Classical computability theory, including the UFT and the theory of semicomputable sets, has been extended by Tucker and Zucker to abstract many-sorted algebras, with algorithms formalized as deterministic While programs, which serves as a foundation for much of my work.
My research involves the extension of this work to the nondeterministic programming languages WhileRA consisting of While programs extended by random assignments, as well as sublanguages of WhileRA formed by restricting the random assignments to booleans or naturals only. The semantics of WhileRA still follows algebraic operational semantics; however, semantic computation trees replace the computation sequences used in the deterministic case, and many-valued semantic functions take the places of those one-valued accordingly.
There are two topics of investigation: