Акулов О.А., Медведев Н.В. Информатика. Базовый курс

THbrx MareMarnKoB.4,.

Fnrrs6epra, K. leAea.a, A. 9ep.ra,

C. Krrxnu,

3.

flocta

n A. TrrcpuHra B

AByx

sKBr.rBa

eHTHrrx

$opr'rynrrpoBKax:

Ha

ocaoBe oco6oro

K acca apraQuerrrecKrirx

Qynxqnfi,

nolftlrBrur.x

Ha3BaHrde

peKypcr{BHbrx

Qyurquli

(!,.

fua-u6epr,

K. feAerr,s, A. 9epv,

C. Ka.llHu)

H

Ha ocHoBe a6crparrubrx aBToMaroa

(3.

Flocr, A. Trro-

prHr).

Bnocrr.e4crauu

a

pa6orax

A, Mapxoaa,

A. Kaay:rurnna uosBr{-

.IlOCb TO KOBaHHe TeOpI,Irr

aArOpr{TMOB, nOCTaBHBrrree B

OCHOBy OIIpe-

AeleHlre

alroplrrMa rax

oco6oro coorBercrBlrr MexAy

cloBaMlr

B ToM

HAH

r4HoM a6crparrnou

aa$aenre.

Tarau o6pasolr, nepBoHaqalbuo

reopr{ff arlropr.rrMoB

Bo3HLrKAa

B

cBff3r,r c BuyrpeHHurrru norpe6uocrsMrir

reoperlrqecKori

MareMarr.r-

rrn, MarevraruqecKag

.lt.ornKa, ocHoBaHLIfl MareMarr{Kl{,

a.lte6pa, reo-

Merpun u

aHa,ru3 ocrarorcff rd

ceroAHr o4nori

r.r3

ocuoBHbrx

o6aacreft

rrprrlox<ennff

Teopuu alropr.rrMoB.

Kpolre roro, Teopnff

eraropltrMoB

oKaSil^acb TecHo csggaHHofr 14

c

pffAoM

o6rracreft /\r{HrBtrcrlrKx,

gKo-

HoMI4KII,

$nezorrorul

Mogra

I{

rtcuxo,torr.l,r,

SuaocoQnra,

ectecraos-

HaHr,rfl.

Flpuuepou

oAHoft

H3

SaAarr srori o6rracrH Mo)r(eT

c^y)KlrTb onr4-

CaHLIe aIATOpLITMOBT

peaAI,I3yeMhIX

qeAOBeKOM

B upoqecCe

yl,rCtAennOri

AeffTeAbHOCTr,r.

Blrecre c reM B 40-x ro4ax flporrrloro

BeKa B cBfl3r4

c co3AaHrreM

3 eKTpOHHBIX BbIrrr.rC^rrTe

bHbIX I4

ynpaBItIOIIIHX

Marrrr,rH

BO3HUK a

o6rlacrr reopurr

alropr,rrMoB, Tecno nsauuo4elicrByrou{aff

c r.rHSop-

uaruxori. Hosgrr.enrae

3BM cnoco6crsosalo

pa3Br,trr.rrc pas4eaoa

erori

Teopulr, nMeror4Hx

flpKo

BbrpoKeHHyro

rlpuK aAHyro HarrpaB^eHHocTb.

B

nacronuqee BpeMff noloxeHr.rfl Teopr{H

alropr{TMoB ffBrrrrorcrr reo-

peruvecxoli

ocnosori raKr{x cocraBHsrx

.racreft

coBpeMeHHorl nHQop-

MaTr,rKHr KaK

TeOpUU npOrpaMMIrpOBaHHt, [OCTpOeHUff

aArOpI,ITMI,IqeC-

Kr{x fl3brKoB n

3BM, aHirar{3a alropr{TMoB c rlelbro au6opa Han6oaee

paqr{ouir

bHoro

44.t

perueHufl

na 3BM, aHaauga allopr{TMnqecKux

fl3brKoB r.r rlrx

crrHTaKcr{qecKoro KoHTpoLs npu

paspaooTKe

TpaHc .fi-

ropoB.

B

o6uqeu c^yqae

rrpz

cocraBleHun a roplrrMa KoHKperHoli

sa4a-

qr.r

aKTyar bHoe 3HaqeHue r{MeeT TaKoe rrpeAcTaB^eHr.re

a^ropr{TMa,

Koropoe no3BoLser

nau6orree 6rrcrpo

pealr,r3oBarb

ero Mexaur43rd-

poBaHHhrM

[yreM, 14 B

qacruocrr,r

c rroMorqrrc

3BM.

llpra

srou

44.a

perrreHr,rfl

3aAatu

c

[oMorrlbro

3BM ee

neo6xo4rauo

garrporpaMMr.r-

poBaTb,

T. e. npe.d,cTaBr,rTb aAropI4TM

perueHr{ff

SaAarru

B BHAe

lroc^e-

AoBare

bHocrI,I KoMaHA, Korophle Mo)Ker BbrrrolHtrb Marrr[Ha.

O4na-

KO npoqecc 3alr4cr{

aN'opr{TMa

B B}rAe rroc^e.aioBaTe^bHocTl4

MaIILIH-

Hbrx KoMaHA

oqeHb

Af|l.r.rTe^bHbrri

u

rpy4oeururl,

Ero rarure Mo)KHo

t78

aBTOMaTT{3I{pOBaTbr eclr{ HCIIOJI_b3OBaTb

A^fl

3aIIHCLr aTATOpHTMOB

C^-

topumuuq'tecrue

n3brxu, npeAcraBl-flrorque

co6ori na6op

cr{MBoIoB }r

TepMHHoB, cBff3anHhrx crrHTaKcuqecxofi

crpyxrypoft.

C r,rx nouou4rro

MOXHO IIO OnpeAe

eHHhrM [paBuAaM

outrcbrBaTb ar^ropr4TMbr

peue-

HHfi

3aAarl. Aaropuruu,

3alrucaHHble B aaropl{TMr,IarecKoM

g3hlKe,

aB-

ToMarlrqecKu cauoft

3BM c noMorrlbro

cneqlrar bHori nporpauuu-

Tpancltropa

Morfr

6urr nepeaeAeHbr B Marur{HHbre

nporpaMMbr

44.a

xonxperxoft

3BM.

Hau6orree Bax(HhrMlr [ourrlrrMr{

Teopr{r4

alroplrrMoB c roqKu

3pe-

xnn

unQoprrraruKr,r

rB rrorcr : irlropnrM

r

a.,rropltTMurrec Kr,re

clcreMbr,

a

TaKx(e cHcTeMbr 14 MeToAbI

il^ropllTMr{3arluu.

5.1.

NOH'ITI4E AATOPI4TMA

I,1 ETO

CBORCTBA

\

,4tropumn

-

roHe.rHbrti na6op

[paBHA H ]r KoMaHA

(yrasaur,ui),

no-

snoaarculuft lrcnolrrlrrelro

peruatr

aro6yro KoHKperH)4o

3aAarry u3 HeKo-

TOpOTO K aCCa OAHOTHIHbrX 3aAaq.

IrlcnoanrureleM Mox(er

6grrr.reaoeeK,

rplm[a

ruoAerl,

ctanor, KoM-

nbrcTep r

ap.

C

yqeroM

oco6euHocreft ucno,rrarlrelr

cocraBrrennrrrl

alroprrrM

Mo)Ker

6urr npe4craBleH

pa3luqHbrMn

cnoco6aua: c no-

Morrtbro

rpaQu.recxoro

ralrr cloBecHoro

orrucaHur, B Br.rAe ra6lr.ulbr,

nocleAoBarelbnocrbro

Qoprrryl,,

3a[r{caHHbrx Ha

a

ropl,rrMr{qecKoM

f,3hlKe

(xerrxe

rporpaMMr{poaanra)

rd

Ap.

[2].

\

flsux- 3HaKoBar cncreMa

(uHoxcecrao

cuMBo oB u upanr.a) rrro6ori

Qusuvecxofi

rrpupoAbr, Bbrno Hrrro[Iarr

rro3HaBarelbrryp ]r

KoMllryr{nKar}B-

nyro

(o6qenue)

Qyuxquu

B [poqecce

qeloBeqecKorl

4earenruocu.

.flgrrx

r"ro:xer

6srrr ecrecrBeHHbrM lr r{cKyccrBeuHbrM.

EcrecrgeH-

nuft sgux

-

Qopua

Bhrp.DKeHrlrr uucaeft

n cpeAcrBo o6qeHua uexr-

Ay

lroADMr,r. HcrcyccrnenHrrri

sgrrx

-

BcnoMorareatusrfi, cos4anHrrfi

ga

6age ecrecrBeHHoro fl3blKa AroA,bMLr

44r

KaKr{x-lu6o vactnrrx

qe-

rrefi.

Hepaonava.rrrxo

44.a

3anllcl{ illropr{TMoB trolbgoBalr,Icb

cpe.licrBa-

MU

ECTECTBEHHOTO

fl

3bIKA.

t79

Ctaonecnuil

e,l.ropuntrit

-

orrncaHlre

nocleAoBarelbnblx eranon

o6pa-

6orrn

4annux

Ha ecrecrBeHHoM

g3hlKe.

YroqHr.rM

[oHrrrre cAoBecHoro

aLLropI,ITMa Ha

npI,IMepax clo>r<eHnfl

n

ql4ce^

ctrr ct2t

...r cn, T. e.

