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Gateway Decompositions for Constrained Reachability Problems

  • Bastian Katz
  • Marcus Krug
  • Andreas Lochbihler
  • Ignaz Rutter
  • Gregor Snelting
  • Dorothea Wagner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6049)

Abstract

Given a directed graph whose vertices are labeled with propositional constraints, is there a variable assignment that connects two given vertices by a path of vertices that evaluate to true? Constrained reachability is a powerful generalization of reachability and satisfiability problems and a cornerstone problem in program analysis. The key ingredient to tackle these computationally hard problems in large graphs is the efficient construction of a short path condition: A formula whose satisfiability is equivalent to constrained reachability and which can be fed into a state-of-the-art constraint solver.

In this work, we introduce a new paradigm of decompositions of digraphs with a source and a target, called gateway decompositions. Based on this paradigm, we provide a framework for the modular generation of path conditions and an efficient algorithm to compute a fine-grained gateway decomposition. In benchmarks, we show that especially the combination of our decomposition and a novel arc filtering technique considerably reduces the size of path conditions and the runtime of a standard SAT solver on real-world program dependency graphs.

Keywords

Conjunctive Normal Form Truth Assignment Variable Assignment Path Condition Propositional Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Bastian Katz
    • 1
  • Marcus Krug
    • 1
  • Andreas Lochbihler
    • 2
  • Ignaz Rutter
    • 1
  • Gregor Snelting
    • 2
  • Dorothea Wagner
    • 1
  1. 1.Institute of Theoretical Informatics 
  2. 2.Institute for Program Structures and Data OrganizationKarlsruhe Institute of Technology (KIT)KarlsruheGermany

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