Journal of Formalized Mathematics
Volume 11, 1999
University of Bialystok
Copyright (c) 1999
Association of Mizar Users
Computation and Program Shift in the SCMPDS Computer
-
Jing-Chao Chen
-
Shanghai Jiaotong University
Summary.
-
A finite partial state is said to be autonomic if
the computation results in any two states containing it are same
on its domain. On the basis of this definition, this article presents
some computation results about autonomic finite partial states of the
SCMPDS computer. Because the instructions of the SCMPDS computer are
more complicated than those of the SCMFSA computer, the results given
by this article are weaker than those reported previously by the article
on the SCMFSA computer. The second task of this article is to define
the notion of program shift. The importance of this notion is that
the computation of some program blocks can be simplified by shifting
a program block to the initial position.
This work was done while the author visited Shinshu University
March--April 1999.
The terminology and notation used in this paper have been
introduced in the following articles
[15]
[20]
[6]
[3]
[2]
[4]
[21]
[5]
[8]
[18]
[1]
[7]
[10]
[11]
[12]
[16]
[14]
[9]
[19]
[13]
[17]
-
Preliminaries
-
Finite Partial States of SCMPDS
-
Autonomic Finite Partial States of SCMPDS and its Computation
-
Program Shift in the SCMPDS Computer
Acknowledgments
We wish to thank Prof. Y. Nakamura for many helpful suggestions.
Bibliography
- [1]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
Journal of Formalized Mathematics,
1, 1989.
- [2]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
- [3]
Grzegorz Bancerek.
Sequences of ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
- [4]
Grzegorz Bancerek.
K\"onig's theorem.
Journal of Formalized Mathematics,
2, 1990.
- [5]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
- [6]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
- [7]
Czeslaw Bylinski.
A classical first order language.
Journal of Formalized Mathematics,
2, 1990.
- [8]
Czeslaw Bylinski.
The modification of a function by a function and the iteration of the composition of a function.
Journal of Formalized Mathematics,
2, 1990.
- [9]
Jing-Chao Chen.
The SCMPDS computer and the basic semantics of its instructions.
Journal of Formalized Mathematics,
11, 1999.
- [10]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
- [11]
Yatsuka Nakamura and Andrzej Trybulec.
A mathematical model of CPU.
Journal of Formalized Mathematics,
4, 1992.
- [12]
Yatsuka Nakamura and Andrzej Trybulec.
On a mathematical model of programs.
Journal of Formalized Mathematics,
4, 1992.
- [13]
Takaya Nishiyama and Yasuho Mizuhara.
Binary arithmetics.
Journal of Formalized Mathematics,
5, 1993.
- [14]
Yasushi Tanaka.
On the decomposition of the states of SCM.
Journal of Formalized Mathematics,
5, 1993.
- [15]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
- [16]
Andrzej Trybulec and Yatsuka Nakamura.
Some remarks on the simple concrete model of computer.
Journal of Formalized Mathematics,
5, 1993.
- [17]
Andrzej Trybulec and Yatsuka Nakamura.
Modifying addresses of instructions of \SCMFSA.
Journal of Formalized Mathematics,
8, 1996.
- [18]
Michal J. Trybulec.
Integers.
Journal of Formalized Mathematics,
2, 1990.
- [19]
Wojciech A. Trybulec.
Groups.
Journal of Formalized Mathematics,
2, 1990.
- [20]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
- [21]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received June 15, 1999
[
Download a postscript version,
MML identifier index,
Mizar home page]