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5 Formalized Mathematics

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Stability ofn-Bit Generalized Full Adder Circuits (GFAs). Part II

100%

Wasaki K.

Formalized Mathematics

2008

tom 16

nr 1

73-80

We continue to formalize the concept of the Generalized Full Addition and Subtraction circuits (GFAs), define the structures of calculation units for the Redundant Signed Digit (RSD) operations, then prove its stability of the calculations. Generally, one-bit binary full adder assumes positive weights to all of its three binary inputs and two outputs. We define the circuit structure of two-types n-bit GFAs using the recursive construction to use the RSD arithmetic logical units that we generalize full adder to have both positive and negative weights to inputs and outputs. The motivation for this research is to establish a technique based on formalized mathematics and its applications for calculation circuits with high reliability.MML identifier: GFACIRC2, version: 7.8.09 4.97.1001

Stability of the 4-2 Binary Addition Circuit Cells. Part I

100%

Wasaki K.

Formalized Mathematics

2008

tom 16

nr 4

377-387

To evaluate our formal verification method on a real-size calculation circuit, in this article, we continue to formalize the concept of the 4-2 Binary Addition Cell primitives (FTAs) to define the structures of calculation units for a very fast multiplication algorithm for VLSI implementation [11]. We define the circuit structure of four-types FTAs, TYPE-0 to TYPE-3, using the series constructions of the Generalized Full Adder Circuits (GFAs) that generalized adder to have for each positive and negative weights to inputs and outputs [15]. We then successfully prove its circuit stability of the calculation outputs after four-steps. The motivation for this research is to establish a technique based on formalized mathematics and its applications for calculation circuits with high reliability.MML identifier: FTACELL1, version: 7.9.03 4.108.1028

Complex Integral

51%

Yamazaki M. , Yamazaki H. , Shidama Y. , Wasaki K.

Formalized Mathematics

2009

tom 17

nr 4

233-236

In this article, we defined complex curve and complex integral. Then we have proved the linearity for the complex integral. Furthermore, we have proved complex integral of complex curve's connection is the sum of each complex integral of individual complex curve.

Morphology for Image Processing. Part I

51%

Yamazaki H. , Byliński C. , Wasaki K.

Formalized Mathematics

2012

tom 20

nr 1

61-63

In this article we defined mathematical morphology image processing with set operations. First, we defined Minkowski set operations and proved their properties. Next, we defined basic image processing, dilation and erosion proving basic fact about them [5], [8].

Riemann Indefinite Integral of Functions of Real Variable

51%

Shidama Y. , Endou N. , Wasaki K.

Formalized Mathematics

2007

tom 15

nr 2

59-63

In this article we define the Riemann indefinite integral of functions of real variable and prove the linearity of that [1]. And we give some examples of the indefinite integral of some elementary functions. Furthermore, also the theorem about integral operation and uniform convergent sequence of functions is proved.