Abstract
Abstract State Machines (ASMs) provide a formal method for transparent design and specification of complex dynamic systems. They combine advantages of informal and formal methods. Applications of this method motivate a number of computability and decidability problems connected to ASMs. Such problems result for example from the area of verifying properties of ASMs. Their high expressive power leads rather directly to undecidability respectively uncomputability results for most interesting problems in the case of unrestricted ASMs. Consequently, it is rather natural to ask whether there exist expressive classes of ASMs for which we can prove positive decidability and computability results. In this work, we introduce such a class of ASMs. The concept is similar to the one of the guarded fragment of first-order logic. We analyze the expressive power of this class and prove that it is stronger than Datalog LITE and the guarded fragment of first-order fixed point logic. Some decidability and computability results have been proven in earlier works.
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References
Andréka, H., van Benthem, J., and Németi, I., 1996, “Modal languages and bounded fragments of predicate logic,” Technical Report ILLC Research Report ML-96-03, ILLC.
Blass, A. and Gurevich, Y., 2003, “Abstract state machines capture parallel algorithms,” ACM Transactions on Computation Logic 4(4) 578–651.
Börger, E., Päppinghaus, P., and Schmid, J., 2000, “Report on a practical application of ASMs in software design,” pp. 361–366 in Y. Gurevich, M. Odersky, and L. Thiele, eds., International Workshop on Abstract State Machines ASM 2000, Vol. 1912 of LNCS, Springer-Verlag.
Börger, E. and Stärk, R., 2003, Abstract State Machines. Springer-Verlag.
Gottlob, G., Grädel, E., and Veith, H., 2002, “Datalog LITE: A deductive query language with linear time model checking,” ACM Transactions on Computational Logic 3(1) 1–35.
Grädel, E. and Nowack, A., 2003, pp. 309–323 “Quantum Computing and Abstract State Machines,” in Abstract State Machines – Advances in Theory and Applications, Vol. 2589 of LNCS. Springer-Verlag.
Grädel, E., 1999a, “On the restraining power of guards,” Journal of Symbolic Logic, 64 1719–1742.
Grädel, E., 1999b, “The decidability of guarded fixed point logic,” in J. Gerbrandy, M. Marx, M. de Rijke, and Y. Venema, eds., JFAK. Essays Dedicated to Johan van Benthem on the Occasion of his 50th Birthday, CD-ROM. Amsterdam University Press.
Grädel, E., 2001, “Guarded fixed point logic and the monadic theory of trees,” Theoretical Computer Science. To appear.
Gurevich, Y., 1995, “Evolving Algebras 1993: Lipari Guide,” pp. 9–36 in E. Börger, ed., Specification and Validation Methods. Oxford University Press.
Gurevich, Y., 2000, “Sequential abstract state machines capture sequential algorithms,” ACM Transactions on Computational Logic, 1, 77–111.
Grädel, E. and Walukiewicz, I., 1999, “Guarded fixed point logic,” pp. 45–54 in Proceedings of 14th IEEE Symposium on Logic in Computer Science LICS ‘99, Trento.
Nowack, A., 2003, “Deciding the Verification Problem for Abstract State Machines,” In Abstract State Machines - Advances in Theory and Applications, Vol. 2589 of LNCS. Springer-Verlag.
Nowack, A., 2004, “Slicing abstract state machines,” in Abstract State Machines 2004. Advances in Theory and Practice, Vol. 3052 of LNCS. Springer-Verlag.
Stärk, R., Schmid, J., and Börger, E., 2001, Java and the Java Virtual Machine: Definition, Verification, Validation. Springer-Verlag.
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Nowack, A. A Guarded Fragment for Abstract State Machines. J Logic Lang Inf 14, 345–368 (2005). https://doi.org/10.1007/s10849-005-5790-2
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DOI: https://doi.org/10.1007/s10849-005-5790-2