The unlimited register machine programmer / Roel B. Reales.

Thesis (Master in Computer Science) -- Cebu Institute of Technology - University, March 2008.

Mathematical theorems, as well as the notions of computing are being applied in different field of studies. The world of computing, however complicated, is governed by sets of procedures in order to achieve an output from a set of inputs. This illustrates the mechanical nature that is being captured and realized into calculating machines, more popularly known as the ?Modern Digital computers? today. Despite the astonishing calculating power of such machines, they are bounded by limitations. For instance, they cannot compute problems.

Some computing problems are found to be non-computable. This means that there exist no set of procedures that will compose an algorithm to solve such problems. Whether a problem is computable or not, the real problem here is proving either of the statement. One way to prove that a problem is computable is through programming on a hypothetical machine called the ?Unlimited Register machine? (or URM). A problem is said to be computable if there exists a URM program that computes it. Some theorems had been established on URM computing, making it possible to compute for complex mathematical functions on natural numbers using only four primitive machine instructions. It is to this extent that this work is aimed ? to illustrate the definitions, theorems and proofs through software that generates URM programs from simple to complex primitive/general/partial-recursive mathematical functions, as well as illustrate how the URM works by executing those programs.