Nondeterminism and an abstract formulation of Ne\v{c}iporuk's lower bound method

TL;DR

This paper presents a generalized formulation of Nece9poruk's lower bound method, analyzes its limitations across various models including nondeterministic and parity branching programs, and establishes upper bounds on achievable lower bounds.

Contribution

It introduces a more inclusive abstract formulation of Nece9poruk's method and derives fundamental limitations for its application to nondeterministic computational models.

Findings

Limitations of the method for nondeterministic branching programs

Upper bounds on lower bounds for parity branching programs

Generalized formulation applicable to multiple models

Abstract

A formulation of "Ne\v{c}iporuk's lower bound method" slightly more inclusive than the usual complexity-measure-specific formulation is presented. Using this general formulation, limitations to lower bounds achievable by the method are obtained for several computation models, such as branching programs and Boolean formulas having access to a sublinear number of nondeterministic bits. In particular, it is shown that any lower bound achievable by the method of Ne\v{c}iporuk for the size of nondeterministic and parity branching programs is at most $O(n^{3/2}/\log n)$.