BbIqIlrcAeHI{a

no

$oprvrya"s

=

io,

I{ Haxo)K-

t=l

AeHrrg

MUHI4MtIAbHOTO

IILICAa

X B MaCCI4Be

U3 n

qHCeA

Q

(

CIl ,,,, Qn,.

B

nepnolr clyqae

[poqecc Mox(er

6rrrr

gauracarr

B BuA,e c eAyIo-

uleri cncreubr

nocleAoBarelbublx

yxasannti

:

1. Ilorraraev S

paauuu

HoAIo I{ nepexoAl,rM

K cleAyroqeMy

yKa3a-

HLIIO.

2. Ilonaraelr i

paaHuu

eAr.IHI,Iqe

I4

nepexoAr{M

K cleAyroqeMy

yKa-

3AHI'IIO.

3,

floaaraer"r

S

pannuu

S*4,

u nepexoAlaM

K cleAyroqeMy

yKa3a-

I{I{rO.

4.

IlponepreM,

paBHo

,lru i.rucay

n.

Ecala i

:

rlr To BbItrI4cAeHHs

[pe-

KparqaeM.

Ecau t

<

n, To

yBelurrltBaeu

i

na eMHI4qy

H [epexoAr'IM

x 3-rwy

yraeaulirlo.

flpoqecc

HaxoxAenut

MIaHI,IMaAbHoro

qucla

x B MaccI,IBe

v3 n'ru-

ceua

t,

e,

..., an, ocyulecrBltercg

cleAyroulurrl

o6paaou,

FlepeoHauaar-

HO

B KaqeCTBe

quc.I|a

x [pI{HI4MaeTCfl

d,,

T, e, no^araeM

x

:

or,

uoc^e

qero

x cpaBHI{BaeM

c noc

e.AyroIr{HMI,I

qnc/laMl'I

MaccI4Ba,

HaqI'IHafl

c

a

r,

Ecl*t

x

1

e

r,

To x cpaBHl4Baercff

c 03, eclrll

x

1

a

I

To x

cpaBnl'IBaercfl

c

a4,

y!

T.

A.r

noKa

He IIo/tyqI{M

qllrc^o

a.

<

x. Torpta

llo^araeM x

:

aivl

npoAo JKaeM

cpaBHeHI4e

c

x nocleAylolrdl,Ix

aII4ceA

I'I3

MaCCITBa'

HaqI{-

Hafl c ci+,,

rr

raK

AO

TeX rrop,

noKa He 6yayr

[pocMorpeHbl

n

qlllce^.

B

pesynrrare npocMorpa

Bcex n

.ruce,r

x

6y4et

fiMerb 3Har{eHI'Ie'

paB-

Hoe

Har4MeHbuIeMy

ql4cly

LI3 MaccHBa

(f

-

rexytrluli

nouep

qucla

L3

uaccura).

Srot

npoqecc

Mox(er

6rtrr

gauncaH

B BrrAe crre4yrorqeri

cn-

creMbr

rroc.rreAoBare.rrbHblx

yxasauuti

:

1. lloaaraeu

i

:

I unepexoMM

K

cleA,yroqeMyyKa3aHI4Io'

2.

Ilorr.araeu

x

:

a,u

nepexoAl{M

K cIeAyIouIeMy

yKa3aHlrro.

3.

CpaaHneaeu

i c

n, eclr.I i

{

n,

ro nepexoAl'IM

K cleAyloqeMyyKa'

3aHI'tIO,

eC

U i

:

n, [poqecc

uo]IcKa ocraHaB^r{BaeM.

4. Ysepr.rusaeu

i na eAlrHI,Iqy

u uepexoAl{M

K c^eAylouleMy

yKa3a-

HI{IO.

5.

CpaaHuraeM

oi c

x. Ec,rrn Q,7

x,

To uepexoAr'Iu

ryraeanuro

3,

ecAH oi

<

x, nepexoAnM

K

yxaaanurc

2,

180

AaropuruaMr,r

B coBpeMennofr MareMarr,rKe nplrHrrro Ha3LrBarb

KoH-

crpyKTr,rBHo

3aAaBaeMhre coorBercrBr"rrr

MexAy

cAoBaMI4 a a6crparr-

Hux aa$aanrax

[2].

Kax 6rno orMeqeHo

Bbrure, uo4

a6crpaKTHbrM aaQaaurou uoHlr-

uaror

aro6yro KoHeqnyro coBoKy[Hocrr o6rexroB, Ha3brBaeMux

6yr-

BaMH

u^u

Cr{MBOAaMr.r

AaHHOTO

arr,$annra. llpu

erou

npupop\a

3Tr4x

o6beKtoB

He lrMeer 3HaqeHr4s, Cratvrgo.troM a6crpaxrHrrx

aaQannroa

Mo)r(Ho

crrrrrarb,

HarrpnMepr

6yxru arrQauura xaxoro-rrrl6o fl 3brKa,

qu$pbr,

ruo6ue

3HaKr4,

pIdcyHKI.I

LI T. n.

A.t$aarr,

rax rrro6oe r"rHo)r(ecrBo, 3aAaercfl rrepeqlrcrrenneM

ero

g

e-

MelrroB,

T.

e. cLtMBoAoa.

Haupurr ep, A

=

fo1,a2,a3,a4),

B

=

lr,b,",I

,v\,

c:

{x,y}.

Ctoao

(cmpoxa

atQazuma)

-

ruo6as KoueqHaff

ynopqAoqenHaJr

rrocle-

AoBarelbHocrb

cr4MBo oB.

t{raero

cra}rsoloB

B

cloBe

Ha3brnaror

gaunofi

unea.

Tax, a aaQanure A cIoBaMr{ 6y4yr ruo6ue nocle.l,oBarelbHocru

cr,

e p!

e

re

je.,

a4a4vr

r. rr.r B aa$arnre C

-

x,

f,

xf,

fx,

xxt

W

vIT, n,

llpu

pacruupeur.rn

aaQaazra,

T.

e.

rrpLt BKAroqeHr.rH B

ero cocraB Ho-

Bbrx cuMBo./r'oB,

rroHtTr{e

cloBa

Mo)KeT npeTepueTb

cyrqecTBeHHoe

r,r3Me-

HeHHe. Tax, a aa$aaureA

:

10,

1,2,3, 4,

5, 6,

7,

B, 9)

Bbrpa)Keur{e

(

15 + 68>

npe.AcraB

.aer co6ofi4aa clloBa, coeArdHeHHbre

3HaKoM cyruMhr,

a

aaSa-

sHTeA'

:

{+,

0,

1,2,3, 4,

5,6,

7, 8,

9}

sro6y4ero4no c

oBo.

AtaQaaumnur onepsmopolr,

Lr u

atQasumnuu onodpax,exuerr

Ha-

3bIBaIOT

BCqKOe COOTBeTCTBI{e, COIOCTaBA-srOil{ee C OBaM HeKOTOpOTO a

-

Qanzta

cloBa B ToM x(e uln Bp,pyroM

Qllrcupoaaunorr

aa@aeure.

flpu erou

nepauf, alSannr Ha3brBaercff

BxoAHbrM, aropofi

-

Bbr-

xoAiHbrM

a,rQaaurou

AaHHoro

olepaTopa.

B cayrae coBuaAeHufl

BxoAHoro H BblxoAuoro arrQarnroB

roBopflT,

uro aaSaaurnrrri oneparop

3aAaH B coorBercrBylouleM aaQaanre.

Ecrru cr

-

cloBo

a

aaQaaure

A, a

F

-

cloBo

a anQaaute B,

ro

a-lSa-

anrHhu;r

o[eparop

fu:

F

<nepepa6arbrBaerD

BxoA,Hoe cloBo o

B BbI-

xoAHoe

cloeo

B.

Eyxra I

a

arrQaararnou

oneparope o3na.raer oro6poKenlle.

Esrs xa-rx-

AoMy

BxoAHoMy cloBy

alQaanrnuri oneparop craBrlT

B coorBercrBne

He

6orree oAnoro

BbD(oAnoro c oBa,

ro raxoft arr$asr4rHblfi oneparop

Ha3bI-

BaIOT OAHO3HarrHbiM,

B rrpOTr4BHOM C

yqae

-

MHOro3HaqHbIM.

181

AaQanunruri

oueparop,

He

conocran

rruoultri

AaHHoMy

BxoAHoMy

c^oBy c,

HIITKaKOTO

BbIXOAHOTO

C OBa br,

ne

Onpe4eleH

Ha

gToM

cAOBe,

Coaoxynnocrb

Bcex cloBr

Ha Koropbrx

arrQaarrnufi onepatop

on-

peAe

eH,

Ha3blBaercff

eto odtacmbro

onpegeleHur.

Hau

6o.rree

[pocrbrMr,r

ff

Blttlorcg aa$anurnue

on eparopbl

I

ocyule

-

crBLff

rorque uocr{MBolbnue

oro6paxenus,

llocr,rMBolbnoe oto6paxe-

HHe cocrol{T

B ToM,

.rro

ra:r<45tft

cr{MBol s

BxoAHoro cloBa a saMeHfl-

ercfl

HeKoropbrM

clIMBoAoM

BblxoAnoro

a.tQaaura

B.

Eoasruoe 3HaqeHI4e

lrMelor raK

Ha3bIBaeMbIe KoAr4pyroque

oro6pa-

xeuux

[21.

