Boolean Satisfiability in Electronic Design Automation

Boolean Satisfiability (SAT) is often used as the underlying model for a significant and increasing number of applications in Electronic Design Automation (EDA) as well as in many other fields of Computer Science and Engineering. In recent years, new and efficient algorithms for SAT have been developed, allowing much larger problem instances to be solved. SAT “packages” are currently expected to have an impact on EDA applications similar to that of BDD packages since their introduction more than a decade ago. This tutorial paper is aimed at introducing the EDA professional to the Boolean satisfiability problem. Specifically, we highlight the use of SAT models to formulate a number of EDA problems in such diverse areas as test pattern generation, circuit delay computation, logic optimization, combinational equivalence checking, bounded model checking and functional test vector generation, among others. In addition, we provide an overview of the algorithmic techniques commonly used for solving SAT, including those that have seen widespread use in specific EDA applications. We categorize these algorithmic techniques, indicating which have been shown to be best suited for which tasks

A Variable Depth Search Algorithm for Binary Constraint Satisfaction Problems

The constraint satisfaction problem (CSP) is a popular used paradigm to model a wide spectrum of optimization problems in artificial intelligence. This paper presents a fast metaheuristic for solving binary constraint satisfaction problems. The method can be classified as a variable depth search metaheuristic combining a greedy local search using a self-adaptive weighting strategy on the constraint weights. Several metaheuristics have been developed in the past using various penalty weight mechanisms on the constraints.What distinguishes the proposed metaheuristic fromthose developed in the past is the update of k variables during each iteration when moving from one assignment of values to another. The benchmark is based on hard random constraint satisfaction problems enjoying several features that make them of a great theoretical and practical interest.The results show that the proposed metaheuristic is capable of solving hard unsolved problems that still remain a challenge for both complete and incomplete methods. In addition, the proposed metaheuristic is remarkably faster than all existing solvers when tested on previously solved instances. Finally, its distinctive feature contrary to other metaheuristics is the absence of parameter tuning making it highly suitable in practical scenarios

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

A discrete lagrangian-based global-search method for solving satisfiability problems

Abstract. Satisfiability is a class of NP-complete problems that model a wide range of real-world applications. These problems are difficult to solve because they have many local minima in their search space, often trapping greedy search methods that utilize some form of descent. In this paper, we propose a new discrete Lagrange-multiplier-based global-search method (DLM) for solving satisfiability problems. We derive new approaches for applying Lagrangian methods in discrete space, we show that an equilibrium is reached when a feasible assignment to the original problem is found and present heuristic algorithms to look for equilibrium points. Our method and analysis provides a theoretical foundation and generalization of local search schemes that optimize the objective alone and penalty-based schemes that optimize the constraints alone. In contrast to local search methods that restart from a new starting point when a search reaches a local trap, the Lagrange multipliers in DLM provide a force to lead the search out of a local minimum and move it in the direction provided by the Lagrange multipliers. In contrast to penalty-based schemes that rely only on the weights of violated constraints to escape from local minima, DLM also uses the value of an objective function (in this case the number of violated constraints) to provide further guidance. The dynamic shift in emphasis between the objective and the constraints, depending on their relative values, is the key of Lagrangia

Integration of constraint programming and linear programming techniques for constraint satisfaction problem and general constrained optimization problem.

