Multi-Core Unit Propagation in Functional Languages

Answer Set Programming is a declarative modeling paradigm enabling specialists in diverse disciplines to describe and solve complicated problems. Growth in high performance computing is driving ever smarter and more scalable parallel answer set solvers. To improve on today\u27s cutting-edge, researchers need to develop increasingly intelligent methods for analysis of a solver\u27s runtime information. Reflecting on the solver\u27s search state typically pauses its progress until the analysis is complete. This work introduces methods from the domain of parallel functional programming and immutable type theory to construct a representation of the search state that is both amenable to introspection and efficiently scalable across multiple processor cores

CDCL SAT solver heuristics: Clause management, instance structure, and decisions

The Boolean satisfiability problem or SAT is the problem of deciding if a Boolean formula has a satisfying assignment. It was the first problem shown to be NP-complete, and remains one of the most well-known and studied NP-complete problems. We do not expect to find a polynomial time algorithm that solves all SAT problems, as this would imply equivalence of the complexity classes P and NP, which seems unlikely. However, there are algorithms and heuristics to solve SAT problems that are often effective in practice. A SAT solver is a program that takes as input a Boolean formula and tries to find a satisfying assignment for it. The most-used algorithm in SAT solvers intended for solving real-world problems is known as Conflict Driven Clause Learning, abbreviated CDCL. Due to its broad usage, improving the performance of these solvers can have a large impact on other fields that use SAT solvers and also make SAT solving a useful tool for more applications. The practical performance of CDCL SAT solvers depends critically on a small number of key heuristic mechanisms, and works on these heuristics over the past 20 years have improved CDCL solver performance significantly. This dissertation contributes to our understanding of two of the key heuristic mechanisms, known as the decision heuristic and the clause database management scheme. There are two main foci, which are closely related. First, we focus on developing light weighted methods to use measures of instance structure in solver heuristics. The structure of instances arising from real-world problems seems to be one of the main features that makes them special but there is little work exploiting structural properties within CDCL solvers. We introduce a new structural measure for SAT instances, called Centrality, and show that this measure can be used in both decision and clause management heuristics to improve solver performance. Second, we study different components of clause database management schemes in order to understand and improve them. We categorize clauses as permanent and temporary, show that the permanent set is key to solver performance and propose modifications to the criteria for permanent clauses to improve performance. In recent years, clause database management strategies used in high-performance solvers have become complex, making their study and refinement difficult. We introduce a new clause reduction scheme, called online deletion, which is simple to implement and results in comparable performance

Distributed SAT solving engine

Master'sMASTER OF SCIENC

Extending the relational model with constraint satisfaction

We propose a new approach to data driven constraint programming. By extending the relational model to handle constraints and variables as first class citizens, we are able to express first order logic SAT problems using an extended SQL which we refer to as SAT/SQL. With SAT/SQL, one can efficiently solve a wide range of practical constraint and optimization problems. SAT/SQL integrates both SAT solver and relational data processing to enable efficient and large scale data driven constraint programming. Furthermore, our research presents two novel meta-programming operators: MINREPAIR and MIN-CONFLICT which are iterative debugging facilities for constraint programming with SAT/SQL

A Case for Simple SAT Solvers ⋆

Abstract. As SAT becomes more popular due to its ability to handle large real-world problems, progress in efficiency appears to have slowed down over the past few years. On the other hand, we now have access to many sophisticated implementations of SAT solvers, sometimes boasting large amounts of code. Although low-level optimizations can help, we argue that the SAT algorithm itself offers opportunities for more significant improvements. Specifically, we start with a no-frills solver implemented in less than 550 lines of code, and show that by focusing on the central aspects of the solver, higher performance can be achieved over some best existing solvers on a large set of benchmarks. This provides motivation for further research into these more important aspects of SAT algorithms, which we hope will lead to future significant advances in SAT.