\

Kogupynqee

omodpax.enue

-

coorBercrBlle,

conocraBl.fi

loulee KiliK-

AoMy

cnMBoIy

BxoAnoro a.lQannta

HeKoropyro KoHerlHylo

nocleAoBare

r'-

Hocrb crrMBo oB

B BLIxoAHou a.lQanute,

Ha3blBaeMyrc xogoL,

Haupar*rep, eclrl

3aAaHbI

axo4noi A

:

{a,b,c,df

n eblxoAuoi

B:

{0,

1, 2, 3, 4, 5, 6,

7,

B,

9} aaSaararur,

a raKrl(e oto6paxtenue

cr4MBo-

aoe

A

cr,tMBoAaMLI

B

(puc.

5.1),

ro

44-s

nocrpoenlrfl

ltcKoMoro Koppy-

rcu{ero oro6pa.:renr4fl

Aocraroqno

3aMeHI{Tb

Bce

cI,IMBo.lrr

ano6oro cao-

Ba cri

B

aaQauure

A

coorsercrByroull4Ml.I

Ko.a,aMt4 arrQaanra

B.

a

A

+931

+78

+456

+

0123

c

d

Puc. 5.1. flpr,rtrep

KoAl{pypu{ero oro6paxrenur

Tax,

44-s

cloBa d

:

bccd I{MeeM

fa:

784564560123.

Horryrennoe

TaKr{M o6pasou cloBo

a a,rr$aeure

B nasbrsaercfl

Ko.a,oM

rtcxoAHoro

c^oBa d.

Hpoqecc, o6patuuti

KoMpoBaHI{Io,

T.

e. 3aMena

B cloBe

B,

xo4on

aaQanura

B culrsolaMz

as arrQaaura

A, Ha3bIBaercfl

AeKoAI,IpoBaHI'I-

eM r,r o6osnatraercff

Tu

F,:

d,.

r82

Hanpur'rep,

44t

c^oBa

9:

9314567878

a aaQannte

B

4exo4llpora-

xne

ftp4aer

cloBo

a=

acbb.

Ko4upoaanue

Ha3brBaetca

o6paruMbrM,

ec

I{

npI.I KOAiI{pOBaHnI{

c^oBa

di

flo^yqaeM

HeKoropoe

c^oBo

fl,

a

4exo4upoBaHue

Aaer

HcxoA-

HOe

CAoBo

qi(r

ai:

F,,

r'

F,:

a,l,

B

npune4eHnor"r

sblue

nfrrr'repe

o6paruuocrb

[Meer

Mecro'

IlyirureuepaurueeuA: {a,

b, c},8:

{0,

l},/-a

:0,fb:l,fc:

0l

N caoeo

aabca

a

a.tQarnre

A. TorAa

laabca:

001010u

ft00

10

:

aababa(nu6o

oano

lr3

c oB

acaba,

aabca,

acca),

t' e'

o6-

PaTUMOCTb

orcyrcrByer.

.{.ns

o6patr.rMocrl,I

KoAIlpoBaHIIt

.aio^x(Hbl

Bblno

Hgrbct

c^eA)ruoqlre

yc oBnt:

1. Koarr

pa3Hbrx

cI,tMBoAoB

ltcxoAHoro

arr$aaura

A

4oaxcrrr

6uts

paSAI,IIIHbI.

2.

Koa,,rro6o10

cl'tMBola

aaSaaura

A

He Mo)Ker

coB[a'd'arb

H]I c

Ka-

KIIM

r{3

HaaIaAbHbIx

roAcAOB

KOAoB

Apyndx

cuMBOAoB

erorO

aaQarnra.

Caoro

p

nasblBaercs

[oAcloBoM

c

oBa

g,

ec

]r cloBo

q

Mox<rro

npeA-

cTaBr{Tb

B Br{Ae

Q

:

pr,

rAe

r

-

alo6oe

c^oBo,

B

TOM

qUC/\e

U nycToe'

T. e.

He coAep)Kaulee

HI4

OAHOTO

CHMBOAa.

Bropoe

yc^oBr4e

Bbrlloj\HfleTcg

B TOM

C^rrae,

ec^l!

KoAbI

Bcex

c]IM-

BoloB

lrcxoAHoro

aaQasura

A

uMelor

oAuuaKoByro

AAr{Hy'

Ko4uponanrle,

[prl KoropoM

Bce KoAbI

uMelor

oMHaKoByIoMIrHy'

Ha-

3HBarOTHOpilC

bltHll.

Ko4upoeanr{e

noSBoAgeT

cBoMTb

r43yrreHue

npo}I3BO

bHrrx

aaQa-

BUTHbTX

oro6pa;<enuft

r aa$arnTHbrM

oto6pa:reru4flM

B

HeKOTOpOM

craHAapTHou

arrQaaure.

Hau6oaee

qacTo

B KaqecTBe

cTaHAapTHOrO

aasanura

arr6r,rpaercs

AsoE.rHbli

aaQaenr,

cocrofiIqsfi

!r3

A,ByX

cllM-

"orto",

roroprre

o6brrrHo

oro'(AecrBLflIor

c

Ilrn$par"rra

O

u l:

B

:

{

0, 1

}

'

flpz

srou,

ec.lr.u

n

-

rtuc,ro

clrMBoloB

n aa$aanre

A, to

rcer4a

MOXHO

rH6pars

MlrHy

cloBa

l rax,

.rro6br

yA,OBAeTBOpfllocb

yclo-

sue

12n.

llocxorrrxy

quc/\o

pa3^uqHbrx c

oB

pl\I4HbLI

U

4nOnvnou

aloaaure

paBHo 2, ro

nce cr4MBOA.br

a a.rrsannre

A

uoxno

3aKOAtIpOBaTb

c^oBa-

MI{

a,nr.rnrr

/

s aa$aaure

B rar,

uro6rr

KoAbI

pa3^LtvHux

6yra

6uuru

pas-

HbrMr{,

Aro6oe

TaKoe

KoMpoBaH}re

6y4er

HOpMaAbHbIM

I{ [Opoxrd'aer

o6parruoe

KoAl,Ipyrcqee

oro6pa-:reHl4e

crroB

r a'rQarure

A

s c osa

e

alQaaute

B.

183

1

r

B

o6uqeu clysae

K alroplrrMy cBoprcr

aro6ue npoqeccbr

upeo6-

pa3oBaHufl

r.rn@oprrlaqzu,

rrosroMy reopul

rrro6rrx upeo6pasosare,\eri

nnQopuaquu

$axruvecKr.r

cBoAHTcfl K H3) {eHuro

al$aaurHbrx

o[e-

paTopoB.

Han6o.rree rRHo

3To BhrpaDKeHo

npu upeo6pa3oBaHrdu

AeKcr{qecKofi

lrlr.r

qprcloBorl

nnSoprrlarluH.

B

groM

clfrae

KaK BxoAHaq,

TaK u Bbr-

xoAHas

unQoprtlaqrafl

Mo)Ker

6urr upe4craBl.ena

B BlrAe

crr.oB, a [pe-

o6pa3oBauue nn$opr'laqLrrd

cBoAt4Tcff

K

ycraHoBleHuro

HeKoroporo

coorBercrBur

Mex(Ay

c oBaM?r.

Haupnr'rep, fipu

[epeBoAe

reKcroB

c oAHoro

fl3brKa Ha

Apyrori

uoxtHo

cynTarb

cloBaMr,r [pe4ox(eHr4t

Hlrl

orAelbHbre

a6saqu Knr{rr4r

a 3aAaqa nepeBoAa

rrolnocrbro

cBoAlrrcfl K

3a

\aqe

ycTaHoBleHr.rfi

cooTBeTcTBHg

MeX(Ay TaKrrMra

O6O6rqenarrur.r

cloBaMrr, T.

e. upoqecc

[epeBoAa

c oAHoro

q3brKa

ua

4pyrori

Mo)Ker

TpaKToBarbcfl

KaK npoqecc pea.,ru3aqur

HeKoroporo

aa$aarlrHoro

o[eparopa. llpu

srou KarrecrBeHHufi

n rpauorHuli

nepeaoA

Aonyc-

KaeT,

KaK

r.I3BeCTHO,

BO3MOX(HOCTb

I{3BeCTHUX UO4UQUXaqUri

[epe-

BoAHoro reKcrar

[ogToMy

npoqecc

[epeBoAa

olncbrBaercx ne

o6H.r-

HbrM

oAHogHarrHbrM

a

+aBarHhrM

oneparopoMr

a MHoro3HarrHbrM.

OcHoeori

Teopulr

aa$aauruux

oueparopoB

sBlrrorcq cuoco6br

rx

sa4auux

[2].

B

c.,ryrae eclr,r o6lacrb

o[peAeleHraa

arr$aeurHoro

oueparopa

Ko-

HeqHa,

o[eparop

lroxter 6urt

3aAaH rrpocrori

ra6auqeri

cooraercrnufl,

cBr3brBarouleri

Bce cloBa,

Bxoprr{lae s

o6aacru

onpeAeleHr4fl

paccMar-

plrBaeMoro

oneparopa

(axo4Hare

crroaa), r4 BbrxoAHbre

cloBa, rrol)

ra-

rculuecq B

pe3y^bTaTe

npr{MeHeHHr

onepaTopa

K KaxAoMy BXOAHOMy

c^oBy.

