A theory for execution-time derivation in real-time programs

Authors:
Karl Lermer;Colin J. Fidge;Ian J. Hayes
Affiliations:
School of Information Technology and Electrical Engineering, The University of Queensland, Queensland, Australia;School of Software Engineering and Data Communications, Queensland University of Technology, Queensland, Australia;School of Information Technology and Electrical Engineering, The University of Queensland, Queensland, Australia
Venue:
Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
Year:
2005

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Abstract

We provide an abstract command language for real-time programs and outline how a partial correctness semantics can be used to compute execution times. The notions of a timed command, refinement of a timed command, the command traversal condition, and the worst-case and best-case execution time of a command are formally introduced and investigated with the help of an underlying weakest liberal precondition semantics. The central result is a theory for the computation of worst-case and best-case execution times from the underlying semantics based on supremum and infimum calculations. The framework is applied to the analysis of a message transmitter program and its implementation.