On Lower Bounds for Parity Branching Programs

Diese Arbeit beschaeftigt sich mit der Komplexität von parity Branching Programmen. Es werden superpolynomiale untere Schranken für verschiedene Varianten bewiesen, nämlich für well-structured graph-driven parity branching programs, general graph-driven parity branching programs und Summen von graph-driven parity branching programs

Characterizing the Complexity of Boolean Functions represented by Well-Structured Graph-Driven Parity-FBDDs

We investigate well-structured graph-driven parity-FBDDs, which strictly generalize the two well-known models parity OBDDs and well-structured graph-driven FBDDs. The first main result is a characterization of the complexity of Boolean functions represented by well-structured graph-driven parity-FBDDs in terms of invariants of the function represented and the graph-ordering used. As a consequence, we derive a lower bound criterion and prove an exponential lower bound for certain linear code functions. The second main result of this paper is a polynomial time algorithm that minimizes the number of nodes in a graph-driven parity-FBDD