Sequential Real Number Computation and Recursive Relations

J. Raymundo Marcial-Romero, M. Andrew Moshier
2008 Electronical Notes in Theoretical Computer Science  
In the first author's thesis [9] , a sequential language, LRT, for real number computation is investigated. The thesis includes a proof that all polynomials are programmable, but that work comes short of giving a complete characterization of the expressive power of the language even for first-order functions. The technical problem is that LRT is non-deterministic. So a natural characterization of its expressive power should be in terms of relations rather than functions. In [2], Brattka
more » ... ates a formalization of recursive relations in the style of Kleene's recursive functions on the natural numbers. This paper establishes the expressive power of LRTp, a variant of LRT, in terms of Brattka's recursive relations. Because Brattka already did the work of establishing the precise connection between his recursive relations and Type 2 Theory of Effectivity, we thus obtain a complete characterization of first-order definability in LRTp.
doi:10.1016/j.entcs.2008.03.014 fatcat:kkkybcgk6va6xm5akqbzubytjm