Abstract
We develop a logic which enables reasoning about single steps of non-deterministic parallel Abstract State Machines (ASMs). Our logic builds upon the unifying logic introduced by Nanchen and Stärk for reasoning about hierarchical (parallel) ASMs. Our main contribution to this regard is the handling of non-determinism (both bounded and unbounded) within the logical formalism. Moreover, we do this without sacrificing the completeness of the logic for statements about single steps of non-deterministic parallel ASMs, such as invariants of rules, consistency conditions for rules, or step-by-step equivalence of rules.
Work supported by the Austrian Science Fund (FWF: [P26452-N15]). Project: Behavioural Theory and Logics for Distributed Adaptive Systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ågotnes, T., Walicki, M.: Complete axiomatisations of properties of finite sets. Logic J. IGPL 16(3), 293–313 (2008)
Alur, R.: Principles of Cyber-Physical Systems. MIT Press, Cambridge (2015)
Blass, A., Gurevich, Y.: Abstract state machines capture parallel algorithms. ACM Trans. Comp. Logic 4(4), 578–651 (2003)
Blass, A., Gurevich, Y.: Abstract state machines capture parallel algorithms: correction and extension. ACM Trans. Comp. Logic 9(3), 1–32 (2008)
Börger, E., Stärk, R.F.: Abstract State Machines: a Method for High-Level System Design and Analysis. Springer, New York (2003)
Ferrarotti, F., Schewe, K., Tec, L., Wang, Q.: A new thesis concerning synchronised parallel computing - simplified parallel ASM thesis. CoRR abs/1504.06203 (2015). http://arxiv.org/abs/1504.06203
Floyd, R.W.: Nondeterministic algorithms. J. ACM 14(4), 636–644 (1967). http://doi.acm.org/10.1145/321420.321422
Grädel, E., Gurevich, Y.: Metafinite model theory. Inf. Comput. 140(1), 26–81 (1998)
Groenboom, R., Renardel de Lavalette, G.: A formalization of evolving algebras. In: Proceedings of Accolade95. Dutch Research School in Logic (1995)
Huggins, J.K., Wallace, C.: An abstract state machine primer. Technical report 02–04, Computer Science Department, Michigan Technological University (2002)
Hughes, G., Cresswell, M.: A New Introduction to Modal Logic. Burns & Oates, London (1996)
Kruskal, J.B.: On the shortest spanning subtree of a graph and the travelling salesman problem. Proc. Amer. Math. Soc. 2, 48–50 (1956)
Stärk, R., Nanchen, S.: A logic for abstract state machines. J. Univ. Comput. Sci. 7(11) (2001)
Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer, New York (1995)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Ferrarotti, F., Schewe, KD., Tec, L., Wang, Q. (2016). A Logic for Non-deterministic Parallel Abstract State Machines. In: Gyssens, M., Simari, G. (eds) Foundations of Information and Knowledge Systems. FoIKS 2016. Lecture Notes in Computer Science(), vol 9616. Springer, Cham. https://doi.org/10.1007/978-3-319-30024-5_18
Download citation
DOI: https://doi.org/10.1007/978-3-319-30024-5_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-30023-8
Online ISBN: 978-3-319-30024-5
eBook Packages: Computer ScienceComputer Science (R0)