157 research outputs found
On QBF Proofs and Preprocessing
QBFs (quantified boolean formulas), which are a superset of propositional
formulas, provide a canonical representation for PSPACE problems. To overcome
the inherent complexity of QBF, significant effort has been invested in
developing QBF solvers as well as the underlying proof systems. At the same
time, formula preprocessing is crucial for the application of QBF solvers. This
paper focuses on a missing link in currently-available technology: How to
obtain a certificate (e.g. proof) for a formula that had been preprocessed
before it was given to a solver? The paper targets a suite of commonly-used
preprocessing techniques and shows how to reconstruct certificates for them. On
the negative side, the paper discusses certain limitations of the
currently-used proof systems in the light of preprocessing. The presented
techniques were implemented and evaluated in the state-of-the-art QBF
preprocessor bloqqer.Comment: LPAR 201
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)
Towards Understanding and Harnessing the Potential of Clause Learning
Efficient implementations of DPLL with the addition of clause learning are
the fastest complete Boolean satisfiability solvers and can handle many
significant real-world problems, such as verification, planning and design.
Despite its importance, little is known of the ultimate strengths and
limitations of the technique. This paper presents the first precise
characterization of clause learning as a proof system (CL), and begins the task
of understanding its power by relating it to the well-studied resolution proof
system. In particular, we show that with a new learning scheme, CL can provide
exponentially shorter proofs than many proper refinements of general resolution
(RES) satisfying a natural property. These include regular and Davis-Putnam
resolution, which are already known to be much stronger than ordinary DPLL. We
also show that a slight variant of CL with unlimited restarts is as powerful as
RES itself. Translating these analytical results to practice, however, presents
a challenge because of the nondeterministic nature of clause learning
algorithms. We propose a novel way of exploiting the underlying problem
structure, in the form of a high level problem description such as a graph or
PDDL specification, to guide clause learning algorithms toward faster
solutions. We show that this leads to exponential speed-ups on grid and
randomized pebbling problems, as well as substantial improvements on certain
ordering formulas
CENSOR: Privacy-preserving Obfuscation for Outsourcing SAT formulas
We propose a novel obfuscation technique that can be used to outsource hard satisfiability (SAT) formulas to the cloud. Servers with large computational power are typically used to solve SAT instances that model real-life problems in task scheduling, AI planning, circuit verification and more. However, outsourcing data to the cloud may lead to privacy and information breaches since satisfying assignments may reveal considerable information about the underlying problem modeled by SAT.
In this work, we develop CENSOR (privaCy prEserviNg obfuScation for Outsourcing foRmulas), a novel SAT obfuscation framework that resembles Indistinguishability Obfuscation. At the core of the framework lies a mechanism that transforms any formula to a random one with the same number of satisfying assignments. As a result, obfuscated formulas are indistinguishable from each other thus preserving the input-output privacy of the original SAT instance. Contrary to prior solutions that are rather adhoc in nature, we formally prove the security of our scheme. Additionally, we show that obfuscated formulas are within a polynomial factor of the original ones thus achieving polynomial slowdown. Finally, the whole process is efficient in practice, allowing solutions to original instances to be easily recovered from obfuscated ones.
A byproduct of our method is that all NP problems can be potentially outsourced to the cloud by means of reducing to SAT
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