, the sequence run * D,t (root t ) enumerates in increasing order the finite set run * A,t (root t ), cf. Definition 17(g) (Section 3) It follows that L(D) = L(A) The language T (F ) ? L(A) is recognized by the fly-automaton F, ) and (4): these assertions are straightforward to prove from the definitions and the constructions of Definition
, P ) is defined, then P can be used for computing the value of t under any interpretation of the function symbols of F by total functions. The following fact is easy to prove by induction on the structure of t
, is val(P ) for some Strh(t)-register program P over F that consists of |t| assignments. The integer Strh(t) is an easy to compute upper bound to the minimal number of registers of a program P that is necessary to get t = val(P ), but it does not give the minimal value
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