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Complexity and Resource Bound Analysis of Imperative Programs Using Difference Constraints.

Moritz Sinn1, Florian Zuleger1, Helmut Veith1

  • 1Institut für Informationssysteme, TU Wien, Favoritenstr. 9-11, Wien, Austria.

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Summary
This summary is machine-generated.

This study introduces a novel bound analysis technique using difference constraints for imperative programs. It enhances complexity analysis for challenging loop patterns and infers invariants, improving scalability and practical relevance.

Keywords:
Amortized analysisAutomatic complexity analysisBound analysisComplexity analysisCost analysisDifference constraintsResource bound analysisStatic analysis

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Area of Science:

  • Computer Science
  • Software Engineering
  • Program Analysis

Background:

  • Difference constraints are established for termination analysis, modeling relational inequalities.
  • Program complexity often stems from counter operations, naturally mappable to difference constraints.
  • Existing bound analysis methods struggle with complex loop iteration patterns.

Purpose of the Study:

  • To propose and evaluate a novel bound analysis technique based on difference constraints for imperative programs.
  • To extend bound analysis capabilities to challenging loop iteration patterns found in practical applications like parsing and string matching.
  • To demonstrate the utility of bound analysis for inferring program invariants, thereby reducing reliance on external invariant generation techniques.

Main Methods:

  • Developed a soundly proven algorithm that utilizes difference constraints for bound analysis and invariant inference.
  • Introduced efficient abstraction techniques to transform imperative code into difference constraint programs.
  • Conducted a comprehensive experimental comparison of state-of-the-art bound analysis tools on diverse benchmarks.

Main Results:

  • The proposed difference constraint-based analysis successfully handles complex loop iteration patterns beyond the scope of current approaches.
  • The analysis effectively infers invariants, which are then used to determine resource bounds, demonstrating a self-contained approach.
  • Experimental results show the analysis to be more scalable and effective on real-world C code and challenging benchmarks compared to existing tools.

Conclusions:

  • Difference constraints provide a suitable abstract program model for automatic complexity and resource bound analysis.
  • The developed method offers enhanced capabilities for analyzing programs with complex iteration patterns.
  • The approach demonstrates improved scalability and practical relevance for static program analysis.