scholarly journals New Inference Rules for Max-SAT

2007 ◽  
Vol 30 ◽  
pp. 321-359 ◽  
Author(s):  
C. M. Li ◽  
F. Manya ◽  
J. Planes
Keyword(s):  
Experimental Investigation ◽  
Inference Rules ◽  
Sat Solvers ◽  
Sat Solver ◽  
Proof Tree ◽  
Max Sat ◽  
Unit Propagation ◽  
Unit Resolution ◽  
Original Formula ◽  
Simplified Formula

Exact Max-SAT solvers, compared with SAT solvers, apply little inference at each node of the proof tree. Commonly used SAT inference rules like unit propagation produce a simplified formula that preserves satisfiability but, unfortunately, solving the Max-SAT problem for the simplified formula is not equivalent to solving it for the original formula. In this paper, we define a number of original inference rules that, besides being applied efficiently, transform Max-SAT instances into equivalent Max-SAT instances which are easier to solve. The soundness of the rules, that can be seen as refinements of unit resolution adapted to Max-SAT, are proved in a novel and simple way via an integer programming transformation. With the aim of finding out how powerful the inference rules are in practice, we have developed a new Max-SAT solver, called MaxSatz, which incorporates those rules, and performed an experimental investigation. The results provide empirical evidence that MaxSatz is very competitive, at least, on random Max-2SAT, random Max-3SAT, Max-Cut, and Graph 3-coloring instances, as well as on the benchmarks from the Max-SAT Evaluation 2006.

scholarly journals Improved Exact Solver for the Weighted MAX-SAT Problem

10.29007/38lm ◽  
2018 ◽  
Author(s):  
Adrian Kuegel
Keyword(s):  
Data Structure ◽  
Lower Bound ◽  
Branch And Bound ◽  
State Of The Art ◽  
Branch And Bound Algorithm ◽  
Sat Problem ◽  
Sat Solvers ◽  
Propagation Algorithm ◽  
Max Sat ◽  
Unit Propagation

Many exact Max-SAT solvers use a branch and bound algorithm, where the lower bound is calculated with a combination of Max-SAT resolution and detection of disjoint inconsistent subformulas. We propose a propagation algorithm which improves the detection of disjoint inconsistent subformulas compared to algorithms previously used in Max-SAT solvers. We implemented this algorithm in our new solver akmaxsat and compared our solver with three solvers using unit propagation and restricted failed literal detection; these solvers are currently state-of-the-art on random Max-SAT instances. We also developed a lazy deletion data structure for our solver which speeds up lower bound calculation on instances with a high clauses-to-variables ratio. Our experiments show that our solver runs faster than the previously best solvers on randomly generated instances with a high clauses-to-variables ratio.

scholarly journals Dolius: A Distributed Parallel SAT Solving Framework

10.29007/hvqt ◽  
2018 ◽  
Author(s):  
Gilles Audemard ◽  
Benoît Hoessen ◽  
Saïd Jabbour ◽  
Cédric Piette
Keyword(s):  
Shared Memory ◽  
State Of The Art ◽  
Divide And Conquer ◽  
Sat Solving ◽  
Sat Solvers ◽  
Sat Solver

Over the years, parallel SAT solving becomes more and more important. However, most of state-of-the-art parallel SAT solvers are portfolio-based ones. They aim at running several times the same solver with different parameters. In this paper, we propose a tool called Dolius, mainly based on the divide and conquer paradigm. In contrast to most current parallel efficient engines, Dolius does not need shared memory, can be distributed, and scales well when a large number of computing units is available. Furthermore, our tool contains an API allowing to plug any SAT solver in a simple way.

scholarly journals FourierSAT: A Fourier Expansion-Based Algebraic Framework for Solving Hybrid Boolean Constraints

2020 ◽  
Vol 34 (02) ◽  
pp. 1552-1560
Author(s):  
Anastasios Kyrillidis ◽  
Anshumali Shrivastava ◽  
Moshe Vardi ◽  
Zhiwei Zhang
Keyword(s):  
Boolean Functions ◽  
Continuous Optimization ◽  
Conjunctive Normal Form ◽  
Cardinality Constraints ◽  
Sat Solvers ◽  
Boolean Satisfiability Problem ◽  
Algebraic Framework ◽  
Clause Learning ◽  
Sat Solver ◽  
Analysis Of Boolean Functions

The Boolean SATisfiability problem (SAT) is of central importance in computer science. Although SAT is known to be NP-complete, progress on the engineering side—especially that of Conflict-Driven Clause Learning (CDCL) and Local Search SAT solvers—has been remarkable. Yet, while SAT solvers, aimed at solving industrial-scale benchmarks in Conjunctive Normal Form (CNF), have become quite mature, SAT solvers that are effective on other types of constraints (e.g., cardinality constraints and XORs) are less well-studied; a general approach to handling non-CNF constraints is still lacking. In addition, previous work indicated that for specific classes of benchmarks, the running time of extant SAT solvers depends heavily on properties of the formula and details of encoding, instead of the scale of the benchmarks, which adds uncertainty to expectations of running time.To address the issues above, we design FourierSAT, an incomplete SAT solver based on Fourier analysis of Boolean functions, a technique to represent Boolean functions by multilinear polynomials. By such a reduction to continuous optimization, we propose an algebraic framework for solving systems consisting of different types of constraints. The idea is to leverage gradient information to guide the search process in the direction of local improvements. Empirical results demonstrate that FourierSAT is more robust than other solvers on certain classes of benchmarks.

