Register complexity of LOOP-, WHILE-, and GOTO-Programs

Authors:
Markus Holzer;Martin Kutrib
Affiliations:
Institut für Informatik, Technische Universität München, Garching bei München, Germany;Institut für Informatik, Universität Gießen, Gießen, Germany
Venue:
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
Year:
2004

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Abstract

We study the register complexity of LOOP-, WHILE-, and GOTO-programs, that is the number of registers (or variables) needed to compute certain unary (partial) functions from the non-negative integers to the non-negative integers. It turns out that the hierarchy of LOOP-computable (WHILE-, and GOTO-computable, respectively) functions f:ℕ0 →ℕ0 (partial functions $f:\mathbb{N}_0 \hookrightarrow \mathbb{N}_0$, respectively) that is induced by the number of registers collapses to a fixed level. In all three cases the first levels are separated. Our results show that there exist universal WHILE- and GOTO-programs with a constant number of registers.