SAT and Planning

2010 ◽  
pp. 27-40
Author(s):  
Carlos Camarão ◽  
Mateus Galvão ◽  
Newton Vieira
Keyword(s):  
Operation Management ◽  
Significant Problem ◽  
Satisfiability Problem ◽  
Sat Solvers ◽  
Wide Range ◽  
Blocks World

This chapter firstly reviews the importance of the Satisfiability Problem (SAT) for a wide range of applications, including applications in Operation Management such as planning. A review of methods nowadays employed by modern SAT-solvers is then presented. The authors then use Classical Planning as an illustrative example of how a significant problem can be translated into SAT. They point out important results and studies concerning reductions of planning into SAT, and explain how to construct a SAT instance which is satisfiable if and only if an instance of a bounded version of the classic blocks-world problem is solvable.

scholarly journals Seeking Practical CDCL Insights from Theoretical SAT Benchmarks

2018 ◽  
Author(s):  
Jan Elffers ◽  
Jesús Giráldez-Cru ◽  
Stephan Gocht ◽  
Jakob Nordström ◽  
Laurent Simon
Keyword(s):  
Systematic Study ◽  
Boolean Satisfiability ◽  
Proof System ◽  
Sat Solvers ◽  
Proof Search ◽  
Wide Range ◽  
Clause Learning ◽  
Resolution Proof ◽  
Shed Light

Over the last decades Boolean satisfiability (SAT) solvers based on conflict-driven clause learning (CDCL) have developed to the point where they can handle formulas with millions of variables. Yet a deeper understanding of how these solvers can be so successful has remained elusive. In this work we shed light on CDCL performance by using theoretical benchmarks, which have the attractive features of being a) scalable, b) extremal with respect to different proof search parameters, and c) theoretically easy in the sense of having short proofs in the resolution proof system underlying CDCL. This allows for a systematic study of solver heuristics and how efficiently they search for proofs. We report results from extensive experiments on a wide range of benchmarks. Our findings include several examples where theory predicts and explains CDCL behaviour, but also raise a number of intriguing questions for further study.

scholarly journals A Theory of Satisfiability-Preserving Proofs in SAT Solving

10.29007/tc7q ◽  
2018 ◽  
Author(s):  
Adrián Rebola-Pardo ◽  
Martin Suda
Keyword(s):  
Propositional Logic ◽  
Logical Truth ◽  
Point Of View ◽  
Traditional View ◽  
Satisfiability Problem ◽  
Sat Solving ◽  
Sat Solvers ◽  
Proof Systems ◽  
Meta Level

We study the semantics of propositional interference-based proof systems such as DRAT and DPR. These are characterized by modifying a CNF formula in ways that preserve satisfiability but not necessarily logical truth. We propose an extension of propositional logic called overwrite logic with a new construct which captures the meta-level reasoning behind interferences. We analyze this new logic from the point of view of expressivity and complexity, showing that while greater expressivity is achieved, the satisfiability problem for overwrite logic is essentially as hard as SAT, and can be reduced in a way that is well-behaved for modern SAT solvers. We also show that DRAT and DPR proofs can be seen as overwrite logic proofs which preserve logical truth. This much stronger invariant than the mere satisfiability preservation maintained by the traditional view gives us better understanding on these practically important proof systems. Finally, we showcase this better understanding by finding intrinsic limitations in interference-based proof systems.

HYBRID INCREMENTAL ALGORITHMS FOR BOOLEAN SATISFIABILITY

2012 ◽  
Vol 21 (06) ◽  
pp. 1250025 ◽  
Author(s):  
FLORIAN LETOMBE ◽  
JOAO MARQUES-SILVA
Keyword(s):  
Boolean Satisfiability ◽  
Equivalence Checking ◽  
Satisfiability Modulo Theory ◽  
Practical Applications ◽  
Sat Solvers ◽  
Hybrid Approaches ◽  
Software Model ◽  
Wide Range ◽  
Model Finding ◽  
Problem Instances

Boolean Satisfiability (SAT) solvers have been successfully applied to a wide range of practical applications, including hardware model checking, software model finding, equivalence checking, and planning, among many others. SAT solvers are also the building block of more sophisticated decision procedures, including Satisfiability Modulo Theory (SMT) solvers. The large number of applications of SAT yields ever more challenging problem instances, and motivate the development of more efficient algorithms. Recent work studied hybrid approaches for SAT, which involves integrating incomplete and complete SAT solvers. This paper proposes a number of improvements to hybrid SAT solvers. Experimental results demonstrate that the proposed optimizations are effective. The resulting algorithms in general perform better and, more importantly, are significantly more robust.

scholarly journals Problems of search for collisions of cryptographic hash functions of the MD family as variants of Boolean satisfiability problem

