368 research outputs found
Recognition and Exploitation of Gate Structure in SAT Solving
In der theoretischen Informatik ist das SAT-Problem der archetypische Vertreter der Klasse der NP-vollständigen Probleme, weshalb effizientes SAT-Solving im Allgemeinen als unmöglich angesehen wird.
Dennoch erzielt man in der Praxis oft erstaunliche Resultate, wo einige Anwendungen Probleme mit Millionen von Variablen erzeugen, die von neueren SAT-Solvern in angemessener Zeit gelöst werden können.
Der Erfolg von SAT-Solving in der Praxis ist auf aktuelle Implementierungen des Conflict Driven Clause-Learning (CDCL) Algorithmus zurückzuführen, dessen Leistungsfähigkeit weitgehend von den verwendeten Heuristiken abhängt, welche implizit die Struktur der in der industriellen Praxis erzeugten Instanzen ausnutzen.
In dieser Arbeit stellen wir einen neuen generischen Algorithmus zur effizienten Erkennung der Gate-Struktur in CNF-Encodings von SAT Instanzen vor, und außerdem drei Ansätze, in denen wir diese Struktur explizit ausnutzen.
Unsere Beiträge umfassen auch die Implementierung dieser Ansätze in unserem SAT-Solver Candy und die Entwicklung eines Werkzeugs für die verteilte Verwaltung von Benchmark-Instanzen und deren Attribute, der Global Benchmark Database (GBD)
Incremental Cardinality Constraints for MaxSAT
Maximum Satisfiability (MaxSAT) is an optimization variant of the Boolean
Satisfiability (SAT) problem. In general, MaxSAT algorithms perform a
succession of SAT solver calls to reach an optimum solution making extensive
use of cardinality constraints. Many of these algorithms are non-incremental in
nature, i.e. at each iteration the formula is rebuilt and no knowledge is
reused from one iteration to another. In this paper, we exploit the knowledge
acquired across iterations using novel schemes to use cardinality constraints
in an incremental fashion. We integrate these schemes with several MaxSAT
algorithms. Our experimental results show a significant performance boost for
these algo- rithms as compared to their non-incremental counterparts. These
results suggest that incremental cardinality constraints could be beneficial
for other constraint solving domains.Comment: 18 pages, 4 figures, 1 table. Final version published in Principles
and Practice of Constraint Programming (CP) 201
On Continuous Local BDD-Based Search for Hybrid SAT Solving
We explore the potential of continuous local search (CLS) in SAT solving by
proposing a novel approach for finding a solution of a hybrid system of Boolean
constraints. The algorithm is based on CLS combined with belief propagation on
binary decision diagrams (BDDs). Our framework accepts all Boolean constraints
that admit compact BDDs, including symmetric Boolean constraints and
small-coefficient pseudo-Boolean constraints as interesting families. We
propose a novel algorithm for efficiently computing the gradient needed by CLS.
