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General aspects of the advancementof theory and practices of

information systemsPeter P. Kuvyrkov and Sergei K. Naidenov

Department of Automation and Control,Penza State Technological Academy, Penza, Russia

Abstract

Purpose The important role of functional and structural generalization of informative andcommunicative processes is considered.

Design/methodology/approach It is denoted that generalitics suggests a means to obtain a newinformation which is more rich in content, more useful, jamproof and optimal. An increasingly

important role of generalitics in the development of the informative equipment is underlined.

Findings Upon the analysis made new attributes of information are suggested and estimated:informativeness, informness and informability. A clear description of the significance of generalizationfor the communication units is presented.

Originality/value Development of the theoretic foundations allows for the creation of newgenerations of the informative technique, automated control and telemechanic systems andcommunications as a whole.

KeywordsCybernetics, Information systems

Paper typeResearch paper

1. Introduction

Everything around us, all collections of information, either already cognized or stillbeing cognized, prove to be the parts of a single whole, possessing both commonnessand diversity. Based on these attributes, the two ways of knowledge acquisition andadvancement were determined specialization and integration.

The first way is that of accumulation of the highly developed diversity giving rise toa considerable body of disunited data, scrappy information. In order to make the bestuse of such information, and to obtain the end result, huge massifs of information haveto be processed.

The second way the way to solve the urgent problems of fundamental sciences isthat of unification, that is, increasing integration of information both within andbetween the sciences. The above becomes evident primarily from the universaltendency to unity, or by virtue of the unity of the world. Besides, the use of the name of

a science Generalitics which derived from the Latin generalis generalization, i.e.raising of the particular to the general, subjecting of particular phenomena to somegeneral principle, proves to be quite reasonable and justified (Kuvyrkov, 2005). In ourcase, the general meaning of the given process is the elimination of informationredundancy and further integration. The general history of science development canserve as proof of the above, according to which an inevitable problem of integration,compression, i.e. generalization of data or knowledge emerged at certain stages of itsspecialization-based accumulation. According to Plank (1966), since the antiquity, ever

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since the investigation of nature began, its ultimate and exalted aim or ideal was togeneralize the plural mixed diversity of the physical phenomena into a united system,or, possibly, to a single formula. So far, no general method is available in modernpractice which could be applied for unification of details into a single whole which

possesses new properties and quality not found in its constituent parts. We see, asbefore, how huge amounts of practical material are built up and used locally forsolution of particular problems; and, again, it is required that generalization, analysis,synthesis, and reasoning are made to provide the basis for further decision making,passing from particular to general, from individual to universal. In this way, or bymeans of generalization, the highest functions of human mind are realized generation of new information, working out laws and making discoveries.

1.1 Levels of generalizationA number of generalization or its levels may be taken as a function of the messagecomplexity, pithiness and of agreement between the result derived and the presetvalues of the generalization indices. From and by the results of generalization of thestarting message, a regeneralization can be performed to generate indices of highervalues.

Let the starting message be one of the zero levels of generalization

X0 {x0i}; i 1; n0, of the first level X1 {x1i}; i 1; n

1 and so on, and in

the general case of the z-th level Xz {xzi}; i 1; nz (Figure 1).

As shown in Figure 1, the message of the zero level may be translated into themessage of the highest levels. In so doing, the number of elements for each message ofthe corresponding level is not equal to the number of elements of the other levels, i.e.n 0#n 1# #nz.

1.2 Indices of generalization

Generalization is a major component of information processes. The message becomesmore compact, compressed or integrated, devoid of redundancy on retention of its essence.

Figure 1.Levels of generalization

X0

X1

Xz

{x01, x0

2, ..., x0

i, ..., x0

n}

{xi0}

{xi1}

{xiz} Zth level of generalization 1, nz

1,n1

1,n0The zero level

The1stlevel

The starting message

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The general indices of the message are its informativeness, informness and informabilitythat associated with multiaspectness of informatization and with a continuing demand forsubsequent formalization of the scientific knowledge and the advancement of informationtheory and its applications in the distinct domains of science, technique and education. As

the names of the indices imply, they show, their common root is the information quantityand hence, there are quantitative definitions of informativeness, informness andinformability. Let us introduce the concept of the relative measure of information quantityof the generalized message that we used as its main index. In such an event,informativeness of the generalized message is the information quantity of the starting (apriori) message which is accounted for as one element of the generalized (a posteriori)message. In other words, the relative measure of the generalized message informationquantity is determined by the ratio of the information quantity of the starting message tothe number of elements contained it in the generalized message:

R0 I0

n 0;R1

I0

n 1; . . .

