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By Waller A., Duncan D. B.

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CIRCUIT-ORIENTED SAT 41 Further improvements can be obtained by dedicated data structures. So called AND-inverter graphs [64] directly simplify the circuit by partial canonization. g. [84]. In all these cases, the trade-off between run time and the benefit in solving the problem instance is crucial. Moreover, in the ATPG domain, a powerful preprocessing step that can be reused for all faults is useful. Such techniques will be further discussed throughout this book. Nonetheless, a disadvantage of SAT-based ATPG is the loss of structural information.

An example is the Variable State Independent Decaying Sum (VSIDS) strategy employed in [82]. Basically, this strategy attempts to satisfy recently learned conflict clauses. A counter exists for each literal to count the number of occurrences in clauses. Each time a conflict clause is added, the appropriate counters are incremented. The value of these counters is regularly divided by two which helps to emphasize the influence of more recently learned clauses. g. in [49, 60, 76]. 4 Correctness and Unsatisfiable Cores Typically, a SAT solver takes a CNF formula as input and determines whether the CNF formula is satisfiable or unsatisfiable.

Often the DPLL procedure is also referred to as DLL. 1. To begin, a decision is made by choosing a variable and a value for this variable according to a variable selection strategy (Step 1). Then, implications due to this assignment are carried out (Step 2). When all clauses are satisfied, the problem is solved (Step 3). Otherwise, the current assignment may only be partial and therefore, no conclusion is possible yet. In this case, further assignments are necessary (Step 4). 2. Then, a new branch in the search tree is explored by inverting the value of the variable.

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A bayes rule for the symmetric multiple comparisons problem II by Waller A., Duncan D. B.

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