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

International audienceWe developed a formal framework for CDCL (conflict-driven clause learning) in Isabelle/HOL. Through a chain of refinements, an abstract CDCL calculus is connected to a SAT solver expressed in a functional programming language, with total correctness guarantees. The framework offers a convenient way to prove metatheorems and experiment with variants. Compared with earlier SAT solver verifications, the main novelties are the inclusion of rules for forget, restart, and incremental solving and the application of refinement

Towards Next Generation Sequential and Parallel SAT Solvers

This thesis focuses on improving the SAT solving technology. The improvements focus on two major subjects: sequential SAT solving and parallel SAT solving. To better understand sequential SAT algorithms, the abstract reduction system Generic CDCL is introduced. With Generic CDCL, the soundness of solving techniques can be modeled. Next, the conflict driven clause learning algorithm is extended with the three techniques local look-ahead, local probing and all UIP learning that allow more global reasoning during search. These techniques improve the performance of the sequential SAT solver Riss. Then, the formula simplification techniques bounded variable addition, covered literal elimination and an advanced cardinality constraint extraction are introduced. By using these techniques, the reasoning of the overall SAT solving tool chain becomes stronger than plain resolution. When using these three techniques in the formula simplification tool Coprocessor before using Riss to solve a formula, the performance can be improved further. Due to the increasing number of cores in CPUs, the scalable parallel SAT solving approach iterative partitioning has been implemented in Pcasso for the multi-core architecture. Related work on parallel SAT solving has been studied to extract main ideas that can improve Pcasso. Besides parallel formula simplification with bounded variable elimination, the major extension is the extended clause sharing level based clause tagging, which builds the basis for conflict driven node killing. The latter allows to better identify unsatisfiable search space partitions. Another improvement is to combine scattering and look-ahead as a superior search space partitioning function. In combination with Coprocessor, the introduced extensions increase the performance of the parallel solver Pcasso. The implemented system turns out to be scalable for the multi-core architecture. Hence iterative partitioning is interesting for future parallel SAT solvers. The implemented solvers participated in international SAT competitions. In 2013 and 2014 Pcasso showed a good performance. Riss in combination with Copro- cessor won several first, second and third prices, including two Kurt-Gödel-Medals. Hence, the introduced algorithms improved modern SAT solving technology

A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality (Extended Abstract)

International audienceWe developed a formal framework for CDCL (conflict-driven clause learning) in Isabelle/HOL. Through a chain of refinements, an abstract CDCL calculus is connected to a SAT solver expressed in a functional programming language, with total correctness guarantees. The framework offers a convenient way to prove metatheorems and experiment with variants. Compared with earlier SAT solver verifications, the main novelties are the inclusion of rules for forget, restart, and incremental solving and the application of refinement

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)

Improving Model Finding for Integrated Quantitative-qualitative Spatial Reasoning With First-order Logic Ontologies

Many spatial standards are developed to harmonize the semantics and specifications of GIS data and for sophisticated reasoning. All these standards include some types of simple and complex geometric features, and some of them incorporate simple mereotopological relations. But the relations as used in these standards, only allow the extraction of qualitative information from geometric data and lack formal semantics that link geometric representations with mereotopological or other qualitative relations. This impedes integrated reasoning over qualitative data obtained from geometric sources and “native” topological information – for example as provided from textual sources where precise locations or spatial extents are unknown or unknowable. To address this issue, the first contribution in this dissertation is a first-order logical ontology that treats geometric features (e.g. polylines, polygons) and relations between them as specializations of more general types of features (e.g. any kind of 2D or 1D features) and mereotopological relations between them. Key to this endeavor is the use of a multidimensional theory of space wherein, unlike traditional logical theories of mereotopology (like RCC), spatial entities of different dimensions can co-exist and be related. However terminating or tractable reasoning with such an expressive ontology and potentially large amounts of data is a challenging AI problem. Model finding tools used to verify FOL ontologies with data usually employ a SAT solver to determine the satisfiability of the propositional instantiations (SAT problems) of the ontology. These solvers often experience scalability issues with increasing number of objects and size and complexity of the ontology, limiting its use to ontologies with small signatures and building small models with less than 20 objects. To investigate how an ontology influences the size of its SAT translation and consequently the model finder’s performance, we develop a formalization of FOL ontologies with data. We theoretically identify parameters of an ontology that significantly contribute to the dramatic growth in size of the SAT problem. The search space of the SAT problem is exponential in the signature of the ontology (the number of predicates in the axiomatization and any additional predicates from skolemization) and the number of distinct objects in the model. Axiomatizations that contain many definitions lead to large number of SAT propositional clauses. This is from the conversion of biconditionals to clausal form. We therefore postulate that optional definitions are ideal sentences that can be eliminated from an ontology to boost model finder’s performance. We then formalize optional definition elimination (ODE) as an FOL ontology preprocessing step and test the simplification on a set of spatial benchmark problems to generate smaller SAT problems (with fewer clauses and variables) without changing the satisfiability and semantic meaning of the problem. We experimentally demonstrate that the reduction in SAT problem size also leads to improved model finding with state-of-the-art model finders, with speedups of 10-99%. Altogether, this dissertation improves spatial reasoning capabilities using FOL ontologies – in terms of a formal framework for integrated qualitative-geometric reasoning, and specific ontology preprocessing steps that can be built into automated reasoners to achieve better speedups in model finding times, and scalability with moderately-sized datasets

