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this paper concurrent transition systems, where communication between concurrent components is modeled explicitly. Assuming boundedness of the treewidth of the communication graph, which we refer to as local treewidth, is reasonable, since the topology of communication in concurrent systems is often constrained physically

Abstract: This paper presents a new technique to derive an initial static variable ordering for efficient SAT search. Our approach not only exploits variable activity and connectivity information simultaneously, but it also analyzes how tightly the variables are related to each other. For this purpose, a new metric is proposed- the degree of correlation among pairs of variables. Variable activity and correlation information is modeled (implicitly) as a weighted graph. A topological analysis of this graph generates an order for SAT search. An algorithm called ACCORD (ACtivity- CORrelation- ORDering) is proposed for this purpose. While ACCORD rigorously analyzes constraint-variable dependencies, it does not account for the effect of decision-assignments on clause-variable dependencies. This issue motivates further refinements to our approach using literal activity and correlation measures- giving rise to the L’ACCORD algorithm. Using efficient implementations of the above, experiments are conducted over a wide range of benchmarks. The results demonstrate that: (i) the variable order generated by our approach significantly improves the performance of SAT solvers; (ii) time to derive this order is a fraction of the overall solving time. As a result, our approach delivers faster performance (often, by orders of magnitude) as compared to contemporary approaches. 1

Abstract: An important aspect of the Boolean Satisfiability problem is to derive an ordering of variables such that branching on that order results in a faster, more efficient search. Contemporary techniques employ either variable-activity or clauseconnectivity based heuristics, but not both, to guide the search. This paper advocates for simultaneous analysis of variableactivity and clause-connectivity to derive an order for SAT search. Preliminary results demonstrate that the variable order derived by our approach can significantly expedite the search. As the search proceeds, clause database is updated due to added conflict clauses. Therefore, the variable activity and connectivity information changes dynamically. Our technique analyzes this information and re-computes the variable order whenever the search is restarted. Preliminary experiments show that such a dynamic analysis of constraint-variable relationships significantly improves the performance of the SAT solvers. Our technique is very fast and this analysis time is a negligible (in milliseconds) even for instances that contain a large number of variables and constraints. This paper presents preliminary experiments, analyzes the results and comments upon future research directions. I.

Weighted maximum satisfiability is a wellstudied problem that has important applicability to artificial intelligence (for instance, MAP inference in Bayesian networks). General-purpose stochastic search algorithms have proven to be accurate and efficient for large problem instances; however, these algorithms largely ignore structural properties of the input. For example, many problems are highly clustered, in that they contain a collection of loosely coupled subproblems (e.g. pipelines of NLP tasks). In this paper, we propose a message passing algorithm to solve weighted maximum satisfiability problems that exhibit this clustering property. Our algorithm fuses local solutions to each subproblem into a global solution by iteratively passing summary information between clusters and recomputing local solutions. Because the size of these messages can become unwieldy for large problems, we explore several message compression techniques to transmit the most valuable information as compactly as possible. We empirically compare our algorithm against a state-of-the-art stochastic solver and show that for certain classes of problems our message passing algorithm finds significantly better solutions.

The constraint satisfaction problem (CSP) instances modeling problems occurring in practice often have structures which can be exploited to speed-up the constraint solving process. This thesis explores the exploitation of three such structures. The three structures explored in this thesis are: 1. Tree-like relationships: Several CSP instances have tree-like relationships between the variables in them. Such a relationship can be observed by using the tree-width parameter. Given a CSP instance with low tree-width, implying close to tree-like relationship, a treedecomposition of the instance could be used to speed-up the constraint solving process. 2. Compact BDD representation: For some finite-domain constraint problem instances, the solutions of each constraint in those instances might be represented by a compact Binary Decision Diagram (BDD). In which case, it is advantageous to represent the constraints using BDDs.

This deliverable contains all the work done in the project in the analysis and definition of specification and knowledge representation languages.