Thread Quantification for Concurrent Shape Analysis

In this paper we address the problem of shape analysis for concurrent programs. We present new algorithms, based on abstract interpretation, for automatically verifying properties of programs with an unbounded number of threads manipulating an unbounded shared heap.

Our algorithms are based on a new abstract domain whose elements represent thread-quantified invariants: i.e., invariants satisfied by all threads. We exploit existing abstractions to represent the invariants. Thus, our technique lifts existing abstractions by wrapping universal quantification around elements of the base abstract domain. Such abstractions are effective because they are thread modular: e.g., they can capture correlations between the local variables of the same thread as well as correlations between the local variables of a thread and global variables, but forget correlations between the states of distinct threads. (The exact nature of the abstraction, of course, depends on the base abstraction lifted in this style.)

We present techniques for computing sound transformers for the new abstraction by using transformers of the base abstract domain. We illustrate our technique in this paper by instantiating it to the Boolean Heap abstraction, producing a Quantified Boolean Heap abstraction. We have implemented an instantiation of our technique with Canonical Abstraction as the base abstraction and used it to successfully verify linearizability of data-structures in the presence of an unbounded number of threads.

thread_quantification.pdf
PDF file

In  Computer Aided Verification, 20th International Conference, CAV 2008, Princeton, NJ, USA, July 7-14, 2008, Proceedings

Publisher  Springer Verlag
All copyrights reserved by Springer 2007.

Details

TypeInproceedings
Pages399-413
Volume5123
SeriesLecture Notes in Computer Science
ISBN978-3-540-70543-7

Previous Versions

Josh Berdine, Tal Lev-Ami, Roman Manevich, Ganesan Ramalingam, and Mooly Sagiv. Thread Quantification for Concurrent Shape Analysis, March 2008.

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