Zero-Suppressed Computation: A New Computation Inspired by ZDDs

TL;DR

This paper introduces zero-suppressed computation, a novel computation model inspired by ZDDs, and explores its implications by adapting classical models like decision trees and branching programs within this framework.

Contribution

It proposes the concept of zero-suppressed computation and extends classical models to this new paradigm, opening avenues for theoretical and practical applications.

Findings

Defined zero-suppressed decision trees and branching programs.

Analyzed the computational complexity of zero-suppressed models.

Suggested broad applicability of zero-suppressed computation across areas.

Abstract

Zero-suppressed binary decision diagrams (ZDDs) are a data structure representing Boolean functions, and one of the most successful variants of binary decision diagrams (BDDs). On the other hand, BDDs are also called branching programs in computational complexity theory, and have been studied as a computation model. In this paper, we consider ZDDs from the viewpoint of computational complexity theory. Our main proposal of this paper is that we regard the basic idea of ZDDs as a new computation, which we call zero-suppressed computation. We consider the zero-suppressed version of two classical computation models, decision trees and branching programs, and show some results. Although this paper is mainly written from the viewpoint of computational complexity theory, the concept of zero-suppressed computation can be widely applied to various areas.