Wong Siu Ham.Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.Includes bibliographical references (leaves 131-138).Abstracts in English and Chinese.Abstract --- p.iiAcknowledgments --- p.viChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation for Integration --- p.2Chapter 1.2 --- Thesis Overview --- p.4Chapter 2 --- Preliminaries --- p.5Chapter 2.1 --- Constraint Programming --- p.5Chapter 2.1.1 --- Constraint Satisfaction Problems (CSP's) --- p.6Chapter 2.1.2 --- Satisfiability (SAT) Problems --- p.10Chapter 2.1.3 --- Systematic Search --- p.11Chapter 2.1.4 --- Local Search --- p.13Chapter 2.2 --- Linear Programming --- p.17Chapter 2.2.1 --- Linear Programming Problems --- p.17Chapter 2.2.2 --- Simplex Method --- p.19Chapter 2.2.3 --- Mixed Integer Programming Problems --- p.27Chapter 3 --- Integration of Constraint Programming and Linear Program- ming --- p.29Chapter 3.1 --- Problem Definition --- p.29Chapter 3.2 --- Related works --- p.30Chapter 3.2.1 --- Illustrating the Performances --- p.30Chapter 3.2.2 --- Improving the Searching --- p.33Chapter 3.2.3 --- Improving the representation --- p.36Chapter 4 --- A Scheme of Integration for Solving Constraint Satisfaction Prob- lem --- p.37Chapter 4.1 --- Integrated Algorithm --- p.38Chapter 4.1.1 --- Overview of the Integrated Solver --- p.38Chapter 4.1.2 --- The LP Engine --- p.44Chapter 4.1.3 --- The CP Solver --- p.45Chapter 4.1.4 --- Proof of Soundness and Completeness --- p.46Chapter 4.1.5 --- Compared with Previous Work --- p.46Chapter 4.2 --- Benchmarking Results --- p.48Chapter 4.2.1 --- Comparison with CLP solvers --- p.48Chapter 4.2.2 --- Magic Squares --- p.51Chapter 4.2.3 --- Random CSP's --- p.52Chapter 5 --- A Scheme of Integration for Solving General Constrained Opti- mization Problem --- p.68Chapter 5.1 --- Integrated Optimization Algorithm --- p.69Chapter 5.1.1 --- Overview of the Integrated Optimizer --- p.69Chapter 5.1.2 --- The CP Solver --- p.74Chapter 5.1.3 --- The LP Engine --- p.75Chapter 5.1.4 --- Proof of the Optimization --- p.77Chapter 5.2 --- Benchmarking Results --- p.77Chapter 5.2.1 --- Weighted Magic Square --- p.77Chapter 5.2.2 --- Template design problem --- p.78Chapter 5.2.3 --- Random GCOP's --- p.79Chapter 6 --- Conclusions and Future Work --- p.97Chapter 6.1 --- Conclusions --- p.97Chapter 6.2 --- Future work --- p.98Chapter 6.2.1 --- Detection of implicit equalities --- p.98Chapter 6.2.2 --- Dynamical variable selection --- p.99Chapter 6.2.3 --- Analysis on help of linear constraints --- p.99Chapter 6.2.4 --- Local Search and Linear Programming --- p.99Appendix --- p.101Proof of Soundness and Completeness --- p.101Proof of the optimization --- p.126Bibliography --- p.13

A progressive stochastic search method for solving constraint satisfaction problems.

Bryan Chi-ho Lam.Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.Includes bibliographical references (leaves 163-166).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 2 --- Background --- p.4Chapter 2.1 --- Constraint Satisfaction Problems --- p.4Chapter 2.2 --- Systematic Search --- p.5Chapter 2.3 --- Stochastic Search --- p.6Chapter 2.3.1 --- Overview --- p.6Chapter 2.3.2 --- GENET --- p.8Chapter 2.3.3 --- CSVC --- p.10Chapter 2.3.4 --- Adaptive Search --- p.12Chapter 2.4 --- Hybrid Approach --- p.13Chapter 3 --- Progressive Stochastic Search --- p.14Chapter 3.1 --- Progressive Stochastic Search --- p.14Chapter 3.1.1 --- Network Architecture --- p.15Chapter 3.1.2 --- Convergence Procedure --- p.16Chapter 3.1.3 --- An Illustrative Example --- p.21Chapter 3.2 --- Incremental Progressive Stochastic Search --- p.23Chapter 3.2.1 --- Network Architecture --- p.24Chapter 3.2.2 --- Convergence Procedure --- p.24Chapter 3.2.3 --- An Illustrative Example --- p.25Chapter 3.3 --- Heuristic Cluster Selection Strategy --- p.28Chapter 4 --- Experiments --- p.31Chapter 4.1 --- N-Queens Problems --- p.32Chapter 4.2 --- Permutation Generation Problems --- p.53Chapter 4.2.1 --- Increasing Permutation Problems --- p.54Chapter 4.2.2 --- Random Permutation Generation Problems --- p.75Chapter 4.3 --- Latin Squares and Quasigroup Completion Problems --- p.96Chapter 4.3.1 --- Latin Square Problems --- p.96Chapter 4.3.2 --- Quasigroup Completion Problems --- p.118Chapter 4.4 --- Random CSPs --- p.120Chapter 4.4.1 --- Tight Random CSPs --- p.139Chapter 4.4.2 --- Phase Transition Random CSPs --- p.156Chapter 5 --- Concluding Remarks --- p.159Chapter 5.1 --- Contributions --- p.159Chapter 5.2 --- Future Work --- p.16