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After establishing the unsatisfiability of a SAT instance encoding a typical design task, there is a practical need to identify its minimal unsatisfiable subsets, which pinpoint the reasons for the infeasibility of the design. Due to the potentially expensive computation, existing tools for the extraction of unsatisfiable subformulas do not guarantee the… (More)

Due to large search spaces, diagnosis of combina-tional circuits is often practical for finding only single and double faults. In principle, system models can be compiled into a tractable representation (such as DNNF) on which faults of arbitrary cardi-nality can be found efficiently. For large circuits, however, compilation can become a bottleneck due to… (More)

We propose a variable ordering heuristic for SAT, which is based on a structural analysis of the SAT problem. We show that when the heuristic is used by a Davis-Putnam SAT solver that employs conflict-directed backtracking, it produces a divide-and-conquer behavior in which the SAT problem is recursively decomposed into smaller problems that are solved… (More)

Fundamentally different from DPLL, a new approach to SAT has recently emerged that abandons search and enlists BDDs to symbolically represent clauses of the CNF. These BDDs are conjoined according to a schedule where some variables may be eliminated by quantification at each step to reduce the size of the intermediate BDDs. SAT solving then reduces to… (More)

The DPLL procedure has found great success in SAT, where search terminates on the first solution discovered. We show that this procedure is equally promising in a problem where exhaustive search is used, given that it is augmented with appropriate caching. Specifically, we propose two DPLL-based algorithms that construct OBDDs for CNF formulas. These… (More)

- Jinbo Huang
- CP
- 2008

While the efficiency and scalability of modern SAT technology offers an intriguing alternative approach to constraint solving via translation to SAT, previous work has mostly focused on the translation of specific types of constraints, such as pseudo Boolean constraints, finite integer linear constraints, and constraints given as explicit listings of… (More)

- Jinbo Huang
- CP
- 2007

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… (More)

The MAP (maximum a posteriori hypothesis) problem in Bayesian networks is to find the most likely states of a set of variables given partial evidence on the complement of that set. Standard structure-based inference methods for finding exact solutions to MAP, such as variable elimination and join-tree algorithms, have complexities that are exponential in… (More)

When a system behaves abnormally, sequential diagnosis takes a sequence of measurements of the system until the faults causing the abnormality are identified, and the goal is to reduce the diagnostic cost, defined here as the number of measurements. To propose measurement points, previous work employs a heuristic based on reducing the entropy over a… (More)

We show that the trace of an exhaustive DPLL search can be viewed as a compilation of the propo-sitional theory. With different constraints imposed or lifted on the DPLL algorithm, this compilation will belong to the language of d-DNNF, FBDD, and OBDD, respectively. These languages are decreas-ingly succinct, yet increasingly tractable, supporting such… (More)