Abstract. We tackle the problem of finding a smallest-cardinality MUS (SMUS) of a given formula. The SMUS provides a succinct explanation of infeasibility and is valuable for applications that rely on such explanations. We present a branch-and-bound algorithm that utilizes iterative MAXSAT solutions to generate lower and upper bounds on the size of the SMUS, and branch on specific subformulas to find it. We report experimental results on formulas from DIMACS and DaimlerChrysler product configuration suites.
Determining the depth of sequential circuits is a crucial step towards the completeness of bounded model checking proofs in hardware verification. In this paper, we formulate sequential depth computation as a logical inference problem for Quantified Boolean Formulas. We introduce a novel technique to simplify the complexity of the constructed formulas by applying simple transformations to the circuit netlist. We also study the structure of the resulting simplified QBFs and construct an efficient SAT-based algorithm to check their satisfiability. We report promising experimental results on some of the ISCAS 89 benchmarks.
Explaining the causes of infeasibility of Boolean formulas has practical applications in numerous fields, such as artificial intelligence (repairing inconsistent knowledge bases), formal verification (abstraction refinement and unbounded model checking), and electronic design (diagnosing and correcting infeasibility). Minimal unsatisfiable subformulas (MUSes) provide useful insights into the causes of infeasibility. An unsatisfiable formula often has many MUSes. Based on the application domain, however, MUSes with specific properties might be of interest. In this paper, we tackle the problem of finding a smallest-cardinality MUS (SMUS) of a given formula. An SMUS provides a succinct explanation of infeasibility and is valuable for applications that are heavily affected by the size of the explanation. We present (1) a baseline algorithm for finding an SMUS, founded on earlier work for finding all MUSes, and (2) a new branch-and-bound algorithm called Digger that computes a strong lower bound on the size of an SMUS and splits the problem into more tractable subformulas in a recursive search tree. Using two benchmark 416 Constraints (2009) 14:415-442 suites, we experimentally compare Digger to the baseline algorithm and to an existing incomplete genetic algorithm approach. Digger is shown to be faster in nearly all cases. It is also able to solve far more instances within a given runtime limit than either of the other approaches.
We introduce a new verification methodology for modern microprocessors that uses a simple checker processor to validate the execution of a companion high-performance processor. The checker can be viewed as an at-speed emulator that is formally verified to be compliant to an ISA specification. This verification approach enables the practical deployment of formal methods without impacting overall performance.
This paper describes a new algorithm for extracting unsatisfiable subformulas from a given unsatisfiable CNF formula. Such unsatisfiable "cores" can be very helpful in diagnosing the causes of infeasibility in large systems. Our algorithm is unique in that it adapts the "learning process" of a modern SAT solver to identify unsatisfiable subformulas rather than search for satisfying assignments. Compared to existing approaches, this method can be viewed as a bottom-up core extraction procedure which can be very competitive when the core sizes are much smaller than the original formula size. Repeated runs of the algorithm with different branching orders yield different cores. We present experimental results on a suite of large automotive benchmarks showing the performance of the algorithm and highlighting its ability to locate not just one but several cores.
We introduce a new approach to Boolean satisfiability (SAT) that combines backtrack search techniques and zero-suppressed binary decision diagrams (ZBDDs). This approach implicitly represents SAT instances using ZBDDs, and performs search using an efficient implementation of unit propagation on the ZBDD structure. The adaptation of backtrack search algorithms to such an implicit representation allows for a potential exponential increase in the size of problems that can be handled.
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