Classifying and Propagating Parity Constraints (extended version)

TL;DR

This paper investigates the effectiveness of unit propagation and equivalence reasoning in propagating parity constraints, providing efficient tests and demonstrating how to simulate equivalence reasoning with unit propagation through added constraints.

Contribution

It introduces efficient approximation tests for deciding propagation sufficiency and shows how to simulate equivalence reasoning with unit propagation using polynomially many redundant constraints.

Findings

Efficient tests for propagation sufficiency are developed.

Equivalence reasoning can be simulated by unit propagation with added constraints.

Without additional variables, exponential constraints are needed in the worst case.

Abstract

Parity constraints, common in application domains such as circuit verification, bounded model checking, and logical cryptanalysis, are not necessarily most efficiently solved if translated into conjunctive normal form. Thus, specialized parity reasoning techniques have been developed in the past for propagating parity constraints. This paper studies the questions of deciding whether unit propagation or equivalence reasoning is enough to achieve full propagation in a given parity constraint set. Efficient approximating tests for answering these questions are developed. It is also shown that equivalence reasoning can be simulated by unit propagation by adding a polynomial amount of redundant parity constraints to the problem. It is proven that without using additional variables, an exponential number of new parity constraints would be needed in the worst case. The presented classification and propagation methods are evaluated experimentally.