scholarly journals Backjumping is Exception Handling

2020 ◽  
pp. 1-20
Author(s):  
ED ROBBINS ◽  
ANDY KING ◽  
JACOB M. HOWE
Keyword(s):  
Graph Coloring ◽  
Exception Handling ◽  
Control Flow ◽  
Specific Point ◽  
Clause Learning ◽  
Sat Solver

Abstract ISO Prolog provides catch and throw to realize the control flow of exception handling. This pearl demonstrates that catch and throw are inconspicuously amenable to the implementation of backjumping. In fact, they have precisely the semantics required: rewinding the search to a specific point and carrying of a preserved term to that point. The utility of these properties is demonstrated through an implementation of graph coloring with backjumping and a backjumping SAT solver that applies conflict-driven clause learning.

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 Post Mortem Analysis of SAT Solver Proofs

10.29007/gpp8 ◽  
2018 ◽  
Author(s):  
Laurent Simon
Keyword(s):  
Complex Systems ◽  
Learning Algorithms ◽  
Point Of View ◽  
Post Mortem ◽  
Learning Mechanism ◽  
Clause Learning ◽  
Sat Solver ◽  
Resolution Proofs ◽  
Final Proof

Conflict-Driven Clause Learning algorithms are well known from an engineerpoint of view. Thanks to Minisat, their designs are well understood, and mostof their implementations follow the same ideas, with essentially the samecomponents. Same heuristics, fast restarts, same learning mechanism.However, their efficiency has an important drawback: they are more and morelike complex systems and harder and harder to handle. Unfortunately, only afew works are focusing on understanding them rather than improving them. Inmost of the cases, their studies are often based on a generate and testpattern: An idea is added to an existing solver and if it improves itsefficiency the idea is published and kept. In this paper, we analyse``post-mortem'' the proofs given by one typical CDCL solver,Glucose. The originality of our approach is that we only consider it as aresolution proofs builder, and then we analyze some of the proofcharacteristics on a set of selected unsatisfiable instances, by shuffling each ofthem 200 times. We particularly focus on trying to characterize useless anduseful clauses in the proof as well as proofs shapes. We also show thatdespite their incredible efficiency, roughly 90% of the time spent in aCDCL is useless for producing the final proof.

A REUSE-ORIENTED WORKFLOW DEFINITION LANGUAGE

2003 ◽  
Vol 12 (01) ◽  
pp. 1-36 ◽  
Author(s):  
MARIE JOSÉ BLIN ◽  
JACQUES WAINER ◽  
CLAUDIA BAUZER MEDEIROS
Keyword(s):  
Programming Languages ◽  
Building Blocks ◽  
Database Systems ◽  
Exception Handling ◽  
Control Flow ◽  
New Formalism ◽  
Definition Of ◽  
High Level ◽  
And Control ◽  
High Degree

This paper presents a new formalism for workflow process definition, which combines research in programming languages and in database systems. This formalism is based on creating a library of workflow building blocks, which can be progressively combined and nested to construct complex workflows. Workflows are specified declaratively, using a simple high level language, which allows the dynamic definition of exception handling and events, as well as dynamically overriding workflow definition. This ensures a high degree of flexibility in data and control flow specification, as well as in reuse of workflow specifications to construct other workflows. The resulting workflow execution environment is well suited to supporting cooperative work.

scholarly journals A Verified SAT Solver Framework including Optimization and Partial Valuations

10.29007/96wb ◽  
2020 ◽  
Author(s):  
Mathias Fleury ◽  
Christoph Weidenbach
Keyword(s):  
Branch And Bound ◽  
Proof Assistant ◽  
Minimal Cost ◽  
Minimal Models ◽  
Total Cost ◽  
Formal Framework ◽  
Clause Learning ◽  
Sat Solver ◽  
Max Sat

Based on our formal framework for CDCL (conflict-driven clause learning) using the proof assistant Isabelle/HOL, we verify an extension of CDCL computing cost-minimal models called OCDCL. It is based on branch and bound and computes models of minimal cost with respect to total valuations. The verification starts by developing a framework for CDCL with branch and bound, called CDCLBnB, which is then instantiated to get OCDCL. We then apply our formalization to three different applications. Firstly, through the dual rail encoding, we reduce the search for cost-optimal models with respect to partial valuations to searching for total cost-optimal models, as derived by OCDCL. Secondly, we instantiate OCDCL to solve MAX-SAT, and, thirdly, CDCLBnB to compute a set of covering models. A large part of the original CDCL verification framework was reused without changes to reduce the complexity of the new formalization. To the best of our knowledge, this is the first rigorous formalization of CDCL with branch and bound and its application to an optimizing CDCL calculus, and the first solution that computes cost-optimal models with respect to partial valuations.

