Compositional Circular Assume-Guarantee Rules Cannot Be Sound and Complete

Circular assume-guarantee reasoning is used for the compositional verification of concurrent systems. Its soundness has been studied in depth, perhaps because circularity makes it anything but obvious. In this paper, we investigate completeness. We show that compositional circular assume-guarantee rules cannot be both sound and complete.

[1]  Colin Stirling,et al.  Modal and temporal logics , 1993, LICS 1993.

[2]  Jean H. Gallier,et al.  Linear-Time Algorithms for Testing the Satisfiability of Propositional Horn Formulae , 1984, J. Log. Program..

[3]  Martín Abadi,et al.  An Abstract Account of Composition , 1995, MFCS.

[4]  K. Mani Chandy,et al.  Proofs of Networks of Processes , 1981, IEEE Transactions on Software Engineering.

[5]  Kenneth L. McMillan,et al.  Circular Compositional Reasoning about Liveness , 1999, CHARME.

[6]  Thomas A. Henzinger,et al.  An assume-guarantee rule for checking simulation , 1998, TOPL.

[7]  Thomas A. Henzinger,et al.  Formal specification and verification of a dataflow processor array , 1999, 1999 IEEE/ACM International Conference on Computer-Aided Design. Digest of Technical Papers (Cat. No.99CH37051).

[8]  Martín Abadi,et al.  Conjoining specifications , 1995, TOPL.

[9]  Patrick Maier.  A Set-Theoretic Framework for Assume-Guarantee Reasoning , 2001, ICALP.

[10]  Zohar Manna,et al.  Temporal Verification of Reactive Systems , 1995, Springer New York.

[11]  Bowen Alpern,et al.  Defining Liveness , 1984, Inf. Process. Lett..

[12]  Zohar Manna,et al.  Temporal verification of reactive systems - safety , 1995 .

[13]  Thomas A. Henzinger,et al.  You Assume, We Guarantee: Methodology and Case Studies , 1998, CAV.

[14]  Stephen N. Freund,et al.  Thread-Modular Verification for Shared-Memory Programs , 2002, ESOP.

[15]  Thomas A. Henzinger,et al.  Reactive Modules , 1999, Formal Methods Syst. Des..

[16]  Bengt Jonsson,et al.  Assumption/Guarantee Specifications in Linear-Time Temporal Logic , 1996, Theor. Comput. Sci..

[17]  Patrick Maier,et al.  A lattice-theoretic framework for circular assume-guarantee reasoning , 2003 .

[18]  Wolfgang Thomas,et al.  Automata on Infinite Objects , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[19]  Kedar S. Namjoshi,et al.  On the Competeness of Compositional Reasoning , 2000, CAV.

[20]  Kenneth L. McMillan,et al.  Verification of an Implementation of Tomasulo's Algorithm by Compositional Model Checking , 1998, CAV.