On Mathematical Laws of Software

Recent studies on the laws and mathematical constraints of software have resulted in fundamental discoveries in computing and software engineering toward exploring the nature of software. It was recognized that software is not 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 of software and computing behaviors. A generic mathematical model of programs is created that reveals the nature of software as abstract processes and its uniqueness beyond other mathematical entities such as sets, relations, functions, and abstract concepts. A comprehensive set of mathematical laws for software and its behaviors is established based on the generic mathematical model of programs and the fundamental computing behaviors elicited in Real-Time Process Algebra (RTPA). A set of 95 algebraic laws of software behaviors is systematically derived, which encompasses the laws of meta-processes, process relations, and system compositions. The comprehensive set of mathematical laws of software lays a theoretical foundation for analyzing and modeling software behaviors and software system architectures, as well as for guiding rigorous practice in programming. They are also widely applicable for the rigorous modeling and manipulation of human cognitive processes and computational intelligent behaviors.