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2006 | OriginalPaper | Chapter

Thread-Modular Verification Is Cartesian Abstract Interpretation

Authors : Alexander Malkis, Andreas Podelski, Andrey Rybalchenko

Published in: Theoretical Aspects of Computing - ICTAC 2006

Publisher: Springer Berlin Heidelberg

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Verification of multithreaded programs is difficult. It requires reasoning about state spaces that grow exponentially in the number of concurrent threads. Successful verification techniques based on modular composition of over-approximations of thread behaviors have been designed for this task. These techniques have been traditionally described in assume-guarantee style, which does not admit reasoning about the abstraction properties of the involved compositional argument. Flanagan and Qadeer thread-modular algorithm is a characteristic representative of such techniques. In this paper, we investigate the formalization of this algorithm in the framework of abstract interpretation. We identify the abstraction that the algorithm implements; its definition involves Cartesian products of sets. Our result provides a basis for the systematic study of similar abstractions for dealing with the state explosion problem. As a first step in this direction, our result provides a characterization of a minimal increase in the precision of the Flanagan and Qadeer algorithm that leads to the loss of its polynomial complexity.

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Metadata
Title
Thread-Modular Verification Is Cartesian Abstract Interpretation
Authors
Alexander Malkis
Andreas Podelski
Andrey Rybalchenko
Copyright Year
2006
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/11921240_13

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