth value undefined in order to improve the resolution efficiency. Using this framework, we have adapted the classic algorithms Tabu Search and Walksat. Promising results are obtained and show the interest of our approach

A Dynamic Island-Based Genetic Algorithms Framework

This work presents a dynamic island model framework for helping the resolution of combinatorial optimization problems with evolutionary algorithms. In this framework, the possible migrations among islands are represented by a complete graph. The migrations probabilities associated to each edge are dynamically updated with respect to the last migrations impact. This new framework is tested on the well-known 0/1 Knapsack problem and MAX-SAT problem. Good results are obtained and several properties of this framework are studied

Castelnuovo-Mumford regularity of products of ideals

We discuss the behavior of the Castelnuovo-Mumford regularity under certain operations on ideals and modules, like products or powers. In particular, we show that reg(IM) can be larger than reg(M)+reg(I) even when I is an ideal of linear forms and M is a module with a linear resolution. On the other hand, we show that any product of ideals of linear forms has a linear resolution. We also discuss the case of polymatroidal ideals and show that any product of determinantal ideals of a generic Hankel matrix has a linear resolution.Comment: 14 page

Identifying Security-Critical Cyber-Physical Components in Industrial Control Systems

In recent years, Industrial Control Systems (ICS) have become an appealing target for cyber attacks, having massive destructive consequences. Security metrics are therefore essential to assess their security posture. In this paper, we present a novel ICS security metric based on AND/OR graphs that represent cyber-physical dependencies among network components. Our metric is able to efficiently identify sets of critical cyber-physical components, with minimal cost for an attacker, such that if compromised, the system would enter into a non-operational state. We address this problem by efficiently transforming the input AND/OR graph-based model into a weighted logical formula that is then used to build and solve a Weighted Partial MAX-SAT problem. Our tool, META4ICS, leverages state-of-the-art techniques from the field of logical satisfiability optimisation in order to achieve efficient computation times. Our experimental results indicate that the proposed security metric can efficiently scale to networks with thousands of nodes and be computed in seconds. In addition, we present a case study where we have used our system to analyse the security posture of a realistic water transport network. We discuss our findings on the plant as well as further security applications of our metric.Comment: Keywords: Security metrics, industrial control systems, cyber-physical systems, AND-OR graphs, MAX-SAT resolutio

Predictive Capacity of Meteorological Data - Will it rain tomorrow

With the availability of high precision digital sensors and cheap storage medium, it is not uncommon to find large amounts of data collected on almost all measurable attributes, both in nature and man-made habitats. Weather in particular has been an area of keen interest for researchers to develop more accurate and reliable prediction models. This paper presents a set of experiments which involve the use of prevalent machine learning techniques to build models to predict the day of the week given the weather data for that particular day i.e. temperature, wind, rain etc., and test their reliability across four cities in Australia {Brisbane, Adelaide, Perth, Hobart}. The results provide a comparison of accuracy of these machine learning techniques and their reliability to predict the day of the week by analysing the weather data. We then apply the models to predict weather conditions based on the available data.Comment: 7 pages, 2 Result Set

Verification of Sequential Circuits by Tests-As-Proofs Paradigm

We introduce an algorithm for detection of bugs in sequential circuits. This algorithm is incomplete i.e. its failure to find a bug breaking a property P does not imply that P holds. The appeal of incomplete algorithms is that they scale better than their complete counterparts. However, to make an incomplete algorithm effective one needs to guarantee that the probability of finding a bug is reasonably high. We try to achieve such effectiveness by employing the Test-As-Proofs (TAP) paradigm. In our TAP based approach, a counterexample is built as a sequence of states extracted from proofs that some local variations of property P hold. This increases the probability that a) a representative set of states is examined and that b) the considered states are relevant to property P. We describe an algorithm of test generation based on the TAP paradigm and give preliminary experimental results