Sequential calculus. (English) Zbl 0875.68202
Summary: This paper presents an algebraic calculus like the relational calculus for reasoning about sequential phenomena. It provides a common foundation for several proposed models of concurrent or reactive systems. It is clearly differentiated from the relational calculus by absence of a general converse operation. This permits the treatment of temporal logic within the sequential calculus.
MSC:
| 68N01 | General topics in the theory of software |
References:
| [1] | Brien, S. M., A time-interval calculus, (Bird, R. S.; Morgan, C. C.; Woodcock, J. C.P., Mathematics of Program Construction. Mathematics of Program Construction, Lecture Notes in Computer Science, 669 (1992), Springer: Springer Berlin) · Zbl 0789.68091 |
| [2] | Dijkstra, E. W., The unification of three calculi, (Broy, M., Program Design Calculi (1993), Springer: Springer Berlin), 197-231 |
| [3] | Higgins, P. J., Categories and Groupoids (1971), van Nostrand Reinhold: van Nostrand Reinhold New York · Zbl 1087.20038 |
| [4] | Hofstee, H. P., A problem in the regularity calculus (1993), California Institute of Technology: California Institute of Technology Pasadena |
| [5] | Hofstee, H. P.; Leino, K. R.M., A proof in the relational calculus (1993), California Institute of Technology: California Institute of Technology Pasadena |
| [6] | von Karger, B., Sequential calculus, (Procos Tech. Rept. [kiel bvk 15/4] (1994), Christian-Albrechts-Universität: Christian-Albrechts-Universität Kiel) · Zbl 0875.68202 |
| [7] | Kleene, S. C., Representation of events in nerve nets and finite automata, (Shannon; McCarthy, Automata Studies (1956), Princeton University Press: Princeton University Press Princeton, NJ), 3-42 |
| [8] | Manna, Z.; Pnueli, A., The Temporal logic of Reactive and Concurrent Systems — Specification (1991), Springer: Springer Berlin · Zbl 0753.68003 |
| [9] | Moszkowski, B., Some very compositional temporal properties, (Tech. Rept. TR-466 (1993), University of Newcastle), (Accepted for Procomet 1994, San Miniato.) |
| [10] | Tarski, A., On the calculus of relations, J. Symbolic Logic, 6, 3, 73-89 (1941) · JFM 67.0973.02 |
| [11] | Zhou, Chaochen; Hoare, C. A.R.; Ravn, A. P., A calculus of durations, Inform. Process. Lett., 40, 269-276 (1992) · Zbl 0743.68097 |
| [12] | Zwiers, J.; Jansen, W., Partial order based design of concurrent systems, (Memoranda Informatica 93-51 (1993), University of Twente) |
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