A cartesian-closed category for higher-order model checking

Abstract

In previous work we have described the construction of an abstract lattice from a given Büchi automaton. The abstract lattice is finite and has the following key properties. (i) There is a Galois insertion between it and the lattice of languages of finite and infinite words over a given alphabet. (ii) The abstraction is faithful with respect to acceptance by the automaton. (iii) Least fixpoints and ω-iterations (but not in general greatest fixpoints) can be computed on the level of the abstract lattice.