Width Hierarchy for k-OBDD of Small Width

TL;DR

This paper establishes a width hierarchy for the k-OBDD model, demonstrating how the complexity of Boolean functions relates to their representability within this computational framework.

Contribution

It introduces a new hierarchy based on width for k-OBDDs and provides a method to distinguish functions that cannot be represented within certain width bounds.

Findings

Proven width-based hierarchy of Boolean function classes for k-OBDDs

Identified sufficient conditions for non-representability of functions as k-OBDDs

Modified Pointer Jumping and ISA functions to demonstrate hierarchy

Abstract

In this paper was explored well known model k-OBDD. There are proven width based hierarchy of classes of boolean functions which computed by k-OBDD. The proof of hierarchy is based on sufficient condition of Boolean function's non representation as k-OBDD and complexity properties of Boolean function SAF. This function is modification of known Pointer Jumping (PJ) and Indirect Storage Access (ISA) functions.