### Abstract

A completeness threshold is required to guarantee the completeness of
planning as satisfiability, and bounded model checking of safety
properties. One valid completeness threshold is the diameter of the
underlying transition system. The diameter is the maximum element in
the set of lengths of all shortest paths between pairs of states. The
diameter is not calculated exactly in our setting, where the
transition system is succinctly described using a (propositionally)
factored representation. Rather, an upper bound on the diameter is
calculated compositionally, by bounding the diameters of small
abstract subsystems, and then composing those. We port a HOL4
formalisation of a compositional algorithm for computing a relatively
tight upper bound on the system diameter. This compositional algorithm
exploits acyclicity in the state space to achieve compositionality,
and it was introduced by Abdulaziz et. al. The formalisation that we
port is described as a part of another paper by Abdulaziz et. al. As a
part of this porting we developed a libray about transition systems,
which shall be of use in future related mechanisation efforts.

BSD License