Model checking of infinite state systems is undecidable, therefore, there are instances for which fixpoint computations used in infinite state model checkers do not converge. Given a widening operator one can compute an upper approximation of a least fixpoint in finite number of steps even if the least fixpoint is uncomputable. We present a widening operator for automata encoding integer sets. ...

Motivated by the recent interest in models of guarded (co-)recursion we study its equational properties. We formulate axioms for guarded fixpoint operators generalizing the axioms of iteration theories of Bloom and Ésik. Models of these axioms include both standard (e.g., cpo-based) models of iteration theories and models of guarded recursion such as complete metric spaces or the topos of trees...

In computer science fixpoints play a crucial role. Most often least and greatest fixpoints are sufficient. However there are situations where other ones are needed. In this paper we study, on an algebraic base, a special fixpoint of the function f (x) = a · x that describes infinite iteration of an element a. We show that the greatest fixpoint is too imprecise. Special problems arise if the ite...

A factor in the complexity of conventional algorithms for model checking Computation Tree Logic (CTL) is the size of the formulae, and, more precisely, the number of fixpoint operators. This paper addresses the following questions: given a CTL formula f , is there an equivalent formula with fewer fixpoint operators? and how term rewriting techniques may be used to find it? Moreover, for some su...

This paper treats the problem of implementing efficiently recursive Horn Clauses queries, including those with function symbols. In particular, the situation is studied where the initial bindings of the arguments in the recursive query goal can be used in the top-down (as in backward chaining) execution phase to improve the efficiency and, often, to guarantee the termination, of the forward cha...