Complete search algorithms for model counting, inference, and optimization problems. Tian Sang

ISBN: 9780549815488

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NOOKstudy eTextbook

113 pages


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Complete search algorithms for model counting, inference, and optimization problems.  by  Tian Sang

Complete search algorithms for model counting, inference, and optimization problems. by Tian Sang
| NOOKstudy eTextbook | PDF, EPUB, FB2, DjVu, audiobook, mp3, ZIP | 113 pages | ISBN: 9780549815488 | 6.24 Mb

Although NP-complete problems including satisfiability testing (SAT) are traditionally thought as intractable, the efficiency of SAT solvers has been hugely improved over the past decade and a half, and modern SAT solvers are successfully used toMoreAlthough NP-complete problems including satisfiability testing (SAT) are traditionally thought as intractable, the efficiency of SAT solvers has been hugely improved over the past decade and a half, and modern SAT solvers are successfully used to solve many practical hard problems in hardware/software verification, planning, diagnosis, and other areas.

Despite the popularity of SAT, #SAT, the problem of counting models of a formula, has been much less exploited. That is partly due to the #P hardness of model counting, which may remain hard even if SAT is in P. This thesis focuses on how to design a new sound, complete, and efficient #SAT algorithm, which is a novel integration of several major techniques including dynamic decomposition, component caching, clause learning, branching heuristics binary clause propagation and backtracking.

Finally, it shows how to apply the resulting #SAT solver Cachet to (1) Bayesian inference via CNF encoding and weighted model counting, and (2) various optimization problems such as Most Probable Explanation (MPE), Maximum Satisfiability (MAX-SAT) and Maximum A Posteriori (MAP) by extending it with dynamic bounding. This thesis reports empirical results on a wide range of problem domains, compares our solver with other state-of-the-art solvers and concludes that our approach is often significantly better than or at least very competitive with others.

The main contribution of this work is to present new efficient #SAT-based algorithms and show how they can be successfully applied to some hard AI problems that require exhaustive search.



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