Abstract
Different temporal logics tend to emphasise different aspects of a hybrid system. In this paper, we study the predicative interpretation of Duration Calculus (DC) and Temporal Logic of Actions (TLA) and the link between them. A notation called generic composition is used to simplify the manipulation of predicates. The modalities of possibility and necessity become generic composition and its inverse of converse respectively. The transformation between different temporal logics is also characterised as such modalities. The formalism provides a framework in which human experience about hybrid system development can be formalised as refinement laws. A high-level durational specification can be decomposed to two durational specifications driven by an automaton. In such a stepwise design process, durational features are reduced while automaton features increase gradually. The application of the technique is demonstrated in the case study of the gas burner problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Back, R., von Wright, J.: Refinement Calculus: A Systematic Introduction. In: Graduate Texts in Computer Science. Springer, Heidelberg (1998)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)
Chen, Y.: Generic composition. Formal Aspects of Computing 14(2), 108–122 (2002)
Chen, Y.: Cumulative computing. In: 19th Conference on the Mathematical Foundations of Programming Semantics. Electronic Notes in Theoretical Computer Science, vol. 38. Elsevier, Amsterdam (2004)
Chen, Y.F., Liu, Z.: Integrating temporal logics. In: Boiten, E.A., Derrick, J., Smith, G.P. (eds.) IFM 2004. LNCS, vol. 2999, pp. 402–420. Springer, Heidelberg (2004)
Hehner, E.C.R.: Predicative programming I, II. Communications of ACM 27(2), 134–151 (1984)
Hoare, C.A.R.: Communicating Sequential Processes. Prentice-Hall, Englewood Cliffs (1985)
Hoare, C.A.R., He, J.: Unifying Theories of Programming. Prentice-Hall, Englewood Cliffs (1998)
Kripke, S.: Semantical considerations on modal logic. Acta Philosophica Fennica 16, 83–94 (1963)
Lamport, L.: Hybrid systems in TLA+. In: Grossman, R.L., Ravn, A.P., Rischel, H., Nerode, A. (eds.) HS 1991 and HS 1992. LNCS, vol. 736, pp. 77–102. Springer, Heidelberg (1993)
Lamport, L.: A temporal logic of actions. ACM Transctions on Programming Languages and Systems 16(3), 872–923 (1994)
Liu, Z., Ravn, A.P., Li, X.: Unifying proof methodologies of duration calculus and linear temporal logic. Technical Report 1999/14, Department of Maths and Computer Science. University of Leicester (July 1999 ), Formal Aspects of Computing, 19 pages (to appear)
Morgan, C.C.: The cuppest capjunctive capping, and Galois. In: Roscoe, A.W. (ed.) A Classical Mind, pp. 317–332. Prentice-Hall, Englewood Cliffs (1994)
Pnueli, A.: The temporal semantics of concurrent programs. Theoretical Computer Science 13, 45–60 (1981)
Pnueli, A., Harel, E.: Applications of temporal logic to the specification of real-time systems. In: Joseph, M. (ed.) FTRTFT 1988. LNCS, vol. 331, pp. 84–98. Springer, Heidelberg (1988)
Ravn, A.P., Rischel, H., Hansen, K.M.: Specifying and verifying requirements of real-time systems. IEEE Transactions on Software Engineering 19(1), 41–55 (1993)
Schenke, M., Olderog, E.: Transformational design of real-time systems part I: From requirements to program specifications. Acta Informatica 36(1), 1–65 (1999)
Shalqvist, H.: Completeness and correspondence in the first and second order semantics for modal logic. In: Proceedings of the third Scandinavian logic symposium, pp. 110–143. North-Holland, Amsterdam (1975)
von Karger, B.: A calculational approach to reactive systems. Science of Computer Programming 37, 139–161 (2000)
Zhou, C., Hoare, C.A.R., Ravn, A.P.: A calculus of durations. Information Processing Letters 40(5), 269–276 (1991)
Zhou, C.C., Ravn, A.P., Hansen, M.R.: An extended duration calculus for hybrid real-time systems. In: Grossman, R.L., Ravn, A.P., Rischel, H., Nerode, A. (eds.) HS 1991 and HS 1992. LNCS, vol. 736, pp. 36–59. Springer, Heidelberg (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, Y., Liu, Z. (2004). From Durational Specifications to TLA Designs of Timed Automata. In: Davies, J., Schulte, W., Barnett, M. (eds) Formal Methods and Software Engineering. ICFEM 2004. Lecture Notes in Computer Science, vol 3308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30482-1_38
Download citation
DOI: https://doi.org/10.1007/978-3-540-30482-1_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23841-6
Online ISBN: 978-3-540-30482-1
eBook Packages: Springer Book Archive