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International Static Analysis Symposium

SAS 2001: Static Analysis pp 213–233Cite as

Solving Regular Tree Grammar Based Constraints

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2126))

Abstract

This paper describes the precise specification, design, analysis, implementation, and measurements of an efficient algorithm for solving regular tree grammar based constraints. The particular constraints are for dead-code elimination on recursive data, but the method used for the algorithm design and complexity analysis is general and applies to other program analysis problems as well. The method is centered around Paige’s finite differencing, i.e., computing expensive set expressions incrementally, and allows the algorithm to be derived and analyzed formally and implemented easily. We propose higher-level transformations that make the derived algorithm concise and allow its complexity to be analyzed accurately. Although a rough analysis shows that the worst-case time complexity is cubic in program size, an accurate analysis shows that it is linear in the number of live program points and in other parameters, including mainly the arity of data constructors and the number of selector applications into whose arguments the value constructed at a program point might flow. These parameters explain the performance of the analysis in practice. Our implementation also runs two to ten times as fast as a previous implementation of an informally designed algorithm.

This work is supported in part by ONR under grants N00014-99-1-0132, N00014-99-1-0358, and N00014-01-1-0109, by NSF under grants CCR-9711253 and CCR-9876058, and by a Motorola University Partnership in Research Grant.

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Authors and Affiliations

  1. Computer Science Dept., State University of New York, Stony Brook, NY, 11794

    Yanhong A. Liu & Scott D. Stoller

  2. Computer Science Dept., University of Wisconsin, Madison, WI, 53706

    Ning Li

Authors
  1. Yanhong A. Liu
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  2. Ning Li
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  3. Scott D. Stoller
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Editors and Affiliations

  1. Département d’Informatique, École Normale Supérieure, 45 rue d’Ulm, 75230, Paris Cedex 05, France

    Patrick Cousot

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Liu, Y.A., Li, N., Stoller, S.D. (2001). Solving Regular Tree Grammar Based Constraints. In: Cousot, P. (eds) Static Analysis. SAS 2001. Lecture Notes in Computer Science, vol 2126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47764-0_13

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  • DOI: https://doi.org/10.1007/3-540-47764-0_13

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  • Print ISBN: 978-3-540-42314-0

  • Online ISBN: 978-3-540-47764-8

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