Attacking the Dimensionality Problem of Parameterized Systems via Bounded Reachability Graphs

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.