Abstract
In this paper, we examine the subclass of RTL formulas considered in [14, 15] which we call path RTL. We propose a formal semantic extension of path RTL covering nonexistent event occurrences and show that all systems specified in path RTL can be reduced to systems which have infinitely many occurrences of all event types. We then show the undecidability of the path RTL satisfiability problem, give a PTIME algorithm for positive cycle detection, and give examples to show why refutation by positive cycles is incomplete for the path RTL satisfiability problem. Finally, we discussed a subclass of path RTL for which refutation by positive cycles is sound and complete in regard to the satisfiability problem.
Professor Mok is supported in part by a research grant from the Office of Naval Research under ONR contract number N00014-89-J-1472.
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References
R. Alur, C. Courcoubetis, D.L. Dill, Model Checking for Real-Time Systems, IEEE LICS, 1990.
W.W. Bledsoe and L.M. Hines, Variable elimination and chaining in a resolution based prover for inequalities, in Proc. 5th Conf. Automated Deduction: Lecture Notes Comput. Sci., W. Bibel and R. Kowalski, Eds. New York:Springer-Verlag, 1980, pp. 70–87.
D. Bjorner, Trusteed Computing Systems: The ProCoS Experience, Proceedings of the 14'th International Conference on Software Engineering, 1992.
M.R. Barbacci, C.B. Weinstock, J.M. Wing, Programming at the Processor-Memory-Switch Level, Proceedings of the 10'th International Conference on Software Engineering, 1988.
C. Chang and R.C. Lee, Symbolic Logic and Mechanical Theorem Proving, New York:Academic, 1973.
M. Degl'Innocenti, G.L. Ferrari, G. Pacini, F. Turini, RSF: A Formalism for Executable Requirement Specifications, IEEE Transactions on Software Engineering, Vol. 16, No. 11, Nov. 1990.
Peter J. Downey, Undecidability of Presburger arithmetic with a single monadic predicate letter
A. Espinosa, A. Garcia-Fornes, A. Crespo, J.A. de la Puente, QUISAP: an Environment for Rapid Prototyping of Real-Time Systems, Proceedings of the IEEE International Conference on Computer Systems and Software Engineering, 1990.
E.A. Emerson, Temporal and Modal Logic, Handbook of Theoretical Computer Science, edited by J.v. Leeuween, North Holland Pub. Co.
C.S. Hsieh, Timing Analysis of Cyclic Concurrent Programs, Proceedings of the 11'th International Conference on Software Engineering, 1989.
J.E. Hopcroft, J.D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, 1979.
J. Jacky, Formal Specifications for a Clinical Cyclotron Control System, Proceedings of the International Workshop on Formal Methods in Software Development, 1990; ACM Software Engineering Notes, Vol. 15, No. 4, 1990.
M.S. Jaffe, N.G. Leveson, Completeness, Robustness, and Safety in Real-Time Software Requirement Specification, Proceedings of the 11'th International Conference on Software Engineering, 1989.
F. Jahanian and A.K. Mok, Safety analysis of timing properties in real-time systems, IEEE Transactions on Software Engineering, Vol. SE-12, No9, 1986, pp. 890–904.
F. Jahanian and A.K. Mok, A graph-theoretic approach for timing analysis and its implementation, IEEE Transactions on Computers, Vol. C-36, No. 8, August 1987.
A. Lister, Design of Dependable Real-Time Systems, Proceedings of the 14'th International Conference on Software Engineering, 1992.
H.R. Lewis, Unsolvable Classes of Quantificational Formulus, 1979, Addison-Wesley Pub. Co.
R.R. Razouk, M.M. Gorlick, A Real-Time Interval Logic for Reasoning about Executions of Real-Time Programs, ACM Proceedings of the Third Symposium on Software Testing, Analysis, and Verification, 1989; ACM Software Engineering Notes, Vol. 14, No. 8, 1989.
R.E. Shostak, A Practical Decision Procedure for Arithmetic with Function Symbols, J. Ass. Comput. Mach., Vol. 26, No. 2, April 1979, pp. 351–360.
A.C. Shaw, Reasoning about Time in Higher-Level Language Software, IEEE Transactions on Software Engineering, Vol. 15, No. 7, Jul. 1989.
D.B. Skillicorn, J.I. Glasgow, Real-Time Specification Using LUCID, IEEE Transactions on Software Engineering, Vol. 15, No. 2, Feb. 1989.
F. Wang and A.K. Mok, Asynchronous real-time event logic, in the proceedings of International Computer Symposium, Taiwan, 1992.
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© 1994 Springer-Verlag Berlin Heidelberg
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Wang, F., Mok, A.K. (1994). RTL and refutation by positive cycles. In: Naftalin, M., Denvir, T., Bertran, M. (eds) FME '94: Industrial Benefit of Formal Methods. FME 1994. Lecture Notes in Computer Science, vol 873. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58555-9_121
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DOI: https://doi.org/10.1007/3-540-58555-9_121
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