scholarly journals Framework for Generating Configurable SAT Solvers

2011 ◽  
Vol 6 (1) ◽  
pp. 50-59
Author(s):  
Bernardo C. Vieira ◽  
Fabrício V. Andrade ◽  
Antônio O. Fernandes
Keyword(s):  
State Of The Art ◽  
The State ◽  
Equivalence Checking ◽  
Decision Heuristics ◽  
Sat Solvers ◽  
The Third ◽  
Sat Solver ◽  
Run Time

The state-of-the-art SAT solvers usually share the same core techniques, for instance: the watched literals structure, conflict clause recording and non-chronological backtracking. Nevertheless, they might differ in the elimination of learnt clauses, as well as in the decision heuristic. This article presents a framework for generating configurable SAT solvers. The proposed framework is composed of the following components: a Base SAT Solver, a Perl Preprocessor, XML files (Solver Description and Heuristics Description files) to describe each heuristic as well as the set of heuristics that the generated solver uses. This solvers may use several techniques and heuristics such as those implemented in BerkMin, and in Equivalence Checking of Dissimilar Circuits, and also in Minisat. In order to demonstrate the effectiveness of the proposed framework, this article also presents three distinct SAT solver instances generated by the framework to address a complex and challenging industry problem: the Combinational Equivalence Checking problem (CEC).The first instance is a SAT solver that uses BerkMin and Dissimilar Circuits core techniques except the learnt clause elimination heuristic that has been adapted from Minisat; the second is another solver that combines BerkMin and Minisat decision heuristics at run-time; and the third is yet another SAT solver that changes the database reducing heuristic at run-time. The experiments demonstrate that the first SAT solver generated is a faster solver than state-of-the-art SAT solver BerkMin for several instances as well as for Minisat in almost every instance.

scholarly journals Exploring Practicability for Solving a Task Based on the Generalized Cellular Automata via SAT Solvers

2019 ◽  
pp. 11-22
Author(s):  
P. G. Klyucharev
Keyword(s):  
Positive Integer ◽  
Cellular Automata ◽  
Operation Time ◽  
Computational Experiments ◽  
Key Recovery ◽  
Sat Solvers ◽  
Initial Values ◽  
Sat Solver ◽  
Key Length ◽  
Exhaustive Method

The paper deals with exploring practicability to solve a task of the recovery key of generalized cellular automata via SAT solvers.The problem, which we call a task of the key recovery of generalized cellular automata, is under consideration. This task is formulated as follows. The generalized cellular automata, the positive integer s, the initial values of some cells, and the values of some cells after the s steps of the automata are given. It is required to find the initial values of the remaining cells (their number will be called the key length).To solve the task, were tested Picosat, MiniSat, Glucose, Lingeling, and CryptoMiniSat SAT solvers. In further computational experiments, was used the MiniSat, which was the best.The key recovery task was solved for the generalized cellular automata of a small size via the MiniSat SAT solver. Pizer's graphs were used as graphs of the automata. The key length was approximately half the number of the cells in the automata. As a result of the study, it turned out that operation time of a SAT solver quite significantly (several orders of magnitude) exceeds the estimated time of solution using the FPGA exhaustive method, and the empirical dependencies of the SAT-solver operation time on the key length are exponential.The obtained results confirm that SAT solvers disable effective solving a task under consideration. This allows giving the better reasons for the cryptographic security of the crypto-algorithms based on the generalized cellular automata with regard to the cryptanalysis methods using SAT solvers.

scholarly journals Towards Improving the Resource Usage of SAT-solvers

10.29007/3vwv ◽  
2018 ◽  
Author(s):  
Norbert Manthey ◽  
Ari Saptawijaya
Keyword(s):  
Data Structures ◽  
Memory Access ◽  
Resource Usage ◽  
Sat Solving ◽  
Sat Solvers ◽  
L2 Cache ◽  
Measurement Results ◽  
Sat Solver ◽  
Cache Analysis ◽  
Runtime Performance

The paper presents our work on cache analysis of SAT-solving. The aim is to study how resources are utilized by a SAT-solver and to use this knowledge to improve the resource usage in SAT-solving. The analysis is performed mainly on our CDCL-based SAT-solver and additionally on MiniSAT and PrecoSAT. The measurement is conducted using sample-based profiling on some industrial benchmark from the SAT-competition 2009. During the measurement the following hardware events are traced: total cycles, stall cycles, L2 cache hits and L2 cache misses. From the measurement results, our runtime and implementation analysis unveil that several improvements on resource usage can be done, i.e. on data structures and memory access. These improvements bring about 60% speedup of runtime performance for our solver.

scholarly journals Tuning Parallel SAT Solvers

10.29007/z3g2 ◽  
2019 ◽  
Author(s):  
Thorsten Ehlers ◽  
Dirk Nowotka
Keyword(s):  
Model Checking ◽  
Database Management ◽  
Bounded Model Checking ◽  
Experimental Results ◽  
Massively Parallel ◽  
Sat Solving ◽  
Sat Solvers ◽  
Sat Solver ◽  
The Impact

In this paper we present new implementation details and benchmarking results for our parallel portfolio solver TopoSAT2. In particular, we discuss ideas and implementation details for the exchange of learned clauses in a massively-parallel SAT solver which is designed to run more that 1, 000 solver threads in parallel. Furthermore, we go back to the roots of portfolio SAT solving, and discuss the impact of diversifying the solver by using different restart- , branching- and clause database management heuristics. We show that these techniques can be used to tune the solver towards different problems. However, in a case study on formulas derived from Bounded Model Checking problems we see the best performance when using a rather simple clause exchange strategy. We show details of these tests and discuss possible explanations for this phenomenon.As computing times on massively-parallel clusters are expensive, we consider it especially interesting to share these kind of experimental results.

Sign in / Sign up

Export Citation Format

Share Document