Efficient Checking of Behavioural Relations and Modal Assertions using Fixed-Point Inversion

This paper presents an algorithm for solving Boolean xed-point equations containing one level of nesting of minimum and maximum xed points. The algorithm assumes that the equations of the inner xed point is of a certain restricted kind and has a worst-case time-and space-complexity that is linear in the size of the equation system. By observing that a range of behavioral relations { in particular weak bisimulation { and modal assertions can be checked using equation systems of this restricted form, the algorithm improves on existing ad hoc constructed algorithms. Finally, we show how the key idea of inverting a xed point can be used in decreasing the number of xed-point iterations needed in BDD-based methods for solving the same class of problems.