Abstract
We present a circular assume-guarantee rule in an abstract setting (of sets over a partially-ordered domain). The rule has a mathematically concise side condition. Now, in order to prove an assume- guarantee rule in a concrete setting, all we need to do is to is to instantiate the abstract setting and check the side condition; i.e., we need not redo the notorious circularity argument again. We use this frame- work to prove a new assume-guarantee rule for Kripke structures. That rule generalizes existing assume-guarantee rules for other settings such as Reactive Modules or Mealy machines.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Martín Abadi and Leslie Lamport. Conjoining specifications. ACM Transactions on Programming Languages and Systems, 17(3):507–534, 1995.
Martín Abadi and Gordon D. Plotkin. A logical view of composition. Theoretical Computer Science, 114(1):3–30, 1993.
Rajeev Alur and Thomas A. Henzinger. Reactive modules. In Proc. 11th Annual Symposium On Logic In Computer Science, pages 207–218, 1996.
Giorgio Delzanno and Andreas Podelski. Model checking in clp. In TACAS’99: Tools and Algorithms for the Construction and Analysis of Systems, Springer LNCS 1579, pages 223–239, 1999.
Thomas A. Henzinger, Shaz Qadeer, Sriram K. Rajamani, and Serdar Tasiran. An assume-guarantee rule for checking simulation. In FMCAD’98: Formal methods in computer-aided design, Springer LNCS 1522, pages 421–432, 1998.
Bengt Jonsson and Yih-Kuen Tsay. Assumption/guarantee specifications in linear-time temporal logic. Theoretical Computer Science, 167(1-2):47–72, 1996.
Robert P. Kurshan. Computer-aided verification of coordinating processes. Princeton University Press, 1994.
Patrick Maier. A set-theoretic framework for assume-guarantee reasoning. Technical Report MPI-I-2001-2-002, Max-Planck-Institut für Informatik, 2001.
K. L. McMillan. A compositional rule for hardware design refinement. In CAV’97: Computer aided verification, Springer LNCS 1254, pages 207–218, 1997.
Jayadev Misra and K. Mani Chandy. Proofs of networks of processes. IEEE Transactions on Software Engineering, 7(4):417–426, 1981.
Andreas Podelski. Model checking as constraint solving. In SAS 2000: Static Analysis, Springer LNCS 1824, pages 22–37, 2000.
Sriram K. Rajamani and Jakob Rehof. A behavioral module system for the π-calculus. In SAS’01: Static Analysis, 2001. To appear.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Maier, P. (2001). A Set-Theoretic Framework for Assume-Guarantee Reasoning. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_67
Download citation
DOI: https://doi.org/10.1007/3-540-48224-5_67
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42287-7
Online ISBN: 978-3-540-48224-6
eBook Packages: Springer Book Archive