Abstract
We establish that every monadic second-order property of the behaviour of a machine (transition systems and tree automata are typical examples of machines) is a monadic second-order property of the machine itself. In this way, we clarify the distinction between “dynamic” properties of machines (i.e., properties of their behaviours), and their “static” properties (i.e., properties of the graphs or relational structures representing them). It is important for program verification that the dynamic properties that one wants to verify can be formulated statically, in the simplest possible way. As a corollary of our main result, we also obtain that the monadic theory of an algebraic tree is decidable.
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