Journal of Formalized Mathematics
Volume 14, 2002
University of Bialystok
Copyright (c) 2002 Association of Mizar Users

Preliminaries to Automatic Generation of Mizar Documentation for Circuits


Grzegorz Bancerek
Bialystok Technical University
This paper was written when the first author visited Shinshu University as a two-year JSPS Fellow.
Adam Naumowicz
University of Bialystok
The paper was prepared during the author's cooperative research at Shinshu University 'Verification of circuit designs with the aid of the Mizar system'

Summary.

In this paper we introduce technical notions used by a system which automatically generates Mizar documentation for specified circuits. They provide a ready for use elements needed to justify correctness of circuits' construction. We concentrate on the concept of stabilization and analyze one-gate circuits and their combinations.

MML Identifier: CIRCCMB3

The terminology and notation used in this paper have been introduced in the following articles [21] [27] [25] [20] [11] [9] [28] [6] [12] [2] [3] [7] [1] [8] [14] [4] [10] [22] [26] [23] [5] [17] [18] [15] [16] [19] [13] [24]

Contents (PDF format)

  1. Stabilizing Circuits
  2. One-gate Circuits
  3. Mono-sorted Circuits
  4. Input of a Compound Circuit
  5. Result of a Compound Circuit
  6. Inputs Without Pairs

Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. Sequences of ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Grzegorz Bancerek. Tarski's classes and ranks. Journal of Formalized Mathematics, 2, 1990.
[4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[5] Grzegorz Bancerek and Yatsuka Nakamura. Full adder circuit. Part I. Journal of Formalized Mathematics, 7, 1995.
[6] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[9] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[10] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[11] Jing-Chao Chen. A small computer model with push-down stack. Journal of Formalized Mathematics, 11, 1999.
[12] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[13] Jaroslaw Kotowicz. Monotone real sequences. Subsequences. Journal of Formalized Mathematics, 1, 1989.
[14] Jaroslaw Kotowicz. The limit of a real function at infinity. Journal of Formalized Mathematics, 2, 1990.
[15] Yatsuka Nakamura and Grzegorz Bancerek. Combining of circuits. Journal of Formalized Mathematics, 7, 1995.
[16] Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto. Preliminaries to circuits, I. Journal of Formalized Mathematics, 6, 1994.
[17] Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto. Preliminaries to circuits, II. Journal of Formalized Mathematics, 6, 1994.
[18] Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto. Introduction to circuits, II. Journal of Formalized Mathematics, 7, 1995.
[19] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Journal of Formalized Mathematics, 5, 1993.
[20] Andrzej Trybulec. Enumerated sets. Journal of Formalized Mathematics, 1, 1989.
[21] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[22] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[23] Andrzej Trybulec. Many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[24] Andrzej Trybulec. Moore-Smith convergence. Journal of Formalized Mathematics, 8, 1996.
[25] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[26] Wojciech A. Trybulec. Groups. Journal of Formalized Mathematics, 2, 1990.
[27] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[28] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received July 26, 2002


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