2015 ◽  
pp. 61-77
Author(s):  
И.А. Богачкова ◽  
О.С. Заикин ◽  
С.Е. Кочемазов ◽  
И.В. Отпущенников ◽  
А.А. Семенов ◽  
...  
Keyword(s):  
Numerical Experiments ◽  
Hash Functions ◽  
Boolean Satisfiability ◽  
Satisfiability Problem ◽  
Sat Solvers ◽  
Boolean Satisfiability Problem ◽  
Single Block ◽  
Message Digest ◽  
Differential Attacks ◽  
Cryptographic Hash Functions

Рассмотрена реализация разностной атаки на криптографические хеш-функции MD4 (Message Digest 4) и MD5 (Message Digest 5) через сведение задачи поиска коллизий для этих хеш-функций к задаче о булевой выполнимости (SAT, SATisfiability). Новизна полученных результатов заключается в том, что предложены существенно более экономные (в сравнении с известными) SAT-кодировки рассматриваемых алгоритмов, а также в использовании для решения полученных SAT-задач современных многопоточных и параллельных SAT-решателей. Задачи поиска одноблоковых коллизий для MD4 в данной постановке оказались чрезвычайно простыми. Кроме того, найдены несколько десятков двухблоковых коллизий для MD5. В процессе соответствующих вычислительных экспериментов определен некоторый класс сообщений, дающих коллизии: построено множество пар дающих коллизии сообщений, у которых первые 10 байтов нулевые. An implementation of the differential attacks on cryptographic hash functions MD4 (Message Digest 4) and MD5 (Message Digest 5) by reducing the problems of search for collisions of these hash functions to the Boolean satisfiability problem (SAT) is considered. The novelty of the results obtained consists in a more compact (compared to already known) SAT encodings for the algorithms considered and in the use of modern parallel and distributed SAT solvers in applications to the formulated SAT problems. Searching for single block collisions of MD4 in this approach turned out to be very simple. In addition, several dozens of double block collisions of MD5 are found. In the process of the corresponding numerical experiments, a certain class of messages that produce the collisions is found: in particular, a set of pairs of such messages with first 10 zero bytes is constructed.

scholarly journals Divide and Conquer: Towards Faster Pseudo-Boolean Solving

2018 ◽  
Author(s):  
Jan Elffers ◽  
Jakob Nordström
Keyword(s):  
Boolean Satisfiability ◽  
Conflict Analysis ◽  
Divide And Conquer ◽  
Theoretical Strength ◽  
Integer Coefficient ◽  
Sat Solvers ◽  
Wide Range ◽  
Clause Learning

The last 20 years have seen dramatic improvements in the performance of algorithms for Boolean satisfiability---so-called SAT solvers---and today conflict-driven clause learning (CDCL) solvers are routinely used in a wide range of application areas. One serious short-coming of CDCL, however, is that the underlying method of reasoning is quite weak. A tantalizing solution is to instead use stronger pseudo-Boolean (PB) reasoning, but so far the promise of exponential gains in performance has failed to materialize---the increased theoretical strength seems hard to harness algorithmically, and in many applications CDCL-based methods are still superior. We propose a modified approach to pseudo-Boolean solving based on division instead of the saturation rule used in [Chai and Kuehlmann '05] and other PB solvers. In addition to resulting in a stronger conflict analysis, this also improves performance by keeping integer coefficient sizes down, and yields a very competitive solver as shown by the results in the Pseudo-Boolean Competitions 2015 and 2016.

Symmetric Neural Networks and Propositional Logic Satisfiability

1991 ◽  
Vol 3 (2) ◽  
pp. 282-291 ◽  
Author(s):  
Gadi Pinkas
Keyword(s):  
Energy Function ◽  
Quadratic Function ◽  
Nonmonotonic Reasoning ◽  
Propositional Calculus ◽  
High Order ◽  
Satisfiability Problem ◽  
Problem Solver ◽  
Energy Functions ◽  
Connectionist Network ◽  
Wide Range

Connectionist networks with symmetric weights (like Hopfield networks and Boltzmann Machines) use gradient descent to find a minimum for quadratic energy functions. We show equivalence between the problem of satisfiability in propositional calculus and the problem of minimizing those energy functions. The equivalence is in the sense that for any satisfiable well-formed formula (WFF) we can find a quadratic function that describes it, such that the set of solutions that minimizes the function is equal to the set of truth assignments that satisfy the WFF. We also show that in the same sense every quadratic energy function describes some satisfiable WFF. Algorithms are given to transform any propositional WFF into an energy function that describes it and vice versa. High-order models that use sigma-pi units are shown to be equivalent to the standard quadratic models with additional hidden units. An algorithm to convert high-order networks to low-order ones is used to implement a satisfiability problem-solver on a connectionist network. The results give better understanding of the role of hidden units and of the limitations and capabilities of symmetric connectionist models. The techniques developed for the satisfiability problem may be applied to a wide range of other problems, such as associative memories, finding maximal consistent subsets, automatic deduction, and even nonmonotonic reasoning.

scholarly journals Relaxed Survey Propagation for The Weighted Maximum Satisfiability Problem