B

crlyrae 6ecxoHe.rnoft

o6aacru

oupeAeleHr4a

aa$aeurHoro

oue-

paropa

3aAaHHe ero

c

noMorrlrro

ra6lzqrr npuHrlunua

bHo

HeBo3Mo)K-

uo. B

groM

clyrrae oueparop

3aAaercfi

cr{creMori npaBH

,

[o3BoLrrrc-

uqeri

sa KoHerrnoe

rrHc.lr'o

lraroB HafiTr.r

BbIxoAHoe

cloBo, coorBercrBy-

putree

ruo6ouy HanepeA

3aAaHHoMy BxoA,HoMy

c OBy ng O6aaCrra

on-

peAe^eHr.rff

paccMaTpr,rBaeMoro

arrQanurnoro

oueparopa,

A,tQanumwe

onepamopht,

3agaBaeMbte

c noMot4bn xaueqnofr

cucmeutt

npAB

uL HQs bIBAIo m

Ar.rOpUmMAIraU,

Taruu

o6pasou, scaxuri

a.rrQauarHrrri oueparop,

xoropsrri Mo)KHo

@axru.recxr{

3a^arb, o6fl3arelbuo

ffBlrercfl alropr,rrMoM.

O4naxo Me)rqy

fioHflTrrflMu

a,lQaar,rrHoro

o[eparopa rzr a,,rropraT-

Ma

cyulecrByer

pa3lur{ue.

Tax, B rroHtrrrau

a,t$arurnoro

o[eparopa

tB4

cyulecTBeHHO

^r{llrb

caMo

coorBeTcTBI'Ie'

ycTaHaB^uBaeMoe

Me)KAy

BxoAHbrMH

I{ BbIxoAHbIMI{

cAoBaMI,tr

a He

crroco6'

xoroprru

9To

coor-

BeTCTBHe

yCTaHaB r,IBaeTcfl.

B nonqrnu

alroplarMa'

Hao6opor,

ocHoB-

HbrM

tB/\fleTct

ciloco6

3aA,aHlrfl

COOTBeTCTBHff,

ycTaHaBlr{BaeMoro

aA-

ropI,rTMoM.

q.

Auopumu

-

a;rQaanrHuti

ouepatop

BMecle

c npaBI{

aMH'

onpeAellr-

roulr{MI,t

ero

4ericraue.

.A,aa

arrSarurHblx

oueparopa

cquratorcr

paBHbIMr' ec.trfi oHIl

I'IMe-

lor

oAHy

r{ ry x(e

o6^acrb

onpeAe^eHl{ff

u

conocraB^qror

aro6otuy

Ha-

uepeA

3aAaHHOMy

BXOAHOMy

CIOBy

Ug

sroli o6,/\acrl'I

oAI4HaKOBbIe

BbI-

xoAHbre

c^oBa,

,A,aa

aaroprnrMa

crILITaIorct

paBH

bIMH' ec^r{

pa

BHbI c

oorBercrByro

-

rrlr4e r4M aa$anuruue

oueparopbl

r4

coB[aAaer

cllcreMa

npaBlrl'

3aAa-

rorrlnx

4elicrarae

gTI{x

aIropI4TMoB

Ha BblxoAHble

cloBa'

.A,na

a.,rropnrMa

cqHTarorcq

9KBHBarreHTHIIMI'l'

ec.,'tr{

y

HIrx coB[aAa-

rcr

aarlanurHbre

o[epaTopbl,

HO He COBrraAaroT

crroco6br

r{x 3aAaHI,IA

{czcteua

npaBrrl).

14g ceoficrsa

alropr{TMa

pe3y^bTaTr,lBHocTr{

BbrTeKaeT

[OHrrTI4e

06-

/\acTH

[prrMeHr.rMocru

a

ropuTMa

rroA

xoropoir

noHlrMaeTcfl

MHo)I(e-

CTBO

CTpOK,

A

-fl KOTOpbIX

aAfopI'ITM

pe3y^lrarl{BeH.

Taxrau

o6pa3oM,

3KBI,IBa

eHTHocrb

ilLropurMoB

Mo)Ker

6urr

onpe-

Ae

eHa

cleAyrcIqnM

o6paaolr:

ABa

a

ropurMa

3KBUBaAeHTHII'

ec,lru

coBnaAaroT

r4x o6^acTr{

[pr4MeHnMOCTr.r

U

pe3y^bTaTbr llepepaoorxra

aro6oro

c^oBa

I,I3 3ToIl

o6 acrI'I.

B o6uletr

cl)^{ae

pa3luqaroT cayrainrre

pr

caMoH3MeHflIOlqUeCt

ir4roprrrMbl

[2]

. A,'rropurM

Ha3blBae'tcn

c,tytali'n]ly'

ec1ll

B CHCTeMe

IIpaBH/rr

OTII'CbIBaIOUIUX

aIAIOpI4TMT

npeAycMaTpuBaeTcfl

Bo3MO)KHOCTb

C11nrafiHoro

eat6Opa

TeX

I4AII

I,IrIbIx C7rOB

LIAH

Tex I{7rI't

I4HbIx

IIpaBLIr1.

I,IM coorsercrByror

MHoro3HarrHrre

a.rr$annrHble

o[eparopbl.

Aaropuru

Ha3brBaeTcg

caMou3MeHftoul,uMcn,

ec,rn

oH

He To

bKo

uepepa6atuBaer

BxoAHbIe

c^oBa,

Ho

14 CaM

U3MeHffercfi

B [poqecce

TaKOft

uepepa6orxu.

Pesyarrar

4ericrnnr

caMolr3MeHfi

rou{efoct

iL

.ro-

pI,ITMa Ha To

I4AI,I IIHoe

BxoAHoe

c^oBo

3aBI4CI,IT

He

ToAbKo oT

SToto

c^o-

Ba,

HO H OT

rrcropl{I4

npeAblAyu{eri

pa6orat aAropI4TMa.

B reopun

alropuTMoB

6olrruoe

BHr4MaHr,re

yAelreTcfl

o6u4rau

cno-

co6aM

3aAaHr4n

arafopr4TMoB,

xapaKTepr43yrotqr.rMcs

csollcraoM

yHHBep-

ca^bHocTr4,

T. e,

TaKLTM

C[OCO6aM,

KOTOpbre

uo3BOAJ{rOT

3aAaTb

aaro-

\

185

1

r

B

o6uqeu clysae

K alroplrrMy cBoprcr

aro6ue npoqeccbr

upeo6-

pa3oBaHufl

r.rn@oprrlaqzu,

rrosroMy reopul

rrro6rrx upeo6pasosare,\eri

nnQopuaquu

$axruvecKr.r

cBoAHTcfl K H3) {eHuro

al$aaurHbrx

o[e-

paTopoB.

Han6o.rree rRHo

3To BhrpaDKeHo

npu upeo6pa3oBaHrdu

AeKcr{qecKofi

lrlr.r

qprcloBorl

nnSoprrlarluH.

B

groM

clfrae

KaK BxoAHaq,

TaK u Bbr-

xoAHas

unQoprtlaqrafl

Mo)Ker

6urr upe4craBl.ena

B BlrAe

crr.oB, a [pe-

o6pa3oBauue nn$opr'laqLrrd

cBoAt4Tcff

K

ycraHoBleHuro

HeKoroporo

coorBercrBur

Mex(Ay

c oBaM?r.

Haupnr'rep, fipu

[epeBoAe

reKcroB

c oAHoro

fl3brKa Ha

Apyrori

uoxtHo

cynTarb

cloBaMr,r [pe4ox(eHr4t

Hlrl

orAelbHbre

a6saqu Knr{rr4r

a 3aAaqa nepeBoAa

rrolnocrbro

cBoAlrrcfl K

3a

\aqe

ycTaHoBleHr.rfi

cooTBeTcTBHg

MeX(Ay TaKrrMra

O6O6rqenarrur.r

cloBaMrr, T.

e. upoqecc

[epeBoAa

c oAHoro

q3brKa

ua

4pyrori

Mo)Ker

TpaKToBarbcfl

KaK npoqecc pea.,ru3aqur

HeKoroporo

aa$aarlrHoro

o[eparopa. llpu

srou KarrecrBeHHufi

n rpauorHuli

nepeaoA

Aonyc-

KaeT,

KaK

r.I3BeCTHO,

BO3MOX(HOCTb

I{3BeCTHUX UO4UQUXaqUri

[epe-

BoAHoro reKcrar

[ogToMy

npoqecc

[epeBoAa

olncbrBaercx ne

o6H.r-

HbrM

oAHogHarrHbrM

a

+aBarHhrM

oneparopoMr

a MHoro3HarrHbrM.

OcHoeori

Teopulr

aa$aauruux

oueparopoB

sBlrrorcq cuoco6br

rx

sa4auux

[2].

B

c.,ryrae eclr,r o6lacrb

o[peAeleHraa

arr$aeurHoro

oueparopa

Ko-

HeqHa,

o[eparop

lroxter 6urt

3aAaH rrpocrori

ra6auqeri

cooraercrnufl,

cBr3brBarouleri

Bce cloBa,

Bxoprr{lae s

o6aacru

onpeAeleHr4fl

paccMar-

plrBaeMoro

oneparopa

(axo4Hare

crroaa), r4 BbrxoAHbre

cloBa, rrol)

ra-

rculuecq B

pe3y^bTaTe

npr{MeHeHHr

onepaTopa

K KaxAoMy BXOAHOMy

c^oBy.