Evaluating CDCL Variable Scoring Schemes

Abstract. The VSIDS (variable state independent decaying sum) decision heuristic invented in the context of the CDCL (conflict-driven clause learning) SAT solver Chaff, is considered crucial for achieving high efficiency of modern SAT solvers on application benchmarks. This paper proposes ACIDS (average conflict-index decision score), a variant of VSIDS. The ACIDS heuristics is compared to the original implementation of VSIDS, its popular modern implementation EVSIDS (exponential VSIDS), the VMTF (variable move-to-front) scheme, and other related decision heuristics. They all share the important principle to select those variables as decisions, which recently participated in conflicts. The main goal of the paper is to provide an empirical evaluation to serve as a starting point for trying to understand the reason for the efficiency of these decision heuristics. In our experiments, it turns out that EVSIDS, VMTF, ACIDS behave very similarly, if implemented carefully

Formalizing the Metatheory of Logical Calculi and Automatic Provers in Isabelle/HOL (Invited Talk)

International audienceIsaFoL (Isabelle Formalization of Logic) is an undertaking that aims at developing formal theories about logics, proof systems, and automatic provers, using Isabelle/HOL. At the heart of the project is the conviction that proof assistants have become mature enough to actually help researchers in automated reasoning when they develop new calculi and tools. In this paper, I describe and reflect on three verification subprojects to which I contributed: a first-order resolution prover, an imperative SAT solver, and generalized term orders for λ-free higher-order logic

New Formal Methods for Automotive Configuration

Die Komplexität der Automobilkonfiguration hat in den letzten Jahrzehnten extrem zugenommen. Ein typischer deutscher Premiumhersteller kann bis zu 10^80 Varianten eines einzigen Fahrzeugmodells bauen. Dieser Variantenreichtum muss jedoch entlang der gesamten Prozesskette—vom Produktentstehungsprozess bis hin zur Fertigung im Werk—verwaltet und beherrscht werden. Hierzu müssen von Experten einerseits die vom Kunden bestellbaren Fahrzeuge dokumentiert werden (High Level Regelwerk), andererseits müssen diesen Fahrzeugen physikalische Teile, Steuergeräte und Softwarekonfigurationen zugeordnet werden (Low Level Regelwerk). Die vorliegende Arbeit führt einen neuen generischen Formalismus für Konfigurationsdaten in der Automobilindustrie ein und präsentiert einen ausführlichen Überblick über die in der Industrie vorkommenden Prüfmöglichkeiten. In verschiedenen Industriekooperationen mit z.B. Audi, BMW, Daimler, Opel und VW wurde verifiziert, dass dieser Formalismus auf diese Hersteller übertragbar ist. Viele der bestehenden Prüfalgorithmen werden in dieser Dissertation entscheidend optimiert und werden im Rahmen des neuen generischen Frameworks formuliert. Es werden neue Prüf- und Analysemöglichkeiten auf Konfigurationsdaten vorgestellt. Dies sind unter anderem das Zählen baubarer Fahrzeuge, die Berechnung minimaler und maximaler Kundenorders oder die Berechnung von direkten Zwängen in der Konfigurationsbasis. Ein Hauptbeitrag dieser Arbeit ist die Einführung der Booleschen Quantorenelimination in der Automobilkonfiguration. Während die Quantorenelimination bisher vor allem im Bereich des symbolischen Modelcheckings zu finden war, werden hier zwei Anwendungen in der Automobilindustrie identifiziert, die großes Interesse in den industriellen Kooperationen erweckt haben. Es werden verschiedene Ansätze zur Booleschen Quantorenelimination vorgestellt und bezüglich der Anwendungen evaluiert. Im Rahmen dieser Arbeit entstand die Softwarebibliothek AutoLib, die die vorgestellten Algorithmen implementiert und vor allem einen neuen SAT Solver mit sich bringt, der sowohl Inkrementalität und Dekrementalität, als auch das sogenannte Proof Tracing, also das Aufzeichnen von Beweisen bei Nicht-Erfüllbarkeit, implementiert. Nach unserem Wissen ist dies der einzige SAT Solver, der diese beiden Funktionen auch in Kombination unterstützt. AutoLib wird aktuell in einem Produktivsystem bei BMW sowie in Prototypen bei Audi/VW und bei Daimler eingesetzt. Alle Algorithmen, die in dieser Arbeit präsentiert werden, wurden in einer Mach- barkeitsstudie bei BMW in den Jahren 2012 und 2013 implementiert und auf ihre industrielle Einsetzbarkeit hin verifiziert. Ein Produktivsystem, das Teile dieser Algorithmen umfasst und auf AutoLib basiert, hatte im Mai 2014 GoLive bei BMW

Proceedings of the Joint Automated Reasoning Workshop and Deduktionstreffen: As part of the Vienna Summer of Logic – IJCAR 23-24 July 2014

Preface For many years the British and the German automated reasoning communities have successfully run independent series of workshops for anybody working in the area of automated reasoning. Although open to the general public they addressed in the past primarily the British and the German communities, respectively. At the occasion of the Vienna Summer of Logic the two series have a joint event in Vienna as an IJCAR workshop. In the spirit of the two series there will be only informal proceedings with abstracts of the works presented. These are collected in this document. We have tried to maintain the informal open atmosphere of the two series and have welcomed in particular research students to present their work. We have solicited for all work related to automated reasoning and its applications with a particular interest in work-in-progress and the presentation of half-baked ideas. As in the previous years, we have aimed to bring together researchers from all areas of automated reasoning in order to foster links among researchers from various disciplines; among theoreticians, implementers and users alike, and among international communities, this year not just the British and German communities