An application of Cohen's result on star height to the theory of control structures

A result/concept on star height is applied to two problems in the theory of control structures. First, Kosaraju's systems RE_n of control structures are generalized and it is shown by using Cohen's result on star height that the generalized systems constitute a pathwise hierarchy with respect to their expressive powers. Second, by using a concept on star height, a result of Peterson et al. (Comm. ACM16 (1973), 503–512) that RE_∞ is pathwise complete is sharpened.