B

crlyrae 6ecxoHe.rnoft

o6aacru

oupeAeleHr4a

aa$aeurHoro

oue-

paropa

3aAaHHe ero

c

noMorrlrro

ra6lzqrr npuHrlunua

bHo

HeBo3Mo)K-

uo. B

groM

clyrrae oueparop

3aAaercfi

cr{creMori npaBH

,

[o3BoLrrrc-

uqeri

sa KoHerrnoe

rrHc.lr'o

lraroB HafiTr.r

BbIxoAHoe

cloBo, coorBercrBy-

putree

ruo6ouy HanepeA

3aAaHHoMy BxoA,HoMy

c OBy ng O6aaCrra

on-

peAe^eHr.rff

paccMaTpr,rBaeMoro

arrQanurnoro

oueparopa,

A,tQanumwe

onepamopht,

3agaBaeMbte

c noMot4bn xaueqnofr

cucmeutt

npAB

uL HQs bIBAIo m

Ar.rOpUmMAIraU,

Taruu

o6pasou, scaxuri

a.rrQauarHrrri oueparop,

xoropsrri Mo)KHo

@axru.recxr{

3a^arb, o6fl3arelbuo

ffBlrercfl alropr,rrMoM.

O4naxo Me)rqy

fioHflTrrflMu

a,lQaar,rrHoro

o[eparopa rzr a,,rropraT-

Ma

cyulecrByer

pa3lur{ue.

Tax, B rroHtrrrau

a,t$arurnoro

o[eparopa

tB4

cyulecTBeHHO

^r{llrb

caMo

coorBeTcTBI'Ie'

ycTaHaB^uBaeMoe

Me)KAy

BxoAHbrMH

I{ BbIxoAHbIMI{

cAoBaMI,tr

a He

crroco6'

xoroprru

9To

coor-

BeTCTBHe

yCTaHaB r,IBaeTcfl.

B nonqrnu

alroplarMa'

Hao6opor,

ocHoB-

HbrM

tB/\fleTct

ciloco6

3aA,aHlrfl

COOTBeTCTBHff,

ycTaHaBlr{BaeMoro

aA-

ropI,rTMoM.

q.

Auopumu

-

a;rQaanrHuti

ouepatop

BMecle

c npaBI{

aMH'

onpeAellr-

roulr{MI,t

ero

4ericraue.

.A,aa

arrSarurHblx

oueparopa

cquratorcr

paBHbIMr' ec.trfi oHIl

I'IMe-

lor

oAHy

r{ ry x(e

o6^acrb

onpeAe^eHl{ff

u

conocraB^qror

aro6otuy

Ha-

uepeA

3aAaHHOMy

BXOAHOMy

CIOBy

Ug

sroli o6,/\acrl'I

oAI4HaKOBbIe

BbI-

xoAHbre

c^oBa,

,A,aa

aaroprnrMa

crILITaIorct

paBH

bIMH' ec^r{

pa

BHbI c

oorBercrByro

-

rrlr4e r4M aa$anuruue

oueparopbl

r4

coB[aAaer

cllcreMa

npaBlrl'

3aAa-

rorrlnx

4elicrarae

gTI{x

aIropI4TMoB

Ha BblxoAHble

cloBa'

.A,na

a.,rropnrMa

cqHTarorcq

9KBHBarreHTHIIMI'l'

ec.,'tr{

y

HIrx coB[aAa-

rcr

aarlanurHbre

o[epaTopbl,

HO He COBrraAaroT

crroco6br

r{x 3aAaHI,IA

{czcteua

npaBrrl).

14g ceoficrsa

alropr{TMa

pe3y^bTaTr,lBHocTr{

BbrTeKaeT

[OHrrTI4e

06-

/\acTH

[prrMeHr.rMocru

a

ropuTMa

rroA

xoropoir

noHlrMaeTcfl

MHo)I(e-

CTBO

CTpOK,

A

-fl KOTOpbIX

aAfopI'ITM

pe3y^lrarl{BeH.

Taxrau

o6pa3oM,

3KBI,IBa

eHTHocrb

ilLropurMoB

Mo)Ker

6urr

onpe-

Ae

eHa

cleAyrcIqnM

o6paaolr:

ABa

a

ropurMa

3KBUBaAeHTHII'

ec,lru

coBnaAaroT

r4x o6^acTr{

[pr4MeHnMOCTr.r

U

pe3y^bTaTbr llepepaoorxra

aro6oro

c^oBa

I,I3 3ToIl

o6 acrI'I.

B o6uletr

cl)^{ae

pa3luqaroT cayrainrre

pr

caMoH3MeHflIOlqUeCt

ir4roprrrMbl

[2]

. A,'rropurM

Ha3blBae'tcn

c,tytali'n]ly'

ec1ll

B CHCTeMe

IIpaBH/rr

OTII'CbIBaIOUIUX

aIAIOpI4TMT

npeAycMaTpuBaeTcfl

Bo3MO)KHOCTb

C11nrafiHoro

eat6Opa

TeX

I4AII

I,IrIbIx C7rOB

LIAH

Tex I{7rI't

I4HbIx

IIpaBLIr1.

I,IM coorsercrByror

MHoro3HarrHrre

a.rr$annrHble

o[eparopbl.

Aaropuru

Ha3brBaeTcg

caMou3MeHftoul,uMcn,

ec,rn

oH

He To

bKo

uepepa6atuBaer

BxoAHbIe

c^oBa,

Ho

14 CaM

U3MeHffercfi

B [poqecce

TaKOft

uepepa6orxu.

Pesyarrar

4ericrnnr

caMolr3MeHfi

rou{efoct

iL

.ro-

pI,ITMa Ha To

I4AI,I IIHoe

BxoAHoe

c^oBo

3aBI4CI,IT

He

ToAbKo oT

SToto

c^o-

Ba,

HO H OT

rrcropl{I4

npeAblAyu{eri

pa6orat aAropI4TMa.

B reopun

alropuTMoB

6olrruoe

BHr4MaHr,re

yAelreTcfl

o6u4rau

cno-

co6aM

3aAaHr4n

arafopr4TMoB,

xapaKTepr43yrotqr.rMcs

csollcraoM

yHHBep-

ca^bHocTr4,

T. e,

TaKLTM

C[OCO6aM,

KOTOpbre

uo3BOAJ{rOT

3aAaTb

aaro-

\

185

l4cuoa-usyx

AaHHbIe Syuxquu

B KaqecrBe

ucxoAHblx'

flyreM

npl{-

MeHeHr,rt

IIpocTbrx

onepaquft

cyneprro3r{qLILIr

IIpLIMLITI4BHOii

pexlpcltl't

r4

1\1r41{r,rMu3arlnr.r

Mo)KHO

UO

r{LITL'

Aro6yro

cKo^b

yroAHO CIO)KHyIO

rrlrc^oByro

$yHxqurc.

onepaqun

cwepnosutluu

$ynrquft

gaK^Io.IaeTcfl

B

no.arcTaHoBKe

oAHlrx

apn$r"rern.recKHx

synxqull

BMeCTo

apryrueHTOB

Apyrr4x

apHQ-

Merl,IqecKlax

SYtxqufi

'

()

nepa1un

npuMumuBHoil

pexypcuu

[o3Bolser

crpol'ITb

SyHrqurc

or

n* I

apryrvrenra

no

ABylu

3sAaHHbIM

$yHrIlnar'l

-

$yHxquu

n-ra

apryrueHra

ra

(n

*

2)-ro

aprylvleHra.

Oynxqnn,

Koropble

Moryr

6urr

uocrpoeHbr

I43 s eMeHTapHbIx

apu$uetnvecKlrtx

Qynr<qr'rr:r

c IroMoulblo

ouepaqrati

cynepno3l'Iql'IH

I'I

npr4Mr4THBHOrl

perypcrr4, npHMeHeHHbrx

aro6oe

KoHeqHoe

qHc

o

pa3

B

npor{3BOAHrOfi

nocaeAoBaTeAbHOCTr,r,

Ha3bIBaroTcfl

npuMumuBHo

p

e

-

Kyp

c uB

HbI Mu

Qynxqunuu.

Onepaqnu

c)mepflo3llquu

n

upplMurueHoft

peKypcHI{, 6ylylll

upll-

MeHeHbr

Ko

BCTOAy

OllpeAe^eHHbrrvr

QynxqunM,

AaIOT

B

pe3y^bTaTe cHo-

Ba BcroAy

olrpeAeleHnue

SYHxquu.

Borrsuruncrao

apusuerruecrux

$ynxqraft

otnocfTcfl

K

IpI4MUTIIB-

Ho

peKypcrBHbIM,

Ter'r

He MeHee

rrpHMr4THBHo

peKypcnBHsre

Qyut<-

rlr4r4

He

oxBaTbrBaroT

Bcex

apnQueruvecKHx

$yurquli,

KOTOpbIe

MO-

ryr

6rrrs

onpeAe^eHbr

KoHCTpyKTT{ano.

