Parallelization of SAT on Reconfigurable Hardware

Quoique très difficile à résoudre, le problème de satisfiabilité Booléenne (SAT) est fréquemment utilisé lors de la modélisation d’applications industrielles. À cet effet, les deux dernières décennies ont vu une progression fulgurante des outils conçus pour trouver des solutions à ce problème NP-complet. Deux grandes avenues générales ont été explorées afin de produire ces outils, notamment l’approche logicielle et matérielle. Afin de raffiner et améliorer ces solveurs, de nombreuses techniques et heuristiques ont été proposées par la communauté de recherche. Le but final de ces outils a été de résoudre des problèmes de taille industrielle, ce qui a été plus ou moins accompli par les solveurs de nature logicielle. Initialement, le but de l’utilisation du matériel reconfigurable a été de produire des solveurs pouvant trouver des solutions plus rapidement que leurs homologues logiciels. Cependant, le niveau de sophistication de ces derniers a augmenté de telle manière qu’ils restent le meilleur choix pour résoudre SAT. Toutefois, les solveurs modernes logiciels n’arrivent toujours pas a trouver des solutions de manière efficace à certaines instances SAT. Le but principal de ce mémoire est d’explorer la résolution du problème SAT dans le contexte du matériel reconfigurable en vue de caractériser les ingrédients nécessaires d’un solveur SAT efficace qui puise sa puissance de calcul dans le parallélisme conféré par une plateforme FPGA. Le prototype parallèle implémenté dans ce travail est capable de se mesurer, en termes de vitesse d’exécution à d’autres solveurs (matériels et logiciels), et ce sans utiliser aucune heuristique. Nous montrons donc que notre approche matérielle présente une option prometteuse vers la résolution d’instances industrielles larges qui sont difficilement abordées par une approche logicielle.Though very difficult to solve, the Boolean satisfiability problem (SAT) is extensively used to model various real-world applications and problems. Over the past two decades, researchers have tried to provide tools that are used, to a certain degree, to find solutions to the Boolean satisfiability problem. The nature of these tools is broadly divided in software and reconfigurable hardware solvers. In addition, the main algorithms used to solve this problem have also been complemented with heuristics of various levels of sophistication to help overcome some of the NP-hardness of the problem. The end goal of these tools has been to provide solutions to industrial-sized problems of enormous size. Initially, reconfigurable hardware tools provided a promising avenue to accelerating SAT solving over traditional software based solutions. However, the level of sophistication of software solvers overcame their hardware counterparts, which remained limited to smaller problem instances. Even so, modern state-of-the-art software solvers still fail unpredictably on some instances. The main focus of this thesis is to explore solving SAT on reconfigurable hardware in order to gain an understanding of what would be essential ingredients to add (and discard) to a very efficient hardware SAT solver that obtains its processing power from the raw parallelism of an FPGA platform. The parallel prototype solver that was implemented in this work has been found to be comparable with other hardware and software solvers in terms of execution speed even though no heuristics or other helping techniques were implemented. We thus show that our approach provides a very promising avenue to solving large, industrial SAT instances that might be difficult to handle by software solvers

Methoden und Beschreibungssprachen zur Modellierung und Verifikation vonSchaltungen und Systemen: MBMV 2015 - Tagungsband, Chemnitz, 03. - 04. März 2015

Der Workshop Methoden und Beschreibungssprachen zur Modellierung und Verifikation von Schaltungen und Systemen (MBMV 2015) findet nun schon zum 18. mal statt. Ausrichter sind in diesem Jahr die Professur Schaltkreis- und Systementwurf der Technischen Universität Chemnitz und das Steinbeis-Forschungszentrum Systementwurf und Test. Der Workshop hat es sich zum Ziel gesetzt, neueste Trends, Ergebnisse und aktuelle Probleme auf dem Gebiet der Methoden zur Modellierung und Verifikation sowie der Beschreibungssprachen digitaler, analoger und Mixed-Signal-Schaltungen zu diskutieren. Er soll somit ein Forum zum Ideenaustausch sein. Weiterhin bietet der Workshop eine Plattform für den Austausch zwischen Forschung und Industrie sowie zur Pflege bestehender und zur Knüpfung neuer Kontakte. Jungen Wissenschaftlern erlaubt er, ihre Ideen und Ansätze einem breiten Publikum aus Wissenschaft und Wirtschaft zu präsentieren und im Rahmen der Veranstaltung auch fundiert zu diskutieren. Sein langjähriges Bestehen hat ihn zu einer festen Größe in vielen Veranstaltungskalendern gemacht. Traditionell sind auch die Treffen der ITGFachgruppen an den Workshop angegliedert. In diesem Jahr nutzen zwei im Rahmen der InnoProfile-Transfer-Initiative durch das Bundesministerium für Bildung und Forschung geförderte Projekte den Workshop, um in zwei eigenen Tracks ihre Forschungsergebnisse einem breiten Publikum zu präsentieren. Vertreter der Projekte Generische Plattform für Systemzuverlässigkeit und Verifikation (GPZV) und GINKO - Generische Infrastruktur zur nahtlosen energetischen Kopplung von Elektrofahrzeugen stellen Teile ihrer gegenwärtigen Arbeiten vor. Dies bereichert denWorkshop durch zusätzliche Themenschwerpunkte und bietet eine wertvolle Ergänzung zu den Beiträgen der Autoren. [... aus dem Vorwort

Hybrid Verification for Analog and Mixed-signal Circuits

With increasing design complexity and reliability requirements, analog and mixedsignal (AMS) verification manifests itself as a key bottleneck. While formal methods and machine learning have been proposed for AMS verification, these two types of techniques suffer from their own limitations, with the former being specifically limited by scalability and the latter by inherent errors in learning-based models. We present a new direction in AMS verification by proposing a hybrid formal/machinelearning- based verification technique (HFMV) to combine the best of the two worlds. HFMV builds formalism on the top of a machine learning model to verify AMS circuits efficiently while meeting a user-specified confidence level. Guided by formal checks, HFMV intelligently explores the high-dimensional parameter space of a given design by iteratively improving the machine learning model. As a result, it leads to accurate failure prediction in the case of a failing circuit or a reliable pass decision in the case of a good circuit. Our experimental results demonstrate that the proposed HFMV approach is capable of identifying hard-to-find failures which are completely missed by a huge number of random simulation samples while significantly cutting down training sample size and verification cycle time

Solving hard industrial combinatorial problems with SAT

The topic of this thesis is the development of SAT-based techniques and tools for solving industrial combinatorial problems. First, it describes the architecture of state-of-the-art SAT and SMT Solvers based on the classical DPLL procedure. These systems can be used as black boxes for solving combinatorial problems. However, sometimes we can increase their efficiency with slight modifications of the basic algorithm. Therefore, the study and development of techniques for adjusting SAT Solvers to specific combinatorial problems is the first goal of this thesis. Namely, SAT Solvers can only deal with propositional logic. For solving general combinatorial problems, two different approaches are possible: - Reducing the complex constraints into propositional clauses. - Enriching the SAT Solver language. The first approach corresponds to encoding the constraint into SAT. The second one corresponds to using propagators, the basis for SMT Solvers. Regarding the first approach, in this document we improve the encoding of two of the most important combinatorial constraints: cardinality constraints and pseudo-Boolean constraints. After that, we present a new mixed approach, called lazy decomposition, which combines the advantages of encodings and propagators. The other part of the thesis uses these theoretical improvements in industrial combinatorial problems. We give a method for efficiently scheduling some professional sport leagues with SAT. The results are promising and show that a SAT approach is valid for these problems. However, the chaotical behavior of CDCL-based SAT Solvers due to VSIDS heuristics makes it difficult to obtain a similar solution for two similar problems. This may be inconvenient in real-world problems, since a user expects similar solutions when it makes slight modifications to the problem specification. In order to overcome this limitation, we have studied and solved the close solution problem, i.e., the problem of quickly finding a close solution when a similar problem is considered

Analytical Modeling of High Performance Reconfigurable Computers: Prediction and Analysis of System Performance.

The use of a network of shared, heterogeneous workstations each harboring a Reconfigurable Computing (RC) system offers high performance users an inexpensive platform for a wide range of computationally demanding problems. However, effectively using the full potential of these systems can be challenging without the knowledge of the system’s performance characteristics. While some performance models exist for shared, heterogeneous workstations, none thus far account for the addition of Reconfigurable Computing systems. This dissertation develops and validates an analytic performance modeling methodology for a class of fork-join algorithms executing on a High Performance Reconfigurable Computing (HPRC) platform. The model includes the effects of the reconfigurable device, application load imbalance, background user load, basic message passing communication, and processor heterogeneity. Three fork-join class of applications, a Boolean Satisfiability Solver, a Matrix-Vector Multiplication algorithm, and an Advanced Encryption Standard algorithm are used to validate the model with homogeneous and simulated heterogeneous workstations. A synthetic load is used to validate the model under various loading conditions including simulating heterogeneity by making some workstations appear slower than others by the use of background loading. The performance modeling methodology proves to be accurate in characterizing the effects of reconfigurable devices, application load imbalance, background user load and heterogeneity for applications running on shared, homogeneous and heterogeneous HPRC resources. The model error in all cases was found to be less than five percent for application runtimes greater than thirty seconds and less than fifteen percent for runtimes less than thirty seconds. The performance modeling methodology enables us to characterize applications running on shared HPRC resources. Cost functions are used to impose system usage policies and the results of vii the modeling methodology are utilized to find the optimal (or near-optimal) set of workstations to use for a given application. The usage policies investigated include determining the computational costs for the workstations and balancing the priority of the background user load with the parallel application. The applications studied fall within the Master-Worker paradigm and are well suited for a grid computing approach. A method for using NetSolve, a grid middleware, with the model and cost functions is introduced whereby users can produce optimal workstation sets and schedules for Master-Worker applications running on shared HPRC resources

Precision analysis for hardware acceleration of numerical algorithms

The precision used in an algorithm affects the error and performance of individual computations, the memory usage, and the potential parallelism for a fixed hardware budget. However, when migrating an algorithm onto hardware, the potential improvements that can be obtained by tuning the precision throughout an algorithm to meet a range or error specification are often overlooked; the major reason is that it is hard to choose a number system which can guarantee any such specification can be met. Instead, the problem is mitigated by opting to use IEEE standard double precision arithmetic so as to be ‘no worse’ than a software implementation. However, the flexibility in the number representation is one of the key factors that can be exploited on reconfigurable hardware such as FPGAs, and hence ignoring this potential significantly limits the performance achievable. In order to optimise the performance of hardware reliably, we require a method that can tractably calculate tight bounds for the error or range of any variable within an algorithm, but currently only a handful of methods to calculate such bounds exist, and these either sacrifice tightness or tractability, whilst simulation-based methods cannot guarantee the given error estimate. This thesis presents a new method to calculate these bounds, taking into account both input ranges and finite precision effects, which we show to be, in general, tighter in comparison to existing methods; this in turn can be used to tune the hardware to the algorithm specifications. We demonstrate the use of this software to optimise hardware for various algorithms to accelerate the solution of a system of linear equations, which forms the basis of many problems in engineering and science, and show that significant performance gains can be obtained by using this new approach in conjunction with more traditional hardware optimisations