Development of Terminology for \bf SCM

Grzegorz Bancerek

Polish Academy of Sciences, Institute of Mathematics, Warsaw

Piotr Rudnicki

University of Alberta, Department of Computing Science, Edmonton

Summary.

We develop a higher level terminology for the {\bf SCM} machine defined by Nakamura and Trybulec in [5]. Among numerous technical definitions and lemmas we define a complexity measure of a halting state of {\bf SCM} and a loader for {\bf SCM} for arbitrary finite sequence of instructions. In order to test the introduced terminology we discuss properties of eight shortest halting programs, one for each instruction.

This work was partially supported by NSERC Grant OGP9207 while the first author visited University of Alberta, May--June 1993.

MML Identifier: SCM_1

Contents (PDF format)

Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.

[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.

[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[4] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.

[5] Yatsuka Nakamura and Andrzej Trybulec. A mathematical model of CPU. Journal of Formalized Mathematics, 4, 1992.

[6] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[7] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.

[8] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.

[9] Andrzej Trybulec and Yatsuka Nakamura. Some remarks on the simple concrete model of computer. Journal of Formalized Mathematics, 5, 1993.

[10] Michal J. Trybulec. Integers. Journal of Formalized Mathematics, 2, 1990.

[11] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[12] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.