;Ri

I0

n i; . . .

;Rz

I0

nz;

whereRi informativeness of the generalized message of thei-th level of generalization;I0 information quantity of the starting message; n i number of the generalizedmessage elements. When passing from the zero level to the highest one the number ofelements received with the given message will decrease, while their informativeness willincrease: n 0 . n 1 . . n i. . n z,R0 , R1 , , Ri , , Rz.

For a second general index, the so-called informness is used which means that thereceiver is completely informed by the transmitted message which was received in full.In other words, if the receiver derived from its source the whole message, then it isconsidered as the informed one with the aim of the selection of its further actions in

generalization, the decisions accepted for control by either objects. The message whichis a starting one at the moment of its transmission, and the message received, with itsinformation obtained in full, are named a priori and a posteriori and denoted as IapandIapo, respectively. As a result, the generalized message contains a smaller numberof elements of the a priori one and, as would be expected under these conditions, it willbe characterized by greater informativeness and informness. By informability of themessage its pithiness is meant. For example, one and the same content of the starting

message X0 {x0i} i1; n0 may be presented by the content of the other one

X1 {x1i} i 1; n1 but with the lesser number of elementsn 1 , n 0. In this case, it

is felt that the informability of the second message proves to be higher as compared tothat of the first one.

This increase derives from the fact that the a priori information has some

redundancy affecting the rate of data transmission through the channel ofcommunication and its compactness under registration on the information carriersof the corresponding memories. After generalization, the a posteriori informationreceived differs from the a priori one in its lesser redundancy, greater compactnesswhich positively affects the rate of its transmission and increase efficiency of thememory use.

Thus, a posteriori information is equal to the generalized representation of a prioriinformation of the starting message, i.e. Iapo qIap.


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As a measure of informability, the ratio is used of the starting message informationquantityIapto the information quantity of the other messageIapoderived from the firstmessage by decreasing its excessiveness or v.v. by introducing the additionalexcessiveness to gain in noise stability.

Let us denote informability byw, then informability of thez-th level generalizationis as follows:

wz Iap

Iapo

n 0

nz;

in the sense that for equally probable states of the message elements p i:

wz I0

Iz

n 0log m

nzlog m

n 0

nz

For not equally probable states, respectively:

wz I0

Iz

n 0Xm

i1

pilog pi

nzXm

i1

pilog pi

n 0

nz;

wherepi probability of the i-th state, m number of states.As is clear from the last ratio the starting message information quantity is equal to:

Iap wIapo or I0 wzIz ; n 0 wznz. If it is required to translate the starting

message by introducing the additional redundancy (rather than by decreasing theredundancy), as in the case of coding for noise stability gaining, then informability of

the resulting message will be decreased in the sense that the content of the startingmessage will be presented by the greater number of elements. The levels of thestarting message generalizing and compressing are denoted by z. The opposite actionto introduce the additional excessiveness (i.e. degeneralization) is denoted by z.

In this case, informability of the excessive message is:

w z I0

Iz or I0 w zIz

As the starting message under generalization and degeneralization are the same then:

wzIz w zIz and hence wz

wz

Iz

Iz:

1.3 Measures of generalizationThus, generalization is a process of elimination of the starting messageredundancy and its representation in the more economical compressed integratedform without losses in its matter and essence with the lesser number of elementscarrying it. The generalization measures may be subdivided into absolute andrelative ones.

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As the absolute measure the difference of elements number between the startingand the generalized messages is considered, i.e. Dq n 0 2 nz; while the ratio of theabsolute value to the number of elements of the starting message is taken as therelative measure:

dq Dq

n 0

n 0 2 nz

n 0 1 2

nz

n 0:

As seen from the formulae the generalization eliminates both the redundancyartificially introduced for the noise stability and the natural one caused by features ofthe language structure used for information representation. In both cases, the measuresof generalization are taken to be a criterion of the eliminated redundancy, reduction of alength or integration on retention message substance and essence. As this takes place,the economical effectness is a pragmatic feature, i.e. the feature which is the mostimportant to decide or to control effectively.