scholarly journals Duplicates of conflict clauses in CDCL derivation and their usage to invert some cryptographic functions

2019 ◽  
pp. 54-66
Author(s):  
В.С. Кондратьев ◽  
А.А. Семенов ◽  
О.С. Заикин
Keyword(s):  
Hash Functions ◽  
Boolean Satisfiability ◽  
Experimental Results ◽  
Sat Solving ◽  
New Approach ◽  
Sat Solvers ◽  
Satisfiability Problems ◽  
Clause Learning ◽  
Sat Solver ◽  
Cryptographic Hash Functions

Изучен феномен повторного порождения конфликтных ограничений SAT-решателями в процессе работы с трудными экземплярами задачи о булевой выполнимости. Данный феномен является следствием применения эвристических механизмов чистки конфликтных баз, которые реализованы во всех современных SAT-решателях, основанных на алгоритме CDCL (Conflict Driven Clause Learning). Описана новая техника, которая позволяет отслеживать повторно порождаемые дизъюнкты и запрещать их последующее удаление. На базе предложенных технических решений построен новый многопоточный SAT-решатель (SAT, SATisfiability), который на ряде SAT-задач, кодирующих обращение криптографических хеш-функций, существенно превзошел по эффективности многопоточные решатели, занимавшие в последние годы высокие места на специализированных соревнованиях. A phenomenon of conflict clauses generated repeatedly by SAT solvers is studied. Such clauses may appear during solving hard Boolean satisfiability problems (SAT). This phenomenon is caused by the fact that the modern SAT solvers are based on the CDCL algorithm that generates conflict clauses. A database of such clauses is periodically and partially cleaned. A new approach for practical SAT solving is proposed. According to this approach, the repeatedly generated conflict clauses are tracked, whereas their further generation is prohibited. Based on this approach, a multithreaded SAT solver was developed. This solver was compared with the best multithreaded SAT solvers awarded during the last SAT competitions. According to the experimental results, the developed solver greatly outperforms its competitors on several SAT instances encoding the inversion of some cryptographic hash functions.

scholarly journals A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality

2017 ◽  
Author(s):  
Jasmin Christian Blanchette ◽  
Mathias Fleury ◽  
Christoph Weidenbach
Keyword(s):  
Proof Assistant ◽  
Sat Solving ◽  
Formal Framework ◽  
Clause Learning ◽  
Sat Solver ◽  
A Chain

We developed a formal framework for SAT solving using the Isabelle/HOL proof assistant. Through a chain of refinements, an abstract CDCL (conflict-driven clause learning) calculus is connected to a SAT solver that always terminates with correct answers. The framework offers a convenient way to prove theorems about the SAT solver and experiment with variants of the calculus. Compared with earlier verifications, the main novelties are the inclusion of the CDCL rules for forget, restart, and incremental solving and the use of refinement.

LEARNING FROM SUCCESSES

2010 ◽  
Vol 19 (04) ◽  
pp. 373-391
Author(s):  
SAÏD JABBOUR
Keyword(s):  
State Of The Art ◽  
Conflict Analysis ◽  
Experimental Results ◽  
Traditional Learning ◽  
Learning Approaches ◽  
Learning Scheme ◽  
New Learning ◽  
Clause Learning ◽  
Sat Solver

In this paper a new learning scheme for SAT is proposed. The originality of our approach arises from its ability to achieve clause learning even if no conflict occurs. This kind of learning from successes clearly contrasts with all the traditional learning approaches which generally refer to conflict analysis. To make such learning possible, relevant clauses, taken from the satisfied part of the formula are conjointly used with the classical implication graph to derive new and more powerful reasons for the implication of a given literal. Based on this extension a first learning scheme called Learning for Dynamic Assignments Reordering (LDAR) is proposed. It exploits the new derived reasons to dynamically reorder partial assignments. Experimental results show that the integration of LDAR within a state-of-the-art SAT solver achieves interesting improvements particularly on satisfiable instances.

scholarly journals Practical Aspects of SAT Solving

10.29007/hnks ◽  
2018 ◽  
Author(s):  
Armin Biere
Keyword(s):  
Automated Reasoning ◽  
Sat Solving ◽  
Current Trends ◽  
Recent Developments ◽  
Clause Learning ◽  
Sat Solver

SAT solving techniques are used in many automated reasoning engines. This talk gives an overview on recent developments in practical aspects of SAT solver development. Beside improvements of the basic conflict driven clause learning (CDCL) algorithm, we also discuss improving and integrating advanced preprocessing techniques as inprocessing during search. The talk concludes with a brief overview on current trends in parallelizing SAT.

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