2009 ◽  
Vol 36 ◽  
pp. 229-266 ◽  
Author(s):  
H.L. Chieu ◽  
W.S. Lee
Keyword(s):  
Phase Transition ◽  
State Of The Art ◽  
Satisfiability Problem ◽  
Maximum Satisfiability ◽  
Sat Problem ◽  
Sat Solvers ◽  
Minimal Weight ◽  
Survey Propagation ◽  
Max Sat

The survey propagation (SP) algorithm has been shown to work well on large instances of the random 3-SAT problem near its phase transition. It was shown that SP estimates marginals over covers that represent clusters of solutions. The SP-y algorithm generalizes SP to work on the maximum satisfiability (Max-SAT) problem, but the cover interpretation of SP does not generalize to SP-y. In this paper, we formulate the relaxed survey propagation (RSP) algorithm, which extends the SP algorithm to apply to the weighted Max-SAT problem. We show that RSP has an interpretation of estimating marginals over covers violating a set of clauses with minimal weight. This naturally generalizes the cover interpretation of SP. Empirically, we show that RSP outperforms SP-y and other state-of-the-art Max-SAT solvers on random Max-SAT instances. RSP also outperforms state-of-the-art weighted Max-SAT solvers on random weighted Max-SAT instances.

scholarly journals The Hard Problems Are Almost Everywhere For Random CNF-XOR Formulas

2017 ◽  
Author(s):  
Jeffrey M. Dudek ◽  
Kuldeep S. Meel ◽  
Moshe Y. Vardi
Keyword(s):  
State Of The Art ◽  
Solution Space ◽  
Sat Solvers ◽  
Universal Hashing ◽  
Almost Everywhere ◽  
Wide Range ◽  
Sat Solver ◽  
Hard Problems ◽  
Transition Location ◽  
Cnf Formulas

Recent universal-hashing based approaches to sampling and counting crucially depend on the runtime performance of SAT solvers on formulas expressed as the conjunction of both CNF constraints and variable-width XOR constraints (known as CNF-XOR formulas). In this paper, we present the first study of the runtime behavior of SAT solvers equipped with XOR-reasoning techniques on random CNF-XOR formulas. We empirically demonstrate that a state-of-the-art SAT solver scales exponentially on random CNF-XOR formulas across a wide range of XOR-clause densities, peaking around the empirical phase-transition location. On the theoretical front, we prove that the solution space of a random CNF-XOR formula 'shatters' at all nonzero XOR-clause densities into well-separated components, similar to the behavior seen in random CNF formulas known to be difficult for many SAT algorithms.

scholarly journals Analysis of comparative effectiveness of state-of-the-art heuristics for CDCL SAT solvers

2021 ◽  
Author(s):  
S. Kochemazov
Keyword(s):  
Comparative Effectiveness ◽  
Major Part ◽  
State Of The Art ◽  
Learning Algorithms ◽  
Boolean Satisfiability ◽  
Satisfiability Problem ◽  
Sat Solvers ◽  
Boolean Satisfiability Problem ◽  
Clause Learning ◽  
Good For

The Conflict-Driven Clause Learning algorithms for solving the Boolean satisfiability problem comprise the major part of the methods used to solve various instances of the problems that arise in industry and science. In recent years there have been proposed several major heuristics for these algorithms which are assumed to be de facto good for the solvers’ performance over diverse sets of benchmarks. The goal of this paper is to evaluate the contribution of each separate heuristic to the performance of a state-of-the-art solver, see the extent to which they are beneficial, and figure out if the heuristics have any particular features that need to be taken into account.

scholarly journals Traffic State Detection Based on Multidimensional Data Fusion System of Internet of Things

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Jinxi Zhang ◽  
Wenying Zhu ◽  
Xueying Wu ◽  
Tianshan Ma
Keyword(s):  
Internet Of Things ◽  
Data Fusion ◽  
Traffic Management ◽  
Mobile Internet ◽  
Operation Management ◽  
Multidimensional Data ◽  
Fusion System ◽  
Management Platform ◽  
Wide Range ◽  
Internet Of Things Technology

In recent years, the rapid development of cloud computing, mobile Internet, Internet of Things, and other technologies has accelerated the explosive growth of the number and types of data in various industries. As one of the current hot research fields, the multidimensional data fusion system has received widespread attention all over the world. Road traffic and traffic management involve a wide range of participants; a variety of traffic behavior and traffic management means have produced a huge volume of traffic management data and have a very high application value. Therefore, it is of great significance to study the application mode of the traffic management multidimensional data fusion system and realize the asset value transformation of the multidimensional data fusion system. Starting from the safety supervision service of operating vehicles, this paper elaborates the traffic management multidimensional data fusion system platform for the safety supervision service of operating vehicles around the application requirements and architecture of the traffic management multidimensional data fusion system and the results of this research team. Paper with city comprehensive transport hub as the research object uses the Internet of Things technology; establishes a set of BIM model-based intelligent Internet operation management platform, multidimensional collection personnel, and vehicles, such as traffic, equipment, and business data information; realizes the integration of data, correlation, and instructions issued by ability, to support the building intelligence operation management needs of the business; and realizes traffic and transportation status detection.

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