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Is every irreducible shift of finite type flow equivalent to a renewalsystem? For the first time, this variation of a classic problem formulated byAdler is investigated, and several partial results are obtained in an attemptto find the range of the Bowen--Franks invariant over the set of renewalsystems of finite type. In particular, it is shown that the Bowen--Franks groupis cyclic for every member of a class of renewal systems known to attain allentropies realised by shifts of finite type, and several classes of renewalsystems with non--trivial values of the invariant are constructed.

Is Every Irreducible Shift of Finite Type Flow Equivalent to a Renewal System?