2. Generalitics of communication processesUnder close examination of causes and effects of generalization of the communicationprocesses and equipment for their realization, the flow of information is regarded as aform of control action. For the most part, it is possible to mark out three aspects ofcommunication: technical, semantic and pragmatic. They are constituent parts of thegeneral aspect taking into account constructional, structural, functional andinformative generalization. For example, the technical aspect of communicationrefers not only to the processes and equipment for information transmission from onepoint, unit or person to another through corresponding channels but also to possibilityof their subsequent optimization due to generalization. Semantic aspect ofcommunication makes allowance for transmission and receiving information as well

as its understanding by the receiver. Owing to generalization informationunderstanding also is retained but effectness of its transmission and receivingincreases many times over. Pragmatic aspect takes into account the effect of thereceived information on the behavior of its receiver. At the same time by virtue ofgeneralization the value and, hence, the effectiveness of information usage also rises bymany folds.

In Figure 2, examples of constructional and structural generalization are shown.Using the base of unity vectors of two-dimensional space e1 and e2 (Figure 2(a)), thecontrol circuits of the input of the communication unit are directed along the givenvectorsX1 {x1i} i1; aand X

2 {x2j } j 1; b(Figure 2(b)) and the number ofthe control circuits is equal to m a b. Under generalization of the given setsof the control circuits, we have the new set with the number of circuits X1;2 {x

1;2

i

}

i 1; c(Figure 2(c)), equal to c a b.Each circuit of the produced set differs from the proceeding ones by the fact that

the circuit is a single whole made out of two united parts directed along unityvectors of the two-dimensional space base. Under subsequent integration of thepresented sets of the control circuits, one derives the grating structures of thetwo-dimensional control of the communication unit non-generalized (Figure 2(d)) andgeneralized (Figure 2(e)). Positioning the controlled elements with two control inputsconnected, respectively, to two common to both control circuits results in structures


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of the communication arrangement with non-generalized (Figure 2(f)) and

generalized (Figure 2(g)) makes.

Comparing the given arrangements one can see that at one and the same number of

the control circuits (m 6) the matrix structures of communications involve the

different number of control circuits or outputs. In the first case N(0) 9, in the

second N(g) 15 that points to the positive effect of the constructive and structural

generalization on communicativeness of the corresponding units.

Figure 2.Elements of constructionaland structural

generalization: (a) base oftwo-dimensional spaceunity vectors; (b), (c)elements of constructionalgeneralization; (d), (e) control circuit input ofnon-generalized; (f), (g) structure of thecommutative device withnon-generalized andgeneralized make

N0= ab= 33 = 9

Controlled

element

X1,2

{Xi1,2}

Generalizedcomponents

{Xi1}{Xj

2}

j= 1,b i = 1, a

i = 1, c

m= a+ b m= c

X2

X1

Non-generalizedcomponents

No connection

Connection

xj2

xi1xj

2=xi

1xj

2= 0

Nq= C2a+b= C

22C= C

26= 15

xi1xj

2=xi

1xj

2= 1

xi1 xj

1,2

xi1, 2

xj1, 2

=xi1, 2

xj1, 2

= 0

xi1, 2

xj1, 2

=xi1, 2

xj1, 2

= 1

xi1,2

e1 e2

O

(a)

(b)

( d )

( f ) ( g )

(c)

(e)

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Denote unit communicativeness by k equal to the ratio of a controlled elementsnumber or outputs N to a control circuits number or inputs by m, i.e. k N/m.Atm 6 with the non-generalized make of the given unit one haskn 9/6 1.5 andwith the generalized make kg 15/6 2.5. With increase in the control inputs

numberm the unit communicativeness with the generalized make becomes more thantwo times as compared to the non-generalized one. In this case, Nn 0.25m

