Volume 13, 2001

University of Bialystok

Copyright (c) 2001 Association of Mizar Users

**Hisayoshi Kunimune**- Shinshu University, Nagano
**Grzegorz Bancerek**- Bialystok Technical University
**Yatsuka Nakamura**- Shinshu University, Nagano

- In this article, we show the properties of the calculating type state machines. In the first section, we have defined calculating type state machines of which the state transition only depends on the first input. We have also proved theorems of the state machines. In the second section, we defined Moore machines with final states. We also introduced the concept of result of the Moore machines. In the last section, we proved the correctness of several calculating type of Moore machines.

- Calculating Type
- State Machine with Final States
- Correctness of a Result of State Machine

- [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.
Binary operations.
*Journal of Formalized Mathematics*, 1, 1989. - [4]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [5]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [6]
Czeslaw Bylinski.
Partial functions.
*Journal of Formalized Mathematics*, 1, 1989. - [7]
Czeslaw Bylinski.
Some basic properties of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [8]
Jing-Chao Chen.
A small computer model with push-down stack.
*Journal of Formalized Mathematics*, 11, 1999. - [9]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [10]
Miroslava Kaloper and Piotr Rudnicki.
Minimization of finite state machines.
*Journal of Formalized Mathematics*, 6, 1994. - [11]
Jan Popiolek.
Some properties of functions modul and signum.
*Journal of Formalized Mathematics*, 1, 1989. - [12]
Andrzej Trybulec.
Binary operations applied to functions.
*Journal of Formalized Mathematics*, 1, 1989. - [13]
Andrzej Trybulec.
Domains and their Cartesian products.
*Journal of Formalized Mathematics*, 1, 1989. - [14]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [15]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [16]
Andrzej Trybulec and Czeslaw Bylinski.
Some properties of real numbers operations: min, max, square, and square root.
*Journal of Formalized Mathematics*, 1, 1989. - [17]
Wojciech A. Trybulec.
Pigeon hole principle.
*Journal of Formalized Mathematics*, 2, 1990. - [18]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989.

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