1 research outputs found
CNF Encodings of Parity
The minimum number of clauses in a CNF representation of the parity function
is . One can obtain a more
compact CNF encoding by using non-deterministic variables (also known as guess
or auxiliary variables). In this paper, we prove the following lower bounds,
that almost match known upper bounds, on the number of clauses and the
maximum width of clauses: 1) if there are at most auxiliary variables,
then and ; 2) the
minimum number of clauses is at least . We derive the first two bounds from
the Satisfiability Coding Lemma due to Paturi, Pudlak, and Zane