Abstract
Threads as contained in a thread algebra are used for the modeling of sequential program behavior. A thread that may use a counter to control its execution is called a ‘one-counter thread’. In this paper the decidability of risk assessment (a certain form of action forecasting) for one-counter threads is proved. This relates to Cohen’s impossibility result on virus detection (Comput. Secur. 6(1), 22–35, 1984). Our decidability result follows from a general property of the traces of one-counter threads: if a state is reachable from some initial state, then it is also reachable along a path in which all counter values stay below a fixed bound that depends only on the initial and final counter value. A further consequence is that the reachability of a state is decidable. These properties are based on a result for ω-one counter machines by Rosier and Yen (SIAM J. Comput. 16(5), 779–807, 1987).
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References
Bergstra, J.A., Bethke, I.: Polarized process algebra and program equivalence. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) Proceedings of ICALP 2003. Lecture Notes in Comput. Sci., vol. 2719, pp. 1–21. Springer, New York (2003)
Bergstra, J.A., Bethke, I.: Polarized process algebra with reactive composition. Theor. Comput. Sci. 343(3), 285–304 (2005)
Bergstra, J.A., Klop, J.W.: Process algebra for synchronous communication. Inf. Control 60(1–3), 109–137 (1984)
Bergstra, J.A., Ponse, A.: Combining programs and state machines. J. Log. Algebr. Program. 51(2), 175–192 (2002)
Bergstra, J.A., Ponse, A.: A bypass of Cohen’s impossibility result. In: Sloot, P.M.A., Hoekstra, A.G., Priol, T., Reinefeld, A. (eds.) Advances in Grid Computing—EGC 2005. Lecture Notes in Comput. Sci., vol. 3470, pp. 1097–1106. Springer, New York (2005)
Bergstra, J.A., Bethke, I., Ponse, A.: Decision problems for pushdown threads. Acta Inf. 44(2), 75–90 (2007)
Bergstra, J.A., Bethke, I., Ponse, A.: Thread algebra and risk assessment services. In: Dimitracopoulos, C., et al. (eds.) Logic Colloquium ’05: Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, Athens, Greece, July 28–August 3, 2005. ASL Lecture Notes in Logic, vol. 28 (to appear)
Cohen, F.: Computer viruses—theory and experiments. Comput. Secur. 6(1), 22–35 (1984). Available as http://vx.netlux.org/lib/afc01.html
de Bakker, J.W., Zucker, J.I.: Processes and the denotational semantics of concurrency. Inf. Control 54(1–2), 70–120 (1982)
Jančar, P., Moller, F., Sawa, Z.: Simulation problems for one-counter machines. In: Proceedings of SOFSEM’99: The 26th Seminar on Current Trends in Theory and Practice of Informatics. Lecture Notes in Comput. Sci., vol. 1725, pp. 398–407. Springer, New York (1999)
Paterson, M.S., Valiant, L.G.: Deterministic one-counter automata. J. Comput. Syst. Sci. 10(3), 340–350 (1975)
Ponse, A., van der Zwaag, M.B.: An introduction to program and thread algebra. In: Beckmann, A. (ed.) Logical Approaches to Computational Barriers: Proceedings CiE 2006. Lecture Notes in Comput. Sci., vol. 3988, pp. 445–458. Springer, New York (2006)
Rosier, L.E., Yen, H.-C.: Logspace hierarchies, polynomial time and the complexity of fairness problems concerning ω-machines. SIAM J. Comput. 16(5), 779–807 (1987)
Vu, T.D.: Metric denotational semantics for BPPA. Report PRG0503, Programming Research Group, University of Amsterdam (2005). To appear in J. Log. Algebr. Program.
Yen, H.-C., Yu, L.-P.: Decidability analysis of self-stabilization for infinite state systems. Fundam. Inf. 70(4), 387–402 (2006)
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Ponse, A., van der Zwaag, M.B. Risk Assessment for One-Counter Threads. Theory Comput Syst 43, 563–582 (2008). https://doi.org/10.1007/s00224-007-9034-5
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DOI: https://doi.org/10.1007/s00224-007-9034-5