Software Cognitive Complexity Measure Based on Scope of Variables

TL;DR

This paper introduces a mathematical model of program structure and a new cognitive complexity measure called SICN, validated through theoretical properties, to better understand software complexity.

Contribution

It presents a unified mathematical framework for program structure and proposes the SICN complexity measure based on variable scope analysis.

Findings

The model treats programs as sets of embedded binary relations.

SICN effectively captures cognitive complexity related to variable scope.

The measure is validated against Weyuker's properties.

Abstract

In this paper, we define a Mathematical model of program structure. Mathematical model of program structure defined here provides unified mathematical treatment of program structure, which reveals that a program is a large and finite set of embedded binary relations between current statement and previous ones. Then, a program is considered as a composed listing and a logical combination of multiple statements according to the certain composing rules. We also define the Scope Information Complexity Number (SICN) and present the cognitive complexity based on functional decomposition of software, including theoretical validation through nine Weyuker's properties.