2,Ng C

2m 0:5 mm2 1,kg 0.5(m 2 1),kg=kn 2m2 1=m 2. If one uses the

three-dimensional communicative units as an alternative to the two-dimensional ones,the effect is much more evident. Note that tetrahedron structures are characterized byquadruple increase in their communicativeness in comparison with the cubicones. Specifically, if for the three-dimensional unit with the non-generalized makeNn 1=3m

3 1=27m 3 then for the generalized one:

Ng C3m

mm2 1m2 2

1 2 3

1

6mm2 1m2 2:

Consequently:

kn 1

27m 2; kg

1

6m2 1m2 2; kn 4:5:

In such a manner, the generalized make of units to realize communicative processes isof paramount importance in the further advancing of the information systems and theirsupplements.

3. Generalitics of information processes

Information processes of data gathering, storing and transmitting of information, theirconversion from one form to another as well as from one code to another determine acontinuing demand for development and use of the large variety of specialized unitsadjusted individually for ensuring of one or another functions. The solution ofproblems in their optimization, universality and multifunction went possibly on a basisof the informative process generalization. This offers considerable scope for the newanswer to all problems of information as follows: interchanging, storing, transmittingas well as receiving the new information, allotting it by the larger pithiness, moreuseful, protected and jamproof. Let us consider some examples of functionalgeneralization, the base of which is constructional and structural generalization(Figure 3). In this case, one and the same unit may be rebuilt in response to action of theswitch functions, i.e. it is the multifunctional one. The switch functions of control bycommutation of the given unit differ from one another and are in accordance with theirfunctional purpose. The form of the switch functions is varied according to the level ofconstructional and structural generalization.

Consider transducers of the first level of their generalization. Denote the inputcircuits of transducers by x11;x

12; . . .;x

1i; . . .;x

1n and their outputs by

y11;y12; . . .;y

1i; . . .;y

1n. On intersections of the control with controlled buses they

position the logic elements with memory connected by their inputs and outputs to thebuses. The elements transmit information from x1i to y

1i in accordance with a control


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action of the switch function fkx1;y 1. In t he abs enc e of c on nec tion

x1i ^y1j x

1i y

1j 0, with connection x

1i ^y

1j x

1i y

1j 1. We consider some switch

functions:

. Follower of input information (Figure 3(a)). Corresponding switch function is asfollows:

Figure 3.Elements of functional

generalization

x'3

x'2

x'1

x'4 y'1

y'2

y'3

y'4

x'3

x'2

x'1

x'4 y'1

y'2

y'3

y'4

x'3

x'2

x'1

x'4 y'1

y'2

y'3

y'4

x'3

x'2

x'1

x'4 y'1

y'2

y'3

y'4

x'3

x'2

x'1

x'4 y'1

y'2

y'3

y'4

x'3

x'2

x'1

x'4 y'1

y'2

y'3

y'4

x'3

x'2

x'1

x'4 y'1

y'2

y'3

y'4

x'3

x'2

x'i y'j x

'i y

'j

x'1

x'1

x'2

x'3

x'4

x'5

x'6

x'7

x'4 y'1

y'1

y'2

y'3

y'4

y'5

y'6

y'7

y'2

y'3

y'4

ConnectionNo connection

(a) (b)

(c) ( d )

(e) (f )

(g) (h)

( i )

xi'yj

'=xi'yj

'= 0 xi'yj

'=xi'yj

'= 1

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f1x1;y 1 x11y

11 x

12y

12 x

1iy

1j x

1ny

1n

Xn

j1i1

x1iy1j

According to the given function the follower circuit faithfully copies at its output theinput information. For example, x 1 1011, y1 1011.

. Mirror-image presentation of the input information (Figure 3(b)). The switchfunction has the appearance:

f2x1;y 1 x11y

1n x

12y

1n21 x

1iy

1j x

1ny

11

Xn

jn2i1i1

x1iy1j

In compliance with the given function the circuit ensures the mirror-image presentationat the input of the information taking place at the output. For example, x 1 1011,

y1 1101.. Control in module 2 (Figure 3(c)). The switch function takes the form:

f3x1;y 1 x11y

1j x

12y

1j x

1iy

1j x

1ny

1j

Xn

jni1

x1iy1j

With the even number of unities at the circuit input a sum of unities at the output y1i is

equal to 0, with the odd number y1i 1. For instance, x1

1011, y 1 1 or

y1 0001.

