The need for new forms of mathematics to express software engineering concepts and entities has been widely recognized. Real-time process algebra (RTPA) is a denotational mathematical structure and a system modeling methodology for describing the architectures and behaviors of real-time and nonrealtime software systems. This article presents an operational semantics of RTPA, which explains how syntactic constructs in RTPA can be reduced to values on an abstract reduction machine. The operational semantics of RTPA provides a comprehensive paradigm of formal semantics that establishes an entire set of operational semantic rules of software. RTPA has been successfully applied in real-world system modeling and code generation for software systems, human cognitive processes, and intelligent systems.
