On the expressive power of program schemes with sets

The author considers flow diagrams with sets, which is the class of program schemes equipped with finite sets of different levels, so that FDSet₁ is such a class equipped with finite sets, FDSet ₂ is such a class equipped with finite sets and finite sets of finite sets, etc. He proves FDSet₁ is semi-universal. In particular, in infinite structures FDSet₁ is able to define every (generalized) computable function. For finite structures, the halting problem for FDSet₁, is decidable, and it is proved that DL(FDSet₁) exactly corresponds to the LINEARSPACE complexity class