. Spreader of the input information (Figure 3(d)). The switch function has the

shape:

f4x1;y 1 x1iy

11 x

1iy

12 x

1iy

1j x

1iy

1n

Xn

j1iconst

x1iy1j

Respectively, a unity at the input of a certain circuit is transformed in unities at alloutput circuits. By way of illustration, i 1, x11 1, x

11000, y1 1111.

. Channeler of the input information (Figure 3(e)). The switch function is:

f5x

1

;y1

x

1

1y

1

j x

1

2y

1

j x

1

iy

1

j x

1

ny

1

j X

n

jconsti1

x

1

iy

1

j

As prescribed by the function, any number of unities at the input we have only at thej-th output 0 when the number of unities is even and 1 when odd. The cite anexample, at x 1 1011, y 1 0010, j 3.

. Shift of the input information (Figure 3(f)). The switch function is represented asfollows:


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f6x1;y 1 x11y

12 x

12y

13 x

1iy

1j x

1n21y

1n

Xn21

ji1i1

x1iy1j

In the given case, we get the shift of input information per one position, i.e.x 1 1010,y 1 0101. Using the similar unit, it is possible to construct a controlled shiftingregister for any number of positions.

. Transducer of the binary code into Gray code (Figure 3(g)). The switch functionmay be described as:

f7x1;y 1 x11y

11 x

12y

12 x

1iy

1j x

1ny

1n

x11y12 x

12y

13 x

1iy

1j x

1n21y

1n

Xn

j1i1

x1iy1j

Xn21

ji1i1

x1iy1j

Having at the input the binary code combination x 1 0010 one derives at the outputcombination of Gray code y 1 0011.

. Transducer of Gray code into the binary one (Figure 3(h)) with the switchfunction of the form:

f8x1;y 1 x11y

11 x

11y

12 x

1iy

1j x

11y

1n

x12y12 x

12y

13 x

1iy

1j x

12y

1n

x1ny

1n

Xn

i1

Xn21

j1

x1iy1j

. Transducer of the binary code into Hamming code (Figure 3(i)). The switchfunction is as follows:

f9x1;y 1 x13y

11 x

15y

11 x

17y

11 x

13y

12 x

16y

12 x

17y

12

x13y13 x

15y

14 x

16y

14 x

15y

15 x

16y

16 x

17y

17

Elements of the binary code arex13;x15;x

16;x

17, i.e. the input x

1 {x13;x15;x

16;x

17}. Check

symbols of Hamming code are formed at outputsy11;y12;y

14 and at the rest outputs one

obtains the coping values of input symbols, i.e.y13 x13,y

15 x

15,y

16 x

16,y

17 x

17. As an

example, x 1 1011, y1 0110011. In perfect analogy to the above-considered, wemay show the effect of generalization upon numerous electronic units and systems

(Kuvyrkov, 1985).

4. ConclusionWe may predict in future that great attention will be given to this important theory,and the generalitics as a whole will be given consideration in respect of the following:definition of the generalized information; generalized measures of information;generalized codes of information; generalized representation, transmission, saving,noise stability and data protection based on whose constructional, structural and

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functional generalization; informative generalization in which the general principles ofthe generalistics of the communication processes are represented.

The development of the theoretical foundations of the given science allows thecreation of the new generations of the informative technique, automated control and

telemechanic systems and communication systems as a whole.

References

Kuvyrkov, P.P. (1985), Teoreticheskiye osnovy kombinatornykch system (Theoreticalfundamentals of combining systems), Informative Systems, No. 11, collected articlesAutomatic control and computing techniques (in Russian).

Kuvyrkov, P.P. (2005), Generalitika informatsionnykch processov (Generalistics ofinformative processes), paper presented at Annals of the International Conference onMathematical Methods and Information Technologies in Economics, Sociology andEducation, Penza, Russia (in Russian).

Plank, M. (1966), Unity of the Physical Picture of the World, Nauka Publishers, Moscow (inRussian).

Corresponding authorPeter P. Kuvyrkov can be contacted at: [email protected]


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