IIpu

[ocTpoeHHI4

BCeX

sTHx

$ynrrlfiri

r4cno^s3yroTcfl

Aipyrr4e

o[epaIII4II,

B

rIacTHocTH

ouepaqllfl

MUHUMU3AqUU,

oueparlur

Mr.rHzMr{3arlr{r{

rro3BOJ\"EeT

oIIpeAell{Tb

HOByIO

apusrte-

Tr{qecKyro

Qynxrlr,rro

f(xu

...,

xn/ or

n

[epeMeHHblx

c

floMolqblo

paHee

uocrpoeHHori

apraQneruqecrofi

$yHrIluu

g(x,,...,xil

y)

oT

n*

1 nepe-

MeHHbrx.

flpn erou

olepaTop

MlrHr.rMx3ar-l,t4H

/,

onpeAeiseTcs

c^eAy-

roudlaM

o6pasou.

Ilycrr

(n+

1)

nepeMeHHblx

Syuxqnn

I

I'IMeIor

HeorpI{IIare

bHbIe

rle^bre

3HaqeHr.rf,

TorAa

trtr(8(x,,xr,...,xn,1)

=

0)

o6pasyer

HaI'IMeHb-

uIIIee

HeoTplrl{are^bHoe

IIe

oe

3HaqeHI4e

f,

AAfl

KOTOpOTO

g(xt,xr,...,xn,f)

=

0,

upn

acex

$rlrcupoBaHlrnx

3HarIeHI'Icx

xrx!""xn'

Ectu

y

cyu{ecTByeTr

TO

rracT?ttrHaa

$yuxqras

f ot

n

[epeMeHHbIX

MO-

trer

6urrr

oupeAeleHa

r.r3 Bbrpax(eilt4f,

g

C

nOMOIIIbIO

O[epaTopa

p:

f

(xr,

xr,...,

x,)

=

lt

r(E(x1,

xr,...,

xn,

/)

=

0)

,

e nporuBHoM

c/\y{ae

f(x

uxr"',x^)

HeorrpeAeJ\I{Ma.

ApuQueruuecKue

Qynxqnu,

Koropbre MoryT

6urr nocrpoeHbr r{3

s^eMeHTapHrrx apraQr"reTr.rtrecKr4x

SyHrqHfi

c rroMorrlbro

ouepaqufr

cynepno3r{rlvrutrrpuuvrrrEsHoi

peKypcrlr,r

H Mrrxr,rMr{garlr{a, Ha3hrBaror-

ca

qacmuqHo

p

el<ypcuBnuuu

QynnlunMu.

9acrra.rHo

peKypcuBHue

$yHrqnu

npeAcraBlnror

co6orl nau6oaee

o6qufi

Klacc KoHcrpyKTIltBHo orrpeAel-fl eMbrx

apu$rvrern.recxux

$1'n-

Kquft,

a [oHrrr{e

qacruqHo

peKypcr{BHoli

$ynxqnr.r

flBlrercfl

oAHr4M

[l|3

rlaBHbrx noustrah Teopuu alropraTMoB.

Taxuu o6pasorrr, Kar(AaJr 3aAaHHar

rracruqHo

peKypclrBHax

<pyHx-

qHfl

BbrquclrrMa flyreM onpeAeleuaori upoqe,4ypbr MexaH[rqecKoro

xapaKTepa,

u nao6oporr

qr{cloBble

Synrrluu,

Bbrqnclr{Mbre nocpeA-

crBoM

arlropl{TMoBr

flBlflrorcfl

tracrr.rrrHo

peKypctlBxbt}r[.

B cootser-

crBnn c

re3r.rcoM

t{ep.ra:

xuocc oxropumwutecxu

(utu

Mcrwunuo) Bbt-

tutcluuhDr

qocmuqnbrx qucloBbtx

Qynxqurt

coBnagaem c

KAaccoM

Bcex

{ ocm

u

qao

p

eKyp c uB Hbtx

Qynnryrt.

Sror resuc

Aaer

araropurMusecKoe rolKoBaufie uoHtrl{Io

qacrurr-

Ho

peKypcurH

ux

QyHxqul:r.

flpaxrrrrr ecKH

rr oHrrue

qacrr.trrHo

peKyp-

c urnax

$ynxqrEft

rlcnoan3yror

AAff

AoKa3arelbcrBa

araropr.rrMr4.recrori

pa3perxlrMo

cTu ut\u Hepa3peruuMocTr/r upo6aeu. I4cnoarsosaHlre

x(e

r{acrHqHo

peKypcnBHux

syuxqzr}

44-a

npe4craB^eHr/rff

Toro r4^}r r.rHo-

ro KoHKperHoro

a,rropurMa [paKTur{ecKn

neqelecoo6pa3Ho BBHAy

CAOXHOCTII

TaKOTO upOqeCCa

aArOpL4TM[3aqIIIil,

5.3.

MATIII4HbI

TbIOPI,IHTA

B 1936--1937

rr. negasucrlMo

Apyr

orApyra

u

norrrn oA,noBpeMeHHo

c

pa6oraun

A.9epua u

C. Karlnu 6sr;ro

4ano

orrpeAeleHne noHfiTr.rs arl-

roplrrMa

aMepr.rKaHcKuM lr aHrrrrarlcxr,rM MaTeMaTr{xauu 3, llocror"r

r

A.TrropuHrorrr. I,Ix no45o4

6asrnpyercs

Ha orrpeAe er{r4r{ crreq}rirabHbrx

a6crparcrHux

(r.

e. cyrqecrByrorqux He

pealbuo,

a lr{rrrb n noo6pa:xe-

xun)

aarouaroa

(r"raurzn).

Ocnonnar

Mbrcrlb rrpn

3ToM 3aK

rorrarlacb

E

TOM,

qTO

eUrOprTMHqeCKr{e

[poqeccbr

-

3TO

rrpoqeccbr,

KOTOphre MO-

xer

coBepuarb flo.Axoprqe

ycrpoeHHar

(Marur{na>.

B coorBercrBur.r

c 9THM

IIMI{ C nOMOIIdbIO TOTIHbXK MaTeMaTFIeCKTID(

repr'rnnOA

6br U On}rca-

HbI K ilccbl Maurr{H, cnoco6nue ocyrqecrBrarbl'l\vtuurrrrpoBarb

Bce aaro-

pI,ITMr{qecK[1e

[poqecchr, xorAa-au6o

onr{cbrBaeMLre

MareMarr{KaMu

[2].

Maruugsr,

BBeAeHHbre llogrou u TaropunroM, or,rrrtritancb He oqeub

cyu{ecrBeHuo

r,r B4aabHeirueu

graarl

Ha3brBarbcfl uaruunaur Trrcpl,IHra.

Haupuuep,

pp.lu-,

f

(x)

=

prllZy

-

xl=

0)

raueeu

f(x)

:

x/2

npu

ncex

qerHblx

3HaqeHIAflX

X.

188

189

B o6uleu

clyrrae raKar

MaIITI,IHa cocrogT

I{3

cleAyloqnx

.ractefr

(pHc.5.2):

I

)

ranSo

pr'raquonnori

IeHTbI

r

npeAcraBlfl

rolrleri co6otl 6e c xoneq

-

Hyro

(HeorpaHuqeHHylo)

naunrr uaurllHbl. B xa.recrse

unQopuaquon-

nori rrenru Moxer clyJKr{Tb

MarHHTHas uara 6yr,ra:rurag 6ecxonesHaff

AeHTa,

pa3Ae^eHHafl

Ha orAelbnrre sqefixu.

B rax<Aoft s.Ielixe

MoxHo

rroMecrr,rrb /\r{Ilrb oAr{H cr,rMBoI,

B TOM

qI,ICAe

I{ HOAb;

2)

<c.rnruaaroulefi

ro oBKLt)

-

cflequalbHoro

qyBcrBuTelbHoro

S eMeHTar CIOCO6HOTO

O6OapeAarr

COAep)KlIMOe ttreeK,

B4orrs ro^oB-

xu uH$opt"talllronnirt

leHTa [epeMelrlaercx

s o6e cropoHbl

TaK,

qro-

6u

a xa:x4ufi

paccrnrarpr.rsaerubui

MoMeHT

BpeMeHI{ roloBKa

HaxoM'

Aacb

B o4noft oupeAeleHHofi

qqelixe

AeHTbr;

3)

ynpanarrou{ero

ycrporictra,

Koropoe

a

xa:r<4rrri

paccMarpfiBae-

usrfi r'rouenr

HaxoALITcs B HeKoropoM

(cocroffunz>.

Ilpe4[olaraer-

csr

qro

ycrpoficrao

ynpaBleHuff

MaITII{HbI

Mo)Ker HaxoA}ITbct B HeKo-

TopoM

KoHeqHoM

ql{cle

cocroflsuti.

CocrotHr4e

ycrporlcrra ynpaarre-

Hug

qacro

Ha3bIBaIor BrryTpeHHuM

cocrolHueM

MaIIrLt HbI. O4Ho us srnx

cocro

gnnri

Ha3blBaercff 3aK

rorrr{TeAbHbIM H

ynpaBlfl

er oKoHqaHI{eM

pa6oru

MarrrlrHbr.

-

YnoaBnnpulee

<|_-

-

yCTpOt/tCTBO

Cqurueatou{an

TOTOBKA

14HOopMaq4oHHae

<-

neHra

Puc. 5.2. Coctaa

MarrrHbr Trropunra

Paccuorpuu

tu\ropr4TMmecKyro

crlcreMy,

npeAAo)Keurrpo

[Ioctot"t

[2].

