Abstract
Mathematical representations of concurrent systems rely on two fundamental notions: an atomic unit of behaviour called an event, and a constraint called independence which asserts that the order in which certain events occur does not affect the final configuration of the system. We apply abstract interpretation to study models of concurrency by treating events and independence as abstractions. Events arise as Boolean abstractions of traces. Independence is a parameter to an abstraction that adds certain permutations to a set of sequences of events. Our main result is that several models of concurrent system are a composition of an event abstraction and an independence specification. These models include Mazurkiewicz traces, pomsets, prime event structures, and transition systems with independence. These results establish the first connections between abstraction interpretation and event-based models of concurrency and show that there is a precise sense in which independence is a form of abstraction.
M. Sousa—Supported by a Google PhD Fellowship.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Baeten, J.C.M.: A brief history of process algebra. Theor. Comput. Sci. 335(2–3), 131–146 (2005)
Bergstra, J.A., Klop, J.W.: Process algebra for synchronous communication. Inf. Control 60(1–3), 109–137 (1984)
Boudol, G.: Flow event structures and flow nets. In: Proceedings of Semantics of Systems of Concurrent Processes, LITP Spring School on Theoretical Computer Science, La Roche Posay, France, 23–27 April 1990, pp. 62–95 (1990)
Cousot, P.: Constructive design of a hierarchy of semantics of a transition system by abstract interpretation. Theor. Comput. Sci. 277(1–2), 47–103 (2002)
Diekert, V.: The Book of Traces. World Scientific Publishing Co., Inc., River Edge (1995)
Esparza, J., Heljanko, K.: Unfoldings - A Partial-Order Approach to Model Checking. EATCS Monographs in Theoretical Computer Science. Springer, Heidelberg (2008)
Flanagan, C., Godefroid, P.: Dynamic partial-order reduction for model checking software. In: Principles of Programming Languages (POPL), pp. 110–121. ACM (2005)
Fokkink, W.: Introduction to Process Algebra. Springer, Heidelberg (2000)
van Glabbeek, R.: The linear time - branching time spectrum I: the semantics of concrete, sequential processes. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra, pp. 3–99. Elsevier, Amsterdam (2001)
van Glabbeek, R.J., Plotkin, G.D.: Configuration structures, event structures and petri nets. Theor. Comput. Sci. 410(41), 4111–4159 (2009)
Godefroid, P. (ed.): Partial-Order Methods for the Verification of Concurrent Systems. LNCS, vol. 1032. Springer, Berlin (1996). doi:10.1007/3-540-60761-7
Kuske, D., Morin, R.: Pomsets for local trace languages. J. Automata Lang. Comb. 7(2), 187–224 (2001)
Mazurkiewicz, A.: Trace theory. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) ACPN 1986. LNCS, vol. 255, pp. 278–324. Springer, Berlin, Heidelberg (1987). doi:10.1007/3-540-17906-2_30
McMillan, K,L.: Using unfoldings to avoid the state explosion problem in the verification of asynchronous circuits. In: Bochmann, Gregor, Probst, David, Karl (eds.) CAV 1992. LNCS, vol. 663, pp. 164–177. Springer, Berlin, Heidelberg (1993). doi:10.1007/3-540-56496-9_14
Padberg, J., Ehrig, H.: Parameterized net classes: a uniform approach to petri net classes. In: Ehrig, H., Padberg, J., Juhás, G., Rozenberg, G. (eds.) Unifying Petri Nets. LNCS, vol. 2128, pp. 173–229. Springer, Berlin, Heidelberg (2001). doi:10.1007/3-540-45541-8_7
Peled, D.: Partial order reduction: model-checking using representatives. In: Penczek, W., Szałas, A. (eds.) MFCS 1996. LNCS, vol. 1113, pp. 93–112. Springer, Berlin, Heidelberg (1996). doi:10.1007/3-540-61550-4_141
Petri, C.A.: Fundamentals of a theory of asynchronous information flow. In: IFIP Congress, pp. 386–390 (1962)
Pinna, G.M., Poigné, A.: On the nature of events: another perspective in concurrency. Theor. Comput. Sci. 138(2), 425–454 (1995)
Pratt, V.: Modeling concurrency with partial orders. Int. J. Parallel Program. 15(1), 33–71 (1986)
Pratt, V.R.: Event-state duality: the enriched case. In: Proceedings of the 13th International Conference on Concurrency Theory, CONCUR 2002, Brno, Czech Republic, 20–23 August 2002, pp. 41–56 (2002)
RodrĂguez, C., Sousa, M., Sharma, S., Kroening, D.: Unfolding-based partial order reduction. In: Concurrency Theory (CONCUR). Leibniz International Proceedings in Informatics, vol. 42, pp. 456–469. Dagstuhl Publishing (2015)
Sassone, V., Nielsen, M., Winskel, G.: Models for concurrency: towards a classification. Theor. Comput. Sci. 170(1–2), 297–348 (1996)
Winskel, G.: An introduction to event structures. In: School/Workshop on Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, pp. 364–397 (1988)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
D’Silva, V., Kroening, D., Sousa, M. (2017). Independence Abstractions and Models of Concurrency. In: Bouajjani, A., Monniaux, D. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2017. Lecture Notes in Computer Science(), vol 10145. Springer, Cham. https://doi.org/10.1007/978-3-319-52234-0_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-52234-0_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-52233-3
Online ISBN: 978-3-319-52234-0
eBook Packages: Computer ScienceComputer Science (R0)