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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Back, R.J., Von Wright, J.: Refinement Calculus: A Systematic Introduction. Springer-Verlag New York, Inc., Secaucus (1998)
Burns, A., Hayes, I.J.: A timeband framework for modelling real-time systems. Real-Time Systems 45(1), 106–142 (2010)
Desharnais, J., Möller, B., Struth, G.: Kleene algebra with domain. ACM Trans. Comput. Log. 7(4), 798–833 (2006)
Dongol, B., Hayes, I.J.: Approximating idealised real-time specifications using time bands. In: AVoCS 2011. ECEASST, vol. 46, pp. 1–16. EASST (2012)
Dongol, B., Hayes, I.J.: Deriving Real-Time Action Systems Controllers from Multiscale System Specifications. In: Gibbons, J., Nogueira, P. (eds.) MPC 2012. LNCS, vol. 7342, pp. 102–131. Springer, Heidelberg (2012)
Dongol, B., Hayes, I.J.: Deriving real-time action systems in a sampling logic. Science of Computer Programming (2012) (accepted October 17, 2011)
Dongol, B., Hayes, I.J.: Rely/Guarantee Reasoning for Teleo-reactive Programs over Multiple Time Bands. In: Derrick, J., Gnesi, S., Latella, D., Treharne, H. (eds.) IFM 2012. LNCS, vol. 7321, pp. 39–53. Springer, Heidelberg (2012)
Dongol, B., Hayes, I.J., Robinson, P.J.: Reasoning about real-time teleo-reactive programs. Technical Report SSE-2010-01, The University of Queensland (2010)
Guttmann, W., Struth, G., Weber, T.: Automating Algebraic Methods in Isabelle. In: Qin, S., Qiu, Z. (eds.) ICFEM 2011. LNCS, vol. 6991, pp. 617–632. Springer, Heidelberg (2011)
Hayes, I.J.: Towards reasoning about teleo-reactive programs for robust real-time systems. In: Proceedings of the 2008 RISE/EFTS Joint International Workshop on Software Engineering for Resilient Systems, pp. 87–94. ACM, New York (2008)
Hayes, I.J., Burns, A., Dongol, B., Jones, C.B.: Comparing models of nondeterministic expression evaluation. Technical Report CS-TR-1273, Newcastle University (2011)
Henzinger, T.A.: The theory of hybrid automata. In: LICS 1996, pp. 278–292. IEEE Computer Society, Washington, DC (1996)
Höfner, P., Möller, B.: Algebraic neighbourhood logic. J. Log. Algebr. Program. 76(1), 35–59 (2008)
Höfner, P., Möller, B.: An algebra of hybrid systems. J. Log. Algebr. Program. 78(2), 74–97 (2009)
Jones, C.B., Hayes, I.J., Jackson, M.A.: Deriving Specifications for Systems That Are Connected to the Physical World. In: Jones, C.B., Liu, Z., Woodcock, J. (eds.) Bjørner/Zhou Festschrift. LNCS, vol. 4700, pp. 364–390. Springer, Heidelberg (2007)
Moszkowski, B.C.: A complete axiomatization of interval temporal logic with infinite time. In: LICS, pp. 241–252 (2000)
Schobbens, P.-Y., Raskin, J.-F., Henzinger, T.A.: Axioms for real-time logics. Theor. Comput. Sci. 274(1-2), 151–182 (2002)
von Wright, J.: From Kleene Algebra to Refinement Algebra. In: Boiten, E.A., Möller, B. (eds.) MPC 2002. LNCS, vol. 2386, pp. 233–262. Springer, Heidelberg (2002)
Zhou, C., Hansen, M.R.: Duration Calculus: A Formal Approach to Real-Time Systems. EATCS: Monographs in Theoretical Computer Science. Springer (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dongol, B., Hayes, I.J., Meinicke, L., Solin, K. (2012). Towards an Algebra for Real-Time Programs. In: Kahl, W., Griffin, T.G. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2012. Lecture Notes in Computer Science, vol 7560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33314-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-33314-9_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33313-2
Online ISBN: 978-3-642-33314-9
eBook Packages: Computer ScienceComputer Science (R0)