We study the capabilities and limitations of our versatile CLS solver, GradSAT,
by applying it on many benchmark instances. The experimental results indicate
that GradSAT can be a useful addition to the portfolio of existing SAT and
MaxSAT solvers for solving Boolean satisfiability and optimization problems.Comment: AAAI 2
SAT-based approaches for constraint optimization
La optimització amb restriccions ha estat utilitzada amb èxit par a resoldre problemes en molts dominis reals (industrials). Aquesta tesi es centra en les aproximacions lògiques, concretament en Màxima Satisfactibilitat (MaxSAT) que és la versió d’optimització del problema de Satisfactibilitat booleana (SAT). A través de MaxSAT, s’han resolt molts problemes de forma eficient. Famílies d’instàncies de la majoria d’aquests problemes han estat sotmeses a la MaxSAT Evaluation (MSE), creant així una col•lecció pública i accessible d’instàncies de referència. En les edicions recents de la MSE, els algorismes SAT-based han estat les aproximacions que han tingut un millor comportament per a les instàncies industrials. Aquesta tesi està centrada en millorar els algorismes SAT-based . El nostre treball ha contribuït a tancar varies instàncies obertes i a reduir dramàticament el temps de resolució en moltes altres. A més, hem trobat sorprenentment que reformular y resoldre el problema MaxSAT a través de programació lineal sencera era especialment adequat per algunes famílies. Finalment, hem desenvolupat el primer portfoli altament eficient par a MaxSAT que ha dominat en totes las categories de la MSE des de 2013.La optimización con restricciones ha sido utilizada con éxito para resolver problemas en muchos dominios reales (industriales). Esta tesis se centra en las aproximaciones lógicas, concretamente en Máxima Satisfacibilidad (MaxSAT) que es la versión de optimización del problema de Satisfacibilidad booleana (SAT). A través de MaxSAT, se han resuelto muchos problemas de forma eficiente. Familias de instancias de la mayoría de ellos han sido sometidas a la MaxSAT Evaluation (MSE), creando así una colección pública y accesible de instancias de referencia. En las ediciones recientes de la MSE, los algoritmos SAT-based han sido las aproximaciones que han tenido un mejor comportamiento para las instancias industriales. Esta tesis está centrada en mejorar los algoritmos SAT-based. Nuestro trabajo ha contribuido a cerrar varias instancias abiertas y a reducir dramáticamente el tiempo de resolución en muchas otras. Además, hemos encontrado sorprendentemente que reformular y resolver el problema MaxSAT a través de programación lineal entera era especialmente adecuado para algunas familias. Finalmente, hemos desarrollado el primer portfolio altamente eficiente para MaxSAT que ha dominado en todas las categorías de la MSE desde 2013.Constraint optimization has been successfully used to solve problems in many real world (industrial) domains. This PhD thesis is focused on logic-based approaches, in particular, on Maximum Satisfiability (MaxSAT) which is the optimization version of Satisfiability (SAT). There have been many problems efficiency solved through MaxSAT. Instance families on the majority of them have been submitted to the international MaxSAT Evaluation (MSE), creating a collection of publicly available benchmark instances. At recent editions of MSE, SAT-based algorithms were the best performing single algorithm approaches for industrial problems. This PhD thesis is focused on the improvement of SAT-based algorithms. All this work has contributed to close up some open instances and to reduce dramatically the solving time in many others. In addition, we have surprisingly found that reformulating and solving the MaxSAT problem through Integer Linear Programming (ILP) was extremely well suited for some families. Finally, we have developed the first highly efficient MaxSAT portfolio that dominated all categories of MSE since 2013
FourierSAT: A Fourier Expansion-Based Algebraic Framework for Solving Hybrid Boolean Constraints
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.Comment: The paper was accepted by Thirty-Fourth AAAI Conference on Artificial
Intelligence (AAAI 2020). V2 (Feb 24): Typos correcte
Optimization Modulo Theories with Linear Rational Costs
In the contexts of automated reasoning (AR) and formal verification (FV),
important decision problems are effectively encoded into Satisfiability Modulo
Theories (SMT). In the last decade efficient SMT solvers have been developed
for several theories of practical interest (e.g., linear arithmetic, arrays,
bit-vectors). Surprisingly, little work has been done to extend SMT to deal
with optimization problems; in particular, we are not aware of any previous
work on SMT solvers able to produce solutions which minimize cost functions
over arithmetical variables. This is unfortunate, since some problems of
interest require this functionality.
In the work described in this paper we start filling this gap. We present and
discuss two general procedures for leveraging SMT to handle the minimization of
linear rational cost functions, combining SMT with standard minimization
techniques. We have implemented the procedures within the MathSAT SMT solver.
Due to the absence of competitors in the AR, FV and SMT domains, we have
experimentally evaluated our implementation against state-of-the-art tools for
the domain of linear generalized disjunctive programming (LGDP), which is
closest in spirit to our domain, on sets of problems which have been previously
proposed as benchmarks for the latter tools. The results show that our tool is
very competitive with, and often outperforms, these tools on these problems,
clearly demonstrating the potential of the approach.Comment: Submitted on january 2014 to ACM Transactions on Computational Logic,
currently under revision. arXiv admin note: text overlap with arXiv:1202.140
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