Breaking Instance-Independent Symmetries In Exact Graph Coloring

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature

SPEEDING UP MODEL-BASEDDIAGNOSIS BYAHEURISTICAPPROACH TOSOLVING SAT

Model-based diagnosis of technical systems requires both a simulation machinery and a logic calculus. The former is responsible for the system’s behavior analysis, the latter controlstheactualdiagnosisprocess. Especiallywhenpursuing qualitative simulation, it makes sense to realize the simulation machinerywith a logic calculus as well. Say, a qualitatively described hypothesis can directly be mapped onto an instance of the well-known SAT problem. Likewise, an entire diagnosis process, i.e., a sequence of hypothesisrefinements,representsa set ofSATproblems. This paper reports on the operationalization of such a SAT-based diagnosis approach. A specific characteristic hereisthe ideato exploitan orderingofthelogicalformulas according to their likeliness of being satisfiable. Thi

Learning in planning with temporally extended goals and uncontrollable events

Recent contributions to advancing planning from the classical model to more realistic problems include using temporal logic such as LTL to express desired properties of a solution plan. This paper introduces a planning model that combines temporally extended goals and uncontrollable events. The planning task is to reach a state such that all event sequences generated from that state satisfy the problem's temporally extended goal. A real-life application that motivates this work is to use planning to configure a system in such a way that its subsequent, non-deterministic internal evolution (nominal behavior) is guaranteed to satisfy a condition expressed in temporal logic. A solving architecture is presented that combines planning, model checking and learning. An online learning process incrementally discovers information about the problem instance at hand. The learned information is useful both to guide the search in planning and to safely avoid unnecessary calls to the model checking module. A detailed experimental analysis of the approach presented in this paper is included. The new method for online learning is shown to greatly improve the system performance.NICTA is funded by the Australian Government’s Department of Communications, Information Technology, and the Arts and the Australian Research Council through Backing Australia’s Ability and the ICT Research Centre of Excellence program

Target oriented relational model finding

Lecture Notes in Computer Science 8411, 2014Model finders are becoming useful in many software engineering problems. Kodkod is one of the most popular, due to its support for relational logic (a combination of first order logic with relational algebra operators and transitive closure), allowing a simpler specification of constraints, and support for partial instances, allowing the specification of a priori (exact, but potentially partial) knowledge about a problem's solution. However, in some software engineering problems, such as model repair or bidirectional model transformation, knowledge about the solution is not exact, but instead there is a known target that the solution should approximate. In this paper we extend Kodkod's partial instances to allow the specification of such targets, and show how its model finding procedure can be adapted to support them (using both PMax-SAT solvers or SAT solvers with cardinality constraints). Two case studies are also presented, including a careful performance evaluation to assess the effectiveness of the proposed extension.(undefined

The Incremental Satisfiability Problem for a Two Conjunctive Normal Form

We propose a novel method to review K ⊢ φ when K and φ are both in Conjunctive Normal Forms (CF). We extend our method to solve the incremental satisfiablity problem (ISAT), and we present different cases where ISAT can be solved in polynomial time. Especially, we present an algorithm for 2-ISAT. Our last algorithm allow us to establish an upper bound for the time-complexity of 2-ISAT, as well as to establish some tractable cases for the 2-ISAT problem