On Efficient Algorithms For Partial Quantifier Elimination (2406.01307v1)

Abstract: Earlier, we introduced Partial Quantifier Elimination (PQE). It is a $\mathit{generalization}$ of regular quantifier elimination where one can take a $\mathit{part}$ of the formula out of the scope of quantifiers. We apply PQE to CNF formulas of propositional logic with existential quantifiers. The appeal of PQE is that many problems like equivalence checking and model checking can be solved in terms of PQE and the latter can be very efficient. The main flaw of current PQE solvers is that they do not $\mathit{reuse}$ learned information. The problem here is that these PQE solvers are based on the notion of clause redundancy and the latter is a $\mathit{structural}$ rather than $\mathit{semantic}$ property. In this paper, we provide two important theoretical results that enable reusing the information learned by a PQE solver. Such reusing can dramatically boost the efficiency of PQE like conflict clause learning boosts SAT solving.