Partial Quantifier Elimination By Certificate Clauses
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We study a modification of the Quantifier Elimination (QE) problem called Partial QE (PQE) for propositional CNF formulas. In PQE, only a small subset of target clauses is taken out of the scope of quantifiers. The appeal of PQE is that many verification problems, e.g. equivalence checking and model checking, reduce to PQE and, intuitively, the latter should be much easier than QE. One can perform PQE by adding a set of clauses depending only on free variables that make the target clauses redundant. Proving redundancy of a target clause is done by derivation of a "certificate" clause implying the former. This idea is implemented in our PQE algorithm called START. It bears some similarity to a SAT-solver with conflict driven learning. A major difference here is that START backtracks when a target clause is proved redundant in the current subspace (a conflict being just one of backtracking conditions). We experimentally evaluate START on a practical problem. We use this problem to show that PQE can be much easier than QE.
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