Mathematical Principles in Software Quality Engineering

TL;DR

This paper explores how mathematical principles, especially discrete mathematics and graph theory, enhance the validation, modeling, and testing of complex software systems through precise, unambiguous methods.

Contribution

It demonstrates the application of mathematical properties to improve validation and analysis in software quality engineering, emphasizing structural and functional testing techniques.

Findings

Mathematics provides high validation accuracy in software modeling.

Structural testing is well-suited for rigorous mathematical analysis.

Discrete mathematics and graph theory are effective for functional and structural testing, respectively.

Abstract

Mathematics has many useful properties for developing of complex software systems. One is that it can exactly describe a physical situation of the object or outcome of an action. Mathematics support abstraction and this is an excellent medium for modeling, since it is an exact medium there is a little possibility of ambiguity. This paper demonstrates that mathematics provides a high level of validation when it is used as a software medium. It also outlines distinguishing characteristics of structural testing which is based on the source code of the program tested. Structural testing methods are very amenable to rigorous definition, mathematical analysis and precise measurement. Finally, it also discusses functional and structural testing debate to have a sense of complete testing. Any program can be considered to be a function in the sense that program input forms its domain and program outputs form its range. In general discrete mathematics is more applicable to functional testing, while graph theory pertains more to structural testing.