B anropuuvu.recxoli

cr{creMe

flocta

zn

@opuaquff

[peAcraB^ff er-

cfl

B

ABonqHou

aa$aaure

A

:

{

1

,0

}

. To ecrb

B rax<4oft x.relixe

unSop-

r'raquoHnoliAeHTbI

Mox(Ho

noMecrl,ITb^t16o

0,

rua6o

1.

A.lropntu

npe4-

cTaB fleTCfl

B BLIAe

KOHeTIHOTO

ylOpflAOqeHHOrO Ha6opa

npaBr4l, Ha-

3brBaeMbrx

npr,rKa3aMu.

Pa6ora aAropHTMa

HaquHaerctt

c reroropoft

na.raa.rnofi

Rvefixu, coorBercrByroqei

nepBoMy

[pl{Ka3y aIropI{TMa.

Cocraerrrrcqne

a

roplrrM rrpnKa3bl

Moryr [pLIHaMe)Karb

K oAHoMy

190

ns 6

npuxa3oB,

Bbr[olHreMbrx ycrporlcreoM

ynpaBleHr,rtr

Marrr]rHbr

flocra:

l.

3anncarr B

paccMarpr{BaeMyro

xveftxy I

u neperiru

r f-uy

upl.l-

Ka3y.

2. 3anucarr

B

paccMarpr{BaeMyro

rverixy

0 u nepefirut

r f

-rrly

upz-

Ka3y.

3. C4nr.rnyrr

eHry BupaBo

Ha oAHy

q.reftxy

u

rrpncryrxrb

K Bbruol-

HeHHro i

-ro

npuxasa.

4.

C4aurHyrb aeHTy B

eBo Ha

oAHy nveixy

u ueperiru

K Bbrno

He-

xnro i

-ro

[puKa3a.

5. Eclrn B

paccMarpusaeMori

s.retrre

3anucaHa

1, ro nepefirr{

K Bbr-

noAHeHI,IIo

/-ro

upI,IKa3a,

a ecllt

3arrucatt 0, to nepefiTu

K

BbInoAHe-

HHro i

-ro

[puKa3a.

6.

OxoH.rauue

pa6oru

aIropHTMa,

ocraHoBKa.

Alroputurr,

cocraBleHHble

LI3

rrro6oro KoHetrHoro

suc^a

trpaBnrr',

[pe,AicraBleHHbrx

npaKa3aMfi

Marur{Hbr

flocra, Ha3blBarorc

fl, cIAf o

p

u

m

-

nauu

flocma.

Alropnrusr

Flocra

cBoMTcfl

K alropr4TMaM,

pearar{3yeMLrM

c

rroMo-

u{bro

qacr}rrrno

peKypcnaHux

QyHxquh,

u xao6opor,

rlro6as

qacrrrrr-

Ho

peKypcnaHax

QyHrqr,rr

Mo)Ker

6urr

upe4craBleHa

irafopurMoM

cHcreMhr llocra.

B orru.rr.re

or Marrrlrnbr

flocra Marrrlrxa

TslopuHra

Mo)Ker

pa6orarr

B npou3BoisnoM

KoHeqHou

aa$aaute

Id Bbr[olrtgrbHeKoropoe

Koneq-

Hoe

rIHcAo

rrpuKa3oB.

flptt stor*,r MaruuHLI

Tuopranra,

KaK r,I

MaIlI,tHbr

flocra,

Moryr

cABurarb

AeHTy Ha

oAHy xvefixy

BnpaBo r,rl.Lr

BAeBor

oc-

TAB J{'

COAepX(I{MOe

tqeeK HeU3MeHHbIM,

It.tru MOryT

}I3MeHflTb

COCTO-

f, HHe Bocfipr.rnuuaer"ro

fi ff

llerixll,

o cTaB/rsfl

/\eHTy Hen oABtrx(H

oil

l2l.

Maruuna TsroprdHra Ha3brBaercr

crarpaprHoli,

ecat oHa rrplr

cABure

AeHTLT

MOXeT

npeABapr{Te^bHo

r43MeHflTb

coCTOgHUe

BOCnpr{HilMae-

trloti R.refir[.

flycrr

aaQaaur MarrruHbr

Trrcpnnra

saAaH B Br{Ae

uuoxrecrga A

:

{So

Sr,..., Sf,

rae

So cooraercrByer

nycrofi

tvefixe, a

quc^o

cocrosnuri

ycrporicrsa yfipaBleHr.rff

3aAaHo B Br{Ae MHo)KecrBa

Q:

{qt

e,,

...

,

4),

rAe

q0

COoTBeTcTByeT

3aK IoqI.ITelbHOMy

CocToffHIiIIO.

Konevnyro coBoKyrrHocrb

cr,rMBoloa aaQaaura,

c xoroporl

pa6ora-

er

Maru[Ha,

Ha3brBaror BHewHuM

atQaaumon,

KoHeqHyro

coBoKyn-

Hocrb cocroaHuri

ycrporfcraa

)mpaBleHr4r,

-BrympeHnuu

atQaau-

moM,

Conoxynnocrs,

o6paaoBaHHyro [ocleAoBarelbnocrbro

cocrosnraft

BCeX ffqeeK

.'reHTbr lt cocToffHr.rer"r

ycrpoficTBa ylpaB

eHl,rtr Ha3bIBaIoT

191

roHQnrypaqueri

r"rarunnu.

KonQzrypallllf

3aAaeTcff

B

BLIAe CAOBa'

orrHcbrBalou(ero

KoHKperHoe

cocrofl

HIne

MaruI4HbI'

llycrt

n uexoropHft

MOMeHT

BpeMeHI4

MauJHna

THOpranra

HaxoAl{T-

cq

B COCTOffHI{H'

[peACTaBAeHHOlvI

na

pUC'

5'3'

Bxyrpexxuil

BHe[uH]4i

anoaBur

r-1

Pnc. 5.3.

Cocrognue

MaluuHbr

Trropuura

KoH$rarypaql{t

MaruIrHhI

44t

AaHHoI'o

clyr{afl

6yAer

rpeAcraBlena

B

BI'TAE CAOBA:

... s

0s,,s,r...e,s,1...\,s

0...,

rAe

S"

-

ctIMBoA,

o6osHa'Iauqnri

uycrpo

n'retiny;

r

-

qnclo

3anoAHeHHbIX

fiqeeK

Ha IeHTe;

S,,

--

coctoflHl'Ie

nepBori

caesa

nenycrorl

qqeriKll;

sru

-

"o"tounue

rqerlxll,

npocMaTpHnaer"roft

n

4aHnnfi

uoueHT

Bpe-

MEHrI;

{,

-

cocroaxze

yctpoticrBa

yrrpaBleHuff'

Ka:rAas

xonQurypaqurl

coAepx(Idr

AlIIIlb

oAHo

Bxox(AeHr{e

cItMBo-

Aa

g,

H3 BHyTpeHHero

aaQaaura.

Srot

ct4MBOl

MOX(eT

6rrrr

s cIOBe

caMbrM

leBbIM,

Ho

He Mo)Ker

6urr

caMbIM

npaBbIM'

TaK

KaK cnpaBa

or

Hero

A,oDKeH

noMeqaTbcfl

cHMBO/t

cocToflHl'Ifl

o6oapeaaeuoi

gqefixra'

Ec.ur

craH4apTHas

Maurr{Ha

TrroprEHra,

Haxopcb

B

cocToflHI,IH

qi

14

BOC[pr,rHr{Mar

3a[r{caHnrrft

na leHTe

cr{MBOA

s,

nepexo4uT

B HOBOe

cocTo'HI,Ieg'locylqecTB^.flfnpl,lSToM3aMeHycI,IMBo^aBpaccMaTpl{-

saeMoft

s.redre

Ha

crlMBoASn

u cABr.rr

eHTbI

B eBo

Ha oAHyflqefrxy,

ro

roBoprr,

qro

MaruuHa

Bblrlo^Hffer

KoMaHAy

qsr->Af

'l'

flpz

lranr.ruy/rfl\Yrflx

c

AeHTaMH

I{c[o^b3yrot

cae,{yroulue

o6osHa-

qeHufl:

z1

-

AsIDKeHlre

eHTbl

BAeBo;

II-

4nuxteHne

eHTbI

BrIPaBo;

C

-

ner

ABI,Ix(eHI{g

rreHTbI.

r92

KouaH4u craHAaprHori

uarururr

TuopuHra Moryr 3a^aBarbct

Ha-

6opornr

[rrrepoK cr,rMBo

oB BHAa

gisr qf

^A,r.e.

crpelKa

o[ycKaercff.

Paccuorpnu

npl.rMep MaIIrrrHbI Trr6punra c arrQaentaus

A

:

{0,

1},

g :

{80,{rl

n rolran4auu

q,/ q,lA, q,0 qotC.

flycra

Ha AeHTe

lrMeercff cloBo 11100.

forrosra crol{T Ha4 nepaoi

cleBa

eAr,rnr.rqei

(puc.

5.4).

B

pe3y

sTare

pa6orrr

MatuLIHbI Trrcpnura

ga

4 urara sro

cloBo npeBpalqaercs

s 11110,

IIo

oKouqauult

pa6orrt

MarulrHbr

roAoBKa cror4T

Ha4rpatlHeri

npanofi e4unuqefi, Moxtno cra-

SaTbr

qTo

AaHHatr

Matrruna BbrnoAHLIlra

clo)r(eHl{e a

4norauHofi

cI{cTeMe

AecsrlltrHbrx

rrncel

28

+

2.

Ns

urara

Kon$nrypaqur

Llcuorrnseurre

KOMaHAbT

(uporpauua)

J

I I

J

I

I 0 0

q/11100

Q,lq,lIt

0

19,1100

e,lq,llt

1

v

I

0

v

0

1

0

119,100

0

111q,00

0

lllq,lO

qlq]^

Q,0qolC

a)

6)

n)

Pnc.5,4, AaropHtrt

pa6oru

natrrnHbt TuroprHra

no nepepa6orxe cloBa

(1

1 100D

B

cloBo

(11

I l0>

Coaoxynnocrb

Bcex KoMaH,ti,

Koropble

Mox(er

Bblno,irngrb

Malun-

Ha, Ha3hrBaercn

ee nporpauuofr

l2l.

MaurzHa

Taropunra

cqlaTaercs

sa4annofr,

eclr,I 3aAaHbI:

.

ee BHeru:g.uiru

BHyrpeHHI,Iti

arrQaauru;

I

[porpaMMa;

r

HasalbHaa

xoHQurypaqux;

.

cr{MBoAL,l

o60grra.IarolrlHe

uycryrc

xvetiry

I{ 3aK^roqnre^bHoe

cocroffHI4e,

Qi+

anQaBur

so

s,

g

s,

q

so

l3 r

zro

193

flycrr

MaIuI4Ha

Trropunra

3aAaHa

BHeIuHI'IM

arrQaanrou

A

:

{0,

o,

b, c, d),

BHyrpeHHr{M

aasaaxrou

Q

:

{qu

Q1,Qv

Ij,

Qo,4J

lr coBoKyr-

HOCTbTO

KOMaHA:

q

.oq

pA,

e

ob

q

ob

A,

q

zaq sdn,

q

0c

q

ocA,

Q

d

q

rcII,

q

3aq

.dn,

4

od

q

rc

II'

llycryro

avefixy

o6osHa'raer

cI4MBo

So,

a sax-ruoqlaTelbuoe

cocro-

flHIde

-

qt

Ha

prac.

5.5

upe4ctaBleH

npoqecc

nepepa6orKlr

MaIIlLtHoft

Tsropua-

ra

ucxo.a,Horo

cloBa

bcadc

B crroBo

bcdcc.

Ha'ra

bHas xoH$urypar1ua

r4Meer

nu4qobcadc.

Psc. 5.5.

Aaroprrr'r

pa6o'ru

MaruuHbl

TuropuHra

no

nepepa6orKe

cloBa

<bcadc>

B cloBo

<bcdcc>

flporpar'rrtra

paccMorpeHnoti

uarurlHu

TrtopuHra

rroxer

6urrb

[peA-

craB^eHa

B

BHAe

ta6rruqsl

coorBercrBlrfl:

MauruHu

TbtopllHra

upeAcraBLfl

ror co6oft

yHI{BepcaAbHbIx

I{cnol-

grnre1eti,

C

HC1OAb3OBaHI{eM

KOTOpbIx

MOX(HO

I,1MI{TI,IpOBaT6

BCe

a71lo-

pHTMr,rqecKHe npoqeccblr

onacblBaeMble

MareMaruKaMI'I.

Euao

4oxa-

3aHOr

IITO

X.r1aCC

QyHrqUli,

ertVr.lCAI4MbIX

Ha 3TI4X

MaIIII4HaX'

TOqHo

CO-

BnaAaer

c

K accoM

Bcex

rracrl'IqHo

peKypcuaHaIx

Syuxqnir'

194

Taxuu o6paaoivr,

Boflpoc o cyrqecrBoBaHr{r,r H,rH HecyqecrBoBaHr{H

A

rOpnTMa

.{.A.ff

3aAarII4

TOrO I4AI,I IIHOTO TDIUa CleAyeT [OHIiIMaTb KaK

Bonpoc

o cyulecrBoBaHr,r

r{ r,rlr{ Hecyule

crBoBaHuu

Marru,rHbr Trro

pnu

-

ra, o6.rrap,arcqeli

nyxrHul,r

csoricrgorur.

B

gasprcHrt{ocrrir

or

trucla

rrcuolbgyeMblx AeHTr nx Ha3Hatrerr4fr vr

qHcrla

cocroxnurl

ycrporicrea ynpaBleHr{r

oflpeAelrrcTcfl

pa3lurrHhre

r'loAHouxaquu

r"raruuH TblopllHra, Ha[prrMep

MauruHa Trropl.rHra

c

AEy-

Mq

BhrxoAaMpl, MHoro^eHTorrHat

r"rauruxa TsropHHra. llprt stot r

pa3^r.Iq

-

HbIe allropraTMbr

ocyulecrBLrllorcq

Ha

pa3.lt.lrqHblx

MaruuH€Ix Trropnnra,

orlrr.r.rarcquxcx

Ha6opoM KoMaHAr

BHyTpeHHHM H BHeTITHI,IM a.tQarura-

un. Ho

Mo)KHo [ocrpor{Tb I,I

yHldBepcalbHyro

MaIUI{Hy Trropunra, cno-

co6rryro

B lr3BecrHoM cMbrcle BbInoIlIffTb aro6ofi arrropzru

[2].

B

ynusepcatraot

uawune Trnpunra, KaK

u so ecsxoll TbIopI4Hro-

soli

Maurr,rHe, ranQoplraqnx zso6pa;raercfl

cr4MBoAaMLI,

pacnoAo)KeH-

HbrMr{

oAHoBpeMeHHo

Ha rvrarnutgori AeHTe.

llpu ator"r

ynuBepca

bHaq

Marrrr,rHa

Tsropnnra Mo)Ker

pacflolararb

rll{Iub

SttxcuporaHHIIM

Ko-

HeqHbrM

BHeTuHHM aa$aautot*r.

Mex<4yreu oHaAoI)KHa 6rrrr

upracuo-

co6rreHa

K

npr{eMy B KaqecTBe

racxoAnori uHsopr"raqHl{

BceBo3Mo)r(-

Hbrx

cocrorHrui

ycrpolicrBa ynpaBleuua

u xoHSIarypaqrlft,

B Koropblx

Moryr

BcTpeqaTbcrr cr.rMBoIbI

us

pasHoo6pa3HbIx

aaQaruroa co cKo^-b

yroAno

6oluu

nr'r

q

ucloM

pa3irllqH

blx c rrMBolro B,

3ro

4o

cturaerca

nyreM KoAu

poBaHua

r<o n$u ryp a\vu n [potpaM-

uu

rrro6orl

Aannofi

MarrrHHhI

TrropNHra B cLIMBoAax BxoAHoro

(aneilr-

nero

)

alQaarara

yH

uB epcarrrHoll

Marlr IIHnL C aruo ro4H

poBaHI{e

AoDK

-

Ho

BbrrrolHrlTbca cleAyrouqutr,t

o6pasou

:

1)

pasaH.rrue

cuMBo.lSI

AoIJKHrI

3aMenrrbcl

pa3;rxtrublMld

KoAo-

BbrMr,r

rplmnaMl4,

Ho oAr{H H ToT )Ke cUMBoAAOA)KeH

3aMeHflTbcfl

BCIO-

Ay,

rAe 6u ou

Hr,r Bcrpeqa cs, oAHori

u rort:xe KoAosoli

rpyuuoll;

2) crporu

KoAoBbrx sanHcei

AoA)KHuI

oA,Ho3HaqHbIrr

o6pasou

pas-

6nsarscq

Ha

orAelbHhre

KoAoBbIe

rpyflrlbl;

3)

4oaxua

rrMerb Mecro

Bo3Mo)r(Hocrb

pacrro3Harb,

KaKI{e KoAoBhIe

rpynnbr

coorBercrBylor

pa3lr4rrHblM

cABI,IraM,

T. e. xax<4ofi

ua

6yrs

zI,

II, C

s orAelbnocrr.Ir

H

pa3lurlarb

KoAoBhIe

rpynnblr coorBercrByloulne

cI,IMBo

aM BgyrpeHHero

aa$anura

H

cI{MBoIaM

BHeruHero

arrQaarata.

Paccuorprau

upl,rMep

raKoro KoAI,IpoBaHvfl.

Ms

MarIrI,IHbI

TarcpnH-

ra ?i

uuercu{erl

eueruHprfi a.rsaarnr

A

:

{s

t,

sr.,., sr}

H BHyrpeHHufi

a;r-

Qaaur

Q

:

{e,,e2...,eJ.

Ec.Ar.r

s H

er.unurl

al$aaI,IT

yH

HBe

pc

a-rrrsoti

Malrr

I,IHsI TrropraHra

c o

-

crolrr

r,r3 cr{MBolou

A:

{0,

1}, ro srm

ycAoBLIs

6yayr

BblrrolrreHbl

rrpl{

cleAyroqeM

cuoco6e

KoAI,IpoBaHIal.

Ne

IUara

1

2

3

4

KoHQurypaqua

bqocadc

bcqoadc

bcaqrdc

bcqracc

bqrcdcc

I4cnoanserrrbl

e

KoMaHAbI

(nporparrrrlta)

@obqobA1

(qocqocAl

(ToaqraA1

(QrdqrcI4

(4raqrdt4

A

a

.f

a

b

C

d

Qo

Qril

qobJl

qocJI

4t

4rcll

Qz

4