Counting false entries in truth tables of bracketed formulae connected by m-implication

TL;DR

This paper analyzes the number of false entries in truth tables of bracketed formulae with n variables connected by modified-implication, providing recurrence relations, asymptotic formulas, and parity results.

Contribution

It introduces a recurrence and asymptotic formulae for counting false entries in truth tables of bracketed formulae with modified-implication, advancing combinatorial logic analysis.

Findings

Derived a recurrence relation for false entries count

Established asymptotic formulae for large n

Determined the parity of the false entries count

Abstract

In this paper we count the number of rows yn with the value "false" in the truth tables of all bracketed formulae with n distinct variables connected by the binary connective of 2modified-implication". We find a recurrence and an asymptotic formulae for yn. We also determine the parity of yn.