Gateway decompositions for constrained reachability problems

  • Authors:

  • Bastian Katz;Marcus Krug;Andreas Lochbihler;Ignaz Rutter;Gregor Snelting;Dorothea Wagner

  • Affiliations:

  • Institute of Theoretical Informatics;Institute of Theoretical Informatics;Institute for Program Structures and Data Organization, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany;Institute of Theoretical Informatics;Institute for Program Structures and Data Organization, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany;Institute of Theoretical Informatics

  • Venue:
  • SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
  • Year:
  • 2010

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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.