PaInleSS: A Framework for Parallel SAT Solving

2017 ◽  
pp. 233-250 ◽  
Author(s):  
Ludovic Le Frioux ◽  
Souheib Baarir ◽  
Julien Sopena ◽  
Fabrice Kordon
Keyword(s):  
Sat Solving

SAT-solving in practice

2008 ◽  
Author(s):  
Koen Claessen ◽  
Niklas Een ◽  
Mary Sheeran ◽  
Niklas Sorensson
Keyword(s):  
Sat Solving

scholarly journals Automated Workarounds from Java Program Specifications Based on SAT Solving

2017 ◽  
pp. 356-373
Author(s):  
Marcelo Uva ◽  
Pablo Ponzio ◽  
Germán Regis ◽  
Nazareno Aguirre ◽  
Marcelo F. Frias
Keyword(s):  
Sat Solving ◽  
Java Program

On the Usefulness of Clause Strengthening in Parallel SAT Solving

2020 ◽  
pp. 222-229
Author(s):  
Vincent Vallade ◽  
Ludovic Le Frioux ◽  
Souheib Baarir ◽  
Julien Sopena ◽  
Fabrice Kordon
Keyword(s):  
Sat Solving

scholarly journals From Parallel SAT to Distributed SAT

10.29007/44vf ◽  
2018 ◽  
Author(s):  
Youssef Hamadi
Keyword(s):  
Divide And Conquer ◽  
Communication Overhead ◽  
Sat Solving ◽  
The Impact

This tutorial will present an overview of parallelism in SAT. It will start with a presentation of classical divide and conquer techniques, discuss their ancient origin and compare them to more recent portfolio- based algorithms. It will then present the impact of clause-sharing on their performances and discuss various strategies used to control the communication overhead. A particular technique used to control the classical diversification/intensification tradeoff will also be presented. Finally, perspectives will be given which will relate the current parallel SAT technologies to the expected evolution of computational platforms, leading to distributed SAT solving scenarios.

scholarly journals Hybrid of Hill Climbing and SAT Solving for Air Traffic Controller Shift Scheduling

2016 ◽  
Vol 10 (2) ◽  
Author(s):  
Mirko Stojadinović
Keyword(s):  
Heuristic Method ◽  
Optimal Solution ◽  
Air Traffic ◽  
Hill Climbing ◽  
Hybrid Technique ◽  
Sat Solving ◽  
Shift Scheduling ◽  
Exact Methods ◽  
Air Traffic Controller ◽  
Three Phases

Modern computers solve many problems by using exact methods, heuristic methods and very often by using their combination. Air Traffic Controller Shift Scheduling Problem has been successfully solved by using SAT technology (reduction to logical formulas) and several models of the problem exist. We present a technique for solving this problem that is a combination of SAT solving and meta-heuristic method hill climbing, and consists of three phases. First, SAT solver is used to generate feasible solution. Then, the hill climbing is used to improve this solution, in terms of number of satisfied wishes of controllers. Finally, SAT solving is used to further improve the found solution by fixing some parts of the solution. Three phases are repeated until optimal solution is found. Usage of exact method (SAT solving) guarantees that the found solution is optimal; usage of meta-heuristic (hill climbing) increases the efficiency in finding good solutions. By using these essentially different ways of solving, we aim to use the best from both worlds. Results indicate that this hybrid technique outperforms previously most efficient developed techniques.

scholarly journals On Division Versus Saturation in Pseudo-Boolean Solving

2019 ◽  
Author(s):  
Stephan Gocht ◽  
Jakob Nordström ◽  
Amir Yehudayoff
Keyword(s):  
Linear Programming ◽  
Cutting Planes ◽  
The Other ◽  
Sat Solving ◽  
Linear Combinations ◽  
Division Rule ◽  
Clause Learning

The conflict-driven clause learning (CDCL) paradigm has revolutionized SAT solving over the last two decades. Extending this approach to pseudo-Boolean (PB) solvers doing 0-1 linear programming holds the promise of further exponential improvements in theory, but intriguingly such gains have not materialized in practice. Also intriguingly, most PB extensions of CDCL use not the division rule in cutting planes as defined in [Cook et al., '87] but instead the so-called saturation rule. To the best of our knowledge, there has been no study comparing the strengths of division and saturation in the context of conflict-driven PB learning, when all linear combinations of inequalities are required to cancel variables. We show that PB solvers with division instead of saturation can be exponentially stronger. In the other direction, we prove that simulating a single saturation step can require an exponential number of divisions. We also perform some experiments to see whether these phenomena can be observed in actual solvers. Our conclusion is that a careful combination of division and saturation seems to be crucial to harness more of the power of cutting planes.

scholarly journals Results on a Super Strong Exponential Time Hypothesis

2020 ◽  
Vol 34 (09) ◽  
pp. 13700-13703
Author(s):  
Nikhil Vyas ◽  
Ryan Williams
Keyword(s):  
Randomized Algorithm ◽  
Time Algorithm ◽  
Critical Threshold ◽  
Polynomial Method ◽  
Variable Ratio ◽  
Sat Solving ◽  
Worst Case ◽  
Exponential Time ◽  
Exponential Time Hypothesis ◽  
Special Case

All known SAT-solving paradigms (backtracking, local search, and the polynomial method) only yield a 2n(1−1/O(k)) time algorithm for solving k-SAT in the worst case, where the big-O constant is independent of k. For this reason, it has been hypothesized that k-SAT cannot be solved in worst-case 2n(1−f(k)/k) time, for any unbounded ƒ : ℕ → ℕ. This hypothesis has been called the “Super-Strong Exponential Time Hypothesis” (Super Strong ETH), modeled after the ETH and the Strong ETH. We prove two results concerning the Super-Strong ETH:1. It has also been hypothesized that k-SAT is hard to solve for randomly chosen instances near the “critical threshold”, where the clause-to-variable ratio is 2k ln 2 −Θ(1). We give a randomized algorithm which refutes the Super-Strong ETH for the case of random k-SAT and planted k-SAT for any clause-to-variable ratio. In particular, given any random k-SAT instance F with n variables and m clauses, our algorithm decides satisfiability for F in 2n(1−Ω( log k)/k) time, with high probability (over the choice of the formula and the randomness of the algorithm). It turns out that a well-known algorithm from the literature on SAT algorithms does the job: the PPZ algorithm of Paturi, Pudlak, and Zane (1998).2. The Unique k-SAT problem is the special case where there is at most one satisfying assignment. It is natural to hypothesize that the worst-case (exponential-time) complexity of Unique k-SAT is substantially less than that of k-SAT. Improving prior reductions, we show the time complexities of Unique k-SAT and k-SAT are very tightly related: if Unique k-SAT is in 2n(1−f(k)/k) time for an unbounded f, then k-SAT is in 2n(1−f(k)(1−ɛ)/k) time for every ɛ > 0. Thus, refuting Super Strong ETH in the unique solution case would refute Super Strong ETH in general.

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.

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