On mathematical laws of software

  • Authors:

  • Yingxu Wang

  • Affiliations:

  • Theoretical and Empirical Software Engineering Research Centre, International Center for Cognitive Informatics, Dept. of Electrical and Computer Engineering, Schulich School of Engineering, Univer ...

  • Venue:
  • Transactions on computational science II
  • Year:
  • 2008

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Abstract

Recent studies on the laws and mathematical constraints of softwarehave resulted in fundamental discoveries in computing and software engineeringtoward exploring the nature of software. It was recognized that software isnot constrained by any physical laws discovered in the natural world. However,software obeys the laws of mathematics, cognitive informatics, system science,and formal linguistics. This paper investigates into the mathematical laws ofsoftware and computing behaviors. A generic mathematical model of programsis created that reveals the nature of software as abstract processes and itsuniqueness beyond other mathematical entities such as sets, relations, functions,and abstract concepts. A comprehensive set of mathematical laws for softwareand its behaviors is established based on the generic mathematical model ofprograms and the fundamental computing behaviors elicited in Real-Time ProcessAlgebra (RTPA). A set of 95 algebraic laws of software behaviors is systematicallyderived, which encompasses the laws of meta-processes, processrelations, and system compositions. The comprehensive set of mathematicallaws of software lays a theoretical foundation for analyzing and modeling softwarebehaviors and software system architectures, as well as for guiding rigorouspractice in programming. They are also widely applicable for the rigorousmodeling and manipulation of human cognitive processes and computational intelligentbehaviors.