Attacking the dimensionality problem of parameterized systems via bounded reachability graphs

  • Authors:

  • Qiusong Yang;Bei Zhang;Jian Zhai;Mingshu Li

  • Affiliations:

  • National Engineering Research Center of Fundamental Software, Institute of Software, Chinese Academy of Sciences, Beijing, China;National Engineering Research Center of Fundamental Software, Institute of Software, Chinese Academy of Sciences, Beijing, China and Graduate University of Chinese Academy of Sciences, Beijing, Ch ...;National Engineering Research Center of Fundamental Software, Institute of Software, Chinese Academy of Sciences, Beijing, China;National Engineering Research Center of Fundamental Software, Institute of Software, Chinese Academy of Sciences, Beijing, China and State Key Laboratory of Computer Science, Institute of Software ...

  • Venue:
  • FSEN'11 Proceedings of the 4th IPM international conference on Fundamentals of Software Engineering
  • Year:
  • 2011

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Abstract

Parameterized systems are systems that involve numerous instantiations of finite-state processes, and depend on parameters which define their size. The verification of parameterized systems is to decide if a property holds in its every size instance, essentially a problem with an infinite state space, and thus poses a great challenge to the community. Starting with a set of undesired states represented by an upward-closed set, the backward reachability analysis will always terminate because of the well-quasi-orderingness. As a result, backward reachability analysis has been widely used in the verification of parameterized systems. However, many existing approaches are facing with the dimensionality problem, which describes the phenomenon that the memory used for storing the symbolic state space grows extremely fast when the number of states of the finite-state process increases, making the verification rather inefficient. Based on bounded backward reachability graphs, a novel abstraction for parameterized systems, we have developed an approach for building abstractions with incrementally increased dimensions and thus improving the precision until a property is proven or a counterexample is detected. The experiments show that the verification efficiencies have been significantly improved because conclusive results tend to be drawn on abstractions with much lower dimensions.