Karem A. Sakallah

Bio: Karem A. Sakallah is an academic researcher from University of Michigan. The author has contributed to research in topics: Boolean satisfiability problem & Boolean function. The author has an hindex of 47, co-authored 201 publications receiving 8866 citations. Previous affiliations of Karem A. Sakallah include Cadence Design Systems & American University of Beirut.

GRASP: a search algorithm for propositional satisfiability

Abstract: This paper introduces GRASP (Generic seaRch Algorithm for the Satisfiability Problem), a new search algorithm for Propositional Satisfiability (SAT). GRASP incorporates several search-pruning techniques that proved to be quite powerful on a wide variety of SAT problems. Some of these techniques are specific to SAT, whereas others are similar in spirit to approaches in other fields of Artificial Intelligence. GRASP is premised on the inevitability of conflicts during the search and its most distinguishing feature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack nonchronologically to earlier levels in the search tree, potentially pruning large portions of the search space. In addition, by "recording" the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Finally, straightforward bookkeeping of the causality chains leading up to conflicts allows GRASP to identify assignments that are necessary for a solution to be found. Experimental results obtained from a large number of benchmarks indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely effective for a large number of representative classes of SAT instances.

GRASP—a new search algorithm for satisfiability

Abstract: This paper introduces GRASP (Generic seaRch Algorithm for the Satisfiability Problem), an integrated algorithmic framework for SAT that unifies several previously proposed search-pruning techniques and facilitates identification of additional ones. GRASP is premised on the inevitability of conflicts during search and its most distinguishing feature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack non-chronologically to earlier levels in the search tree, potentially pruning large portions of the search space. In addition, by "recording" the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Finally, straightforward bookkeeping of the causality chains leading up to conflicts allows GRASP to identify assignments that are necessary for a solution to be found. Experimental results obtained from a large number of benchmarks, including many from the field of test pattern generation, indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely effective for a large number of representative classes of SAT instances.

Algorithms for Computing Minimal Unsatisfiable Subsets of Constraints

Abstract: Much research in the area of constraint processing has recently been focused on extracting small unsatisfiable "cores" from unsatisfiable constraint systems with the goal of finding minimal unsatisfiable subsets (MUSes). While most techniques have provided ways to find an approximation of an MUS (not necessarily minimal), we have developed a sound and complete algorithm for producing all MUSes of an unsatisfiable constraint system. In this paper, we describe a relationship between satisfiable and unsatisfiable subsets of constraints that we subsequently use as the foundation for MUS extraction algorithms, implemented for Boolean satisfiability constraints. The algorithms provide a framework with which many related subproblems can be solved, including relaxations of completeness to handle intractable instances, and we develop several variations of the basic algorithms to illustrate this. Experimental results demonstrate the performance of our algorithms, showing how the base algorithms run quickly on many instances, while the variations are valuable for producing results on instances whose complete results are intractably large. Furthermore, our algorithms are shown to perform better than the existing algorithms for solving either of the two distinct phases of our approach.

SATIRE: a new incremental satisfiability engine

Abstract: We introduce SATIRE, a new satisfiability solver that is particular-ly suited to verification and optimization problems in electronic de-sign automation. SATIRE builds on the most recent advances in satisfiability research, and includes two new features to achieve even higher performance: a facility for incrementally solving sets of related problems, and the ability to handle non-CNF constraints. We provide experimental evidence showing the effectiveness of these additions to classical satisfiability solvers.

Generic ILP versus specialized 0-1 ILP: an update

Abstract: Optimized solvers for the Boolean Satisfiability (SAT) problem have many applications in areas such as hardware and software verification, FPGA routing, planning, etc. Further uses are complicated by the need to express "counting constraints" in conjunctive normal form (CNF). Expressing such constraints by pure CNF leads to more complex SAT instances. Alternatively, those constraints can be handled by Integer Linear Programming (ILP), but generic ILP solvers may ignore the Boolean nature of 0--1 variables. Therefore specialized 0--1 ILP solvers extend SAT solvers to handle these so-called "pseudo-Boolean" constraints.This work provides an update on the on-going competition between generic ILP techniques and specialized 0--1 ILP techniques. To make a fair comparison, we generalize recent ideas for fast SAT-solving to more general 0--1 ILP problems that may include counting constraints and optimization. Another aspect of our comparison is evaluation on 0--1 ILP benchmarks that originate in Electronic Design Automation (EDA), but that cannot be directly solved by a SAT solver. Specifically, we solve instances of the Max-SAT and Max-ONEs optimization problems which seek to maximize the number of satisfied clauses and the "true" values over all satisfying assignments, respectively. Those problems have straightforward applications to SAT-based routing and are additionally important due to reductions from Max-Cut, Max-Clique, and Min Vertex Cover. Our experimental results show that specialized 0--1 techniques tend to outperform generic ILP techniques on Boolean optimization problems as well as on general EDA SAT problems.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

An Extensible SAT-solver

Abstract: In this article, we present a small, complete, and efficient SAT-solver in the style of conflict-driven learning, as exemplified by Chaff. We aim to give sufficient details about implementation to enable the reader to construct his or her own solver in a very short time.This will allow users of SAT-solvers to make domain specific extensions or adaptions of current state-of-the-art SAT-techniques, to meet the needs of a particular application area. The presented solver is designed with this in mind, and includes among other things a mechanism for adding arbitrary boolean constraints. It also supports solving a series of related SAT-problems efficiently by an incremental SAT-interface.

Chaff: engineering an efficient SAT solver

Abstract: Boolean satisfiability is probably the most studied of the combinatorial optimization/search problems. Significant effort has been devoted to trying to provide practical solutions to this problem for problem instances encountered in a range of applications in electronic design automation (EDA), as well as in artificial intelligence (AI). This study has culminated in the development of several SAT packages, both proprietary and in the public domain (e.g. GRASP, SATO) which find significant use in both research and industry. Most existing complete solvers are variants of the Davis-Putnam (DP) search algorithm. In this paper we describe the development of a new complete solver, Chaff which achieves significant performance gains through careful engineering of all aspects of the search-especially a particularly efficient implementation of Boolean constraint propagation (BCP) and a novel low overhead decision strategy. Chaff has been able to obtain one to two orders of magnitude performance improvement on difficult SAT benchmarks in comparison with other solvers (DP or otherwise), including GRASP and SATO.

Circuit techniques for reducing the effects of op-amp imperfections: autozeroing, correlated double sampling, and chopper stabilization

Abstract: In linear IC's fabricated in a low-voltage CMOS technology, the reduction of the dynamic range due to the dc offset and low frequency noise of the amplifiers becomes increasingly significant. Also, the achievable amplifier gain is often quite low in such a technology, since cascoding may not be a practical circuit option due to the resulting reduction of the output signal swing. In this paper, some old and some new circuit techniques are described for the compensation of the amplifier's most important nonideal effects including the noise (mainly thermal and 1/f noise), the input-referred dc offset voltage as well as the finite gain resulting in a nonideal virtual ground at the input.

Constraint Processing

Abstract: Constraint satisfaction is a simple but powerful tool. Constraints identify the impossible and reduce the realm of possibilities to effectively focus on the possible, allowing for a natural declarative formulation of what must be satisfied, without expressing how. The field of constraint reasoning has matured over the last three decades with contributions from a diverse community of researchers in artificial intelligence, databases and programming languages, operations research, management science, and applied mathematics. Today, constraint problems are used to model cognitive tasks in vision, language comprehension, default reasoning, diagnosis, scheduling, temporal and spatial reasoning. In Constraint Processing, Rina Dechter, synthesizes these contributions, along with her own significant work, to provide the first comprehensive examination of the theory that underlies constraint processing algorithms. Throughout, she focuses on fundamental tools and principles, emphasizing the representation and analysis of algorithms. ·Examines the basic practical aspects of each topic and then tackles more advanced issues, including current research challenges ·Builds the reader's understanding with definitions, examples, theory, algorithms and complexity analysis ·Synthesizes three decades of researchers work on constraint processing in AI, databases and programming languages, operations research, management science, and applied mathematics Table of Contents Preface; Introduction; Constraint Networks; Consistency-Enforcing Algorithms: Constraint Propagation; Directional Consistency; General Search Strategies; General Search Strategies: Look-Back; Local Search Algorithms; Advanced Consistency Methods; Tree-Decomposition Methods; Hybrid of Search and Inference: Time-Space Trade-offs; Tractable Constraint Languages; Temporal Constraint Networks; Constraint Optimization; Probabilistic Networks; Constraint Logic Programming; Bibliography