Towards an algebra for real-time programs

Authors:
Brijesh Dongol;Ian J. Hayes;Larissa Meinicke;Kim Solin
Affiliations:
Department of Computer Science, The University of Sheffield, UK;School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane, Australia;School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane, Australia;School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane, Australia
Venue:
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
Year:
2012

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Abstract

We develop an algebra for an interval-based model that has been shown to be useful for reasoning about real-time programs. In that model, a system's behaviour over all time is given by a stream (mapping each time to a state) and the behaviour over an interval is determined using an interval predicate, which maps an interval and a stream to a Boolean. Intervals are allowed to be open/closed at either end and adjoining (i.e., immediately adjacent) intervals do not share any common points but are contiguous over their boundary. Values of variables at the ends of open intervals are determined using limits, which allows the possible piecewise continuity of a variable at the boundaries of an interval to be handled in a natural manner. What sort of an algebra does this model give rise to? In this paper, we take a step towards answering that question by investigating an algebra of interval predicates.