Exploiting Structure in Backtracking Algorithms for Propositional and Probabilistic Reasoning

Boolean propositional satisfiability (SAT) and probabilistic reasoning represent two core problems in AI. Backtracking based algorithms have been applied in both problems. In this thesis, I investigate structure-based techniques for solving real world SAT and Bayesian networks, such as software testing and medical diagnosis instances. When solving a SAT instance using backtracking search, a sequence of decisions must be made as to which variable to branch on or instantiate next. Real world problems are often amenable to a divide-and-conquer strategy where the original instance is decomposed into independent sub-problems. Existing decomposition techniques are based on pre-processing the static structure of the original problem. I propose a dynamic decomposition method based on hypergraph separators. Integrating this dynamic separator decomposition into the variable ordering of a modern SAT solver leads to speedups on large real world SAT problems. Encoding a Bayesian network into a CNF formula and then performing weighted model counting is an effective method for exact probabilistic inference. I present two encodings for improving this approach with noisy-OR and noisy-MAX relations. In our experiments, our new encodings are more space efficient and can speed up the previous best approaches over two orders of magnitude. The ability to solve similar problems incrementally is critical for many probabilistic reasoning problems. My aim is to exploit the similarity of these instances by forwarding structural knowledge learned during the analysis of one instance to the next instance in the sequence. I propose dynamic model counting and extend the dynamic decomposition and caching technique to multiple runs on a series of problems with similar structure. This allows us to perform Bayesian inference incrementally as the evidence, parameter, and structure of the network change. Experimental results show that my approach yields significant improvements over previous model counting approaches on multiple challenging Bayesian network instances

Decentralized Constraint Satisfaction

We show that several important resource allocation problems in wireless networks fit within the common framework of Constraint Satisfaction Problems (CSPs). Inspired by the requirements of these applications, where variables are located at distinct network devices that may not be able to communicate but may interfere, we define natural criteria that a CSP solver must possess in order to be practical. We term these algorithms decentralized CSP solvers. The best known CSP solvers were designed for centralized problems and do not meet these criteria. We introduce a stochastic decentralized CSP solver and prove that it will find a solution in almost surely finite time, should one exist, also showing it has many practically desirable properties. We benchmark the algorithm's performance on a well-studied class of CSPs, random k-SAT, illustrating that the time the algorithm takes to find a satisfying assignment is competitive with stochastic centralized solvers on problems with order a thousand variables despite its decentralized nature. We demonstrate the solver's practical utility for the problems that motivated its introduction by using it to find a non-interfering channel allocation for a network formed from data from downtown Manhattan

Efficient Automated Planning with New Formulations

Problem solving usually strongly relies on how the problem is formulated. This fact also applies to automated planning, a key field in artificial intelligence research. Classical planning used to be dominated by STRIPS formulation, a simple model based on propositional logic. In the recently introduced SAS+ formulation, the multi-valued variables naturally depict certain invariants that are missed in STRIPS, make SAS+ have many favorable features. Because of its rich structural information SAS+ begins to attract lots of research interest. Existing works, however, are mostly limited to one single thing: to improve heuristic functions. This is in sharp contrast with the abundance of planning models and techniques in the field. On the other hand, although heuristic is a key part for search, its effectiveness is limited. Recent investigations have shown that even if we have almost perfect heuristics, the number of states to visit is still exponential. Therefore, there is a barrier between the nice features of SAS+ and its applications in planning algorithms. In this dissertation, we have recasted two major planning paradigms: state space search and planning as Satisfiability: SAT), with three major contributions. First, we have utilized SAS+ for a new hierarchical state space search model by taking advantage of the decomposable structure within SAS+. This algorithm can greatly reduce the time complexity for planning. Second, planning as Satisfiability is a major planning approach, but it is traditionally based on STRIPS. We have developed a new SAS+ based SAT encoding scheme: SASE) for planning. The state space modeled by SASE shows a decomposable structure with certain components independent to others, showing promising structure that STRIPS based encoding does not have. Third, the expressiveness of planning is important for real world scenarios, thus we have also extended the planning as SAT to temporally expressive planning and planning with action costs, two advanced features beyond classical planning. The resulting planner is competitive to state-of-the-art planners, in terms of both quality and performance. Overall, our work strongly suggests a shifting trend of planning from STRIPS to SAS+, and shows the power of formulating planning problems as Satisfiability. Given the important roles of both classical planning and temporal planning, our work will inspire new developments in other advanced planning problem domains

Boosting local search thanks to {CDCL}

International audienceIn this paper, a novel hybrid and complete approach for propositional satisfiability, called SAT HYS (Sat Hybrid Solver), is introduced. It efficiently combines the strength of both local search and CDCL based SAT solvers. Considering the consistent partial assignment under construction by the CDCL SAT solver, local search is used to extend it to a model of the Boolean formula, while the CDCL component is used by the local search one as a strategy to escape from a local minimum. Additionally, both solvers heavily cooperate thanks to relevant information gathered during search. Experimentations on SAT instances taken from the last competitions demonstrate the efficiency and the robustness of our hybrid solver with respect to the state-of-the-art CDCL based, local search and hybrid SAT solvers

Optimized Framework based on Rough Set Theory for Big Data Pre-processing in Certain and Imprecise Contexts” -- Marie Sklodowska-Curie Project: Open Problems’

Peer reviewe

ON EQUIVALENCY REASONING FOR CONFLICT DRIVEN CLAUSE LEARNING SATISFIABILITY SOLVERS

Satisfiability problem or SAT is the problem of deciding whether a Boolean function evaluates to true for at least one of the assignments in its domain. The satisfiability problem is the first problem to be proved NP-complete. Therefore, the problems in NP can be encoded into SAT instances. Many hard real world problems can be solved when encoded efficiently into SAT instances. These facts give SAT an important place in both theoretical and practical computer science. In this thesis we address the problem of integrating a special class of equivalency reasoning techniques, the strongly connected components or SCC based reasoning, into the class of conflict driven clause learning or CDCL SAT solvers. Because of the complications that arise from integrating the equivalency reasoning in CDCL SAT solvers, to our knowledge, there has been no CDCL solver which has applied SCC based equivalency reasoning dynamically during the search. We propose a method to overcome these complications. The method is integrated into a prominent satisfiability solver: MiniSat. The equivalency enhanced MiniSat, Eq-MiniSat, is used to explore the advantages and disadvantages of the equivalency reasoning in conflict clause learning satisfiability solvers. Different implementation approaches for Eq-MiniSat are discussed. The experimental results on 16 families of instances shows that equivalency reasoning does not have noticeable effects for the instances in one family. The equivalency reasoning enables Eq-MiniSat to outperform MiniSat on eight classes of instances. For the remaining seven families, MiniSat outperforms Eq- MiniSat. The experimental results for random instances demonstrate that almost in all cases the number of branchings for Eq-Minisat is smaller than Minisat