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Parity constraints, common in application domains such as circuitverification, bounded model checking, and logical cryptanalysis, are notnecessarily most efficiently solved if translated into conjunctive normal form.Thus, specialized parity reasoning techniques have been developed in the pastfor propagating parity constraints. This paper studies the questions ofdeciding whether unit propagation or equivalence reasoning is enough to achievefull propagation in a given parity constraint set. Efficient approximatingtests for answering these questions are developed. It is also shown thatequivalence reasoning can be simulated by unit propagation by adding apolynomial amount of redundant parity constraints to the problem. It is proventhat without using additional variables, an exponential number of new parityconstraints would be needed in the worst case. The presented classification andpropagation methods are evaluated experimentally.

Classifying and Propagating Parity Constraints (extended version)