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### Abstract

This entry provides a formalisation of a refinement of an adaptive
state counting algorithm, used to test for reduction between finite
state machines. The algorithm has been originally presented by Hierons
in the paper Testing from a
Non-Deterministic Finite State Machine Using Adaptive State
Counting. Definitions for finite state machines and
adaptive test cases are given and many useful theorems are derived
from these. The algorithm is formalised using mutually recursive
functions, for which it is proven that the generated test suite is
sufficient to test for reduction against finite state machines of a
certain fault domain. Additionally, the algorithm is specified in a
simple WHILE-language and its correctness is shown using Hoare-logic.