On Lower Bounds for Parity Branching Programs

Abstract

This thesis concerns the complexity of parity branching programs with limitations on the way in which variables may be read.Interest in such branching programs has been raised by a popular method for verifying hardware circuits. Oblivious read-once branching programs (or OBDDs). Recently, Parity OBDDs have been studied intensively and have been found very useful in this application, too.Thus, one is interested in lower bounds for restricted parity branching programs. While exponential lower bounds for deterministic as well as nondeterministic read-once branching programs are known for a long time, superpolynomial lower bounds for parity read-once branching programs are still a challenge.In this thesis three different restricted variants of parity read-once branching programs are under consideration, well-structured graph-driven parity branching programs, general graph-driven parity branching programs and sums of graph-driven parity branching programs. We present superpolynomial lower bounds for these models and natural functions, for instance, for linear codes and permutation matrices. These lower bounds are the most general ones known in this area. In addition, algorithmic properties of the considered models are discussed.