Grid based propositional satisfiability solving

This work studies how grid and cloud computing can be applied to efficiently solving propositional satisfiability problem (SAT) instances. Propositional logic provides a convenient language for expressing real-world originated problems such as AI planning, automated test pattern generation, bounded model checking and cryptanalysis. The interest in SAT solving has increased mainly due to improvements in the solving algorithms, which recently have increasingly focused on using parallelism offered by multi-CPU computers. Partly orthogonally to these improvements this work studies several novel approaches to parallel solving of SAT instances in a grid of widely distributed "virtual" computers instead of workstations or supercomputers. Two types of parallel SAT solving approaches are analyzed and used as building blocks for more complex systems: using several solvers which compete to solve a given instance in parallel, and splitting the search space of the instance and solving the resulting partitions in parallel. The work presents several efficient partitioning functions, critical in successful splitting according to an analytical result, and presents novel solving systems that are less dependent on the partitioning function efficiency. Finally, the work studies combining clause learning, a key technique in modern SAT solvers, with the novel types of parallel solvers. Different heuristics are studied for filtering clauses learned in parallel, and the work proposes techniques which allow exchanging the clauses between different splits. The practical significance of the results are studied using large, standard benchmark sets from SAT competitions. Some of the approaches are able to solve several instances that have either not been solved at all by any other solver, or which are significantly slower to solve with other solvers

Approaches to grid-based SAT solving

In this work we develop techniques for using distributed computing resources to efficiently solve instances of the propositional satisfiability problem (SAT). The computing resources considered in this work are assumed to be geographically distributed and connected by a non-dedicated network. Such systems are typically referred to as computational grid environments. The time a modern SAT solver consumes while solving an instance varies according to a random distribution. Unlike many other methods for distributed SAT solving, this work identifies the random distribution as a valuable resource for solving-time reduction. The methods which use randomness in the run times of a search algorithm, such as the ones discussed in this work, are examples of multi-search. The main contribution of this work is in developing and analyzing the multi-search approach in SAT solving and showing its efficiency with several experiments. For the purpose of the analysis, the work introduces a grid simulation model which captures several of the properties of a grid environment which are not observed in more traditional parallel computing systems. The work develops two algorithmic frameworks for multi-search in SAT. The first, SDSAT, is based on using properties of the distribution of the solving time so that the expected time required to solve an instance is reduced. Based on the analysis of SDSAT, the work proposes an algorithm for efficiently using large number of computing resources simultaneously to solve collections of SAT instances. The analysis of SDSAT also motivates the second algorithmic framework, CL-SDSAT. The framework is used to efficiently solve many industrial SAT instances by carefully combining information learned in the distributed SAT solvers. All methods described in the work are directly applicable in a wide range of grid environments and can be used together with virtually unmodified state-of-the-art SAT solvers. The methods are experimentally verified using standard benchmark SAT instances in a production-level grid environment. The experiments show that using the relatively simple methods developed in the work, SAT instances which cannot be solved efficiently in sequential settings can be now solved in a grid environment

Tarmo: A Framework for Parallelized Bounded Model Checking

This paper investigates approaches to parallelizing Bounded Model Checking (BMC) for shared memory environments as well as for clusters of workstations. We present a generic framework for parallelized BMC named Tarmo. Our framework can be used with any incremental SAT encoding for BMC but for the results in this paper we use only the current state-of-the-art encoding for full PLTL. Using this encoding allows us to check both safety and liveness properties, contrary to an earlier work on distributing BMC that is limited to safety properties only. Despite our focus on BMC after it has been translated to SAT, existing distributed SAT solvers are not well suited for our application. This is because solving a BMC problem is not solving a set of independent SAT instances but rather involves solving multiple related SAT instances, encoded incrementally, where the satisfiability of each instance corresponds to the existence of a counterexample of a specific length. Our framework includes a generic architecture for a shared clause database that allows easy clause sharing between SAT solver threads solving various such instances. We present extensive experimental results obtained with multiple variants of our Tarmo implementation. Our shared memory variants have a significantly better performance than conventional single threaded approaches, which is a result that many users can benefit from as multi-core and multi-processor technology is widely available. Furthermore we demonstrate that our framework can be deployed in a typical cluster of workstations, where several multi-core machines are connected by a network

SATU: A SYSTEM FOR DISTRIBUTED PROPOSITIONAL SATISFIABILITY CHECKING IN COMPUTATIONAL GRIDS

In addition to data storage and indexing systems, computational grids are used for solving computationally demanding tasks. Because of the inherent communication delays and high failure probabilities of a loosely coupled and large computational grid, such an environment poses a great challenge for highly data-dependent algorithms. In this work we present a distribution scheme for solving propositional satisfiability problem (SAT) instances, called scattering. The key advantages of scattering are that it can be used in conjunction with any sequential or parallel satisfiability checker, including industrial black box checkers, and that the distribution heuristic is strictly separated from the heuristic used in sequential solving. We also give an implementation of the scheme and benchmark it using a productionlevel grid. The benchmarks range from factorization to cryptanalysis and random 3SAT. Some benchmarks not known to have been solved previously are solved with the distribution scheme. Scattering is analysed with respect to the challenges posed by the gri

Using linear algebra in decomposition of Farkas interpolants

The use of propositional logic and systems of linear inequalities over reals is a common means to model software for formal verification. Craig interpolants constitute a central building block in this setting for over-approximating reachable states, e.g. as candidates for inductive loop invariants. Interpolants for a linear system can be efficiently computed from a Simplex refutation by applying the Farkas’ lemma. However, these interpolants do not always suit the verification task - in the worst case, they can even prevent the verification algorithm from converging. This work introduces the decomposed interpolants, a fundamental extension of the Farkas interpolants, obtained by identifying and separating independent components from the interpolant structure, using methods from linear algebra. We also present an efficient polynomial algorithm to compute decomposed interpolants and analyse its properties.We experimentally show that the use of decomposed interpolants inmodel checking results in immediate convergence on instances where state-of-the-art approaches diverge. Moreover, since being based on the efficient Simplex method, the approach is very competitive in general