Youssef Hamadi

Propositional Satisfiability and Constraint Programming: A comparative survey

Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research cross-fertilizing occasionally. These two approaches to problem solving have a lot in common as evidenced by similar ideas underlying the branch and prune algorithms that are most successful at solving both kinds of problems. They also exhibit differences in the way they are used to state and solve problems since SATs approach is, in general, a black-box approach, while CP aims at being tunable and programmable. This survey overviews the two areas in a comparative way, emphasizing the similarities and differences between the two and the points where we feel that one technology can benefit from ideas or experience acquired from the other.

Control-based clause sharing in parallel SAT solving

Conflict driven clause learning, one of the most important component of modern SAT solvers, is also recognized as very important in parallel SAT solving. Indeed, it allows clause sharing between multiple processing units working on related (sub) problems. However, without limitation, sharing clauses might lead to an exponential blow up in communication or to the sharing of irrelevant clauses. This paper, proposes two innovative policies to dynamically adjust the size of shared clauses between any pair of processing units. The first approach controls the overall number of exchanged clauses whereas the second additionally exploits the relevance quality of shared clauses. Experimental results show important improvements of the state-of the-art parallel SAT solver.

Efficiently solving quantified bit-vector formulas

In recent years, bit-precise reasoning has gained importance in hardware and software verification. Of renewed interest is the use of symbolic reasoning for synthesising loop invariants, ranking functions, or whole program fragments and hardware circuits. Solvers for the quantifier-free fragment of bit-vector logic exist and often rely on SAT solvers for efficiency. However, many techniques require quantifiers in bit-vector formulas to avoid an exponential blow-up during construction. Solvers for quantified formulas usually flatten the input to obtain a quantified Boolean formula, losing much of the word-level information in the formula. We present a new approach based on a set of effective word-level simplifications that are traditionally employed in automated theorem proving, heuristic quantifier instantiation methods used in SMT solvers, and model finding techniques based on skeletons/templates. Experimental results on two different types of benchmarks indicate that our method outperforms the traditional flattening approach by multiple orders of magnitude of runtime.

Interleaved backtracking in distributed constraint networks

The adaptation of software technology to distributed environments is an important challenge today. In this work we combine parallel and distributed search. By this way we add the potential speed-up of a parallel exploration in the processing of distributed problems. This paper extends DIBT a distributed search procedure operating in distributed constraint networks. The extension is twofold. First the procedure is updated to face delayed information problems upcoming in heterogeneous systems. Second, the search is extended to simultaneously explore independent parts of a distributed search tree. By this way we introduce parallelism into distributed search, which brings to interleaved distributed intelligent backtracking (IDIBT). Our results show that 1) insoluble problems do not greatly degrade performance over DIBT and 2) superlinear speed-up can be achieved when the distribution of solution is nonuniform.

A Concurrent Portfolio Approach to SMT Solving

With the availability of multi-core processors and large-scale computing clusters, the study of parallel algorithms has been revived throughout the industry. We present a portfolio approach to deciding the satisfiability of SMT formulas, based on the recent success of related algorithms for the SAT problem. Our parallel version of Z3 outperforms the sequential solver, with speedups of well over an order of magnitude on many benchmarks.

A generalized framework for conflict analysis

This paper presents an extension of Conflict Driven Clauses Learning (CDCL). It relies on an extended notion of implication graph containing additional arcs, called inverse arcs. These are obtained by taking into account the satisfied clauses of the formula, which are usually ignored by conflict analysis. This extension captures more conveniently the whole propagation process, and opens new perspectives for CDCL-based approaches. Among other benefits, our extension leads to a new conflict analysis scheme that exploits the additional arcs to back-jump to higher levels. Experimental results show that the integration of our generalized conflict analysis scheme within two state-of-the-art solvers improves their performance.

What Is Autonomous Search

Autonomous search is a particular case of adaptive systems that improve their solving performance by modifying and adjusting themselves to the problem at hand, either by self-adaptation or by supervised adaptation. We propose a general definition and a taxonomy of search processes with respect to their computation characteristics. For this purpose, we decompose solvers into components and their configurations. Some computation rules between computation stages are used to formalize the solver modifications and adaptations. Using these rules, we then sketch out and classify some well known solvers and try to answer the question: “What is Autonomous Search?”

Diversification and intensification in parallel SAT solving

In this paper, we explore the two well-known principles of diversification and intensification in portfolio-based parallel SAT solving. These dual concepts play an important role in several search algorithms including local search, and appear to be a key point in modern parallel SAT solvers. To study their trade-off, we define two roles for the computational units. Some of them classified as Masters perform an original search strategy, ensuring diversification. The remaining units, classified as Slaves are there to intensify their masters strategy. Several important questions have to be answered. The first one is what information should be given to a slave in order to intensify a given search effort? The second one is, how often, a subordinated unit has to receive such information? Finally, the question of finding the number of subordinated units and their connections with the search efforts has to be answered. Our results lead to an original intensification strategy which outperforms the best parallel SAT solver ManySAT, and solves some open SAT instances.

Seven Challenges in Parallel SAT Solving

This paper provides a broad overview of the situation in the area of Parallel Search with a specific focus on Parallel SAT Solving. A set of challenges to researchers is presented which, we believe, must be met to ensure the practical applicability of Parallel SAT Solvers in the future. All these challenges are described informally, but put into perspective with related research results, and a (subjective) grading of difficulty for each of them is provided.

Tractability: Practical Approaches to Hard Problems

Contributors Introduction Lucas Bordeaux, Youssef Hamadi and Pushmeet Kohli Part I. Graphical Structure: 1. Treewidth and hypertree width Georg Gottlob, Gianluigi Greco and Francesco Scarcello 2. Perfect graphs and graphical modeling Tony Jebara Part II. Language Restrictions: 3. Submodular function maximization Andreas Krause and Daniel Golovin 4. Tractable valued constraints Peter G. Jeavons and Stanislav Zivny 5. Tractable knowledge representation formalisms Adnan Darwiche Part III. Algorithms and their Analysis: 6. Tree-reweighted message passing Vladimir Kolmogorov 7. Tractable optimization in machine learning Suvrit Sra 8. Approximation algorithms Mohit Singh and Kunal Talwar 9. Kernelization methods for fixed-parameter tractability Fedor V. Fomin and Saket Saurabh Part IV. Tractability in Some Specific Areas: 10. Efficient submodular function minimization for computer vision Pushmeet Kohli 11. Towards practical graph-based, iteratively decoded channel codes: insights through absorbing sets Lara Dolecek Part V. Heuristics: 12. SAT solvers Joao Marques-Silva and Ines Lynce 13. Tractability and modern satisfiability modulo theories solvers Nikolaj Bjorner and Leonardo de Moura.