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Path-Sensitive Analysis for Linear Arithmetic and Uninterpreted Functions

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Static Analysis (SAS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3148))

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Abstract

We describe data structures and algorithms for performing a path-sensitive program analysis to discover equivalences of expressions involving linear arithmetic or uninterpreted functions. We assume that conditionals are abstracted as boolean variables, which may be repeated to reflect equivalent conditionals. We introduce free conditional expression diagrams (FCEDs), which extend binary decision diagrams (BDDs) with internal nodes corresponding to linear arithmetic operators or uninterpreted functions. FCEDs can represent values of expressions in a program involving conditionals and linear arithmetic (or uninterpreted functions). We show how to construct them easily from a program, and give a randomized linear time algorithm (or quadratic time for uninterpreted functions) for comparing FCEDs for equality. FCEDs are compact due to maximal representation sharing for portions of the program with independent conditionals. They inherit from BDDs the precise reasoning about boolean expressions needed to handle dependent conditionals.

This research was supported in part by the National Science Foundation Grant CCR-0081588, and gifts from Microsoft Research. The information presented here does not necessarily reflect the position or the policy of the Government and no official endorsement should be inferred.

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Authors and Affiliations

  1. University of California, Berkeley

    Sumit Gulwani & George C. Necula

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  1. Sumit Gulwani
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  2. George C. Necula
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Editors and Affiliations

  1. Dipartimento di Informatica, Università di Verona, Strada Le Grazie, 15, 37134, Verona, Italy

    Roberto Giacobazzi

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Gulwani, S., Necula, G.C. (2004). Path-Sensitive Analysis for Linear Arithmetic and Uninterpreted Functions. In: Giacobazzi, R. (eds) Static Analysis. SAS 2004. Lecture Notes in Computer Science, vol 3148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27864-1_24

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  • DOI: https://doi.org/10.1007/978-3-540-27864-1_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22791-5

  • Online ISBN: 978-3-540-27864-1

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