Recursive Abstractions for Parameterized Systems

Joxan Jaffar and Andrew Santosa


We consider a language of recursively defined formulas about arrays of variables, suitable for specifying safety properties of parameterized systems. We then present an abstract interpretation framework which translates a paramerized system as a symbolic transition system which propagates such formulas as abstractions of underlying concrete states. The main contribution is a proof method for implications between the formulas, which then provides for an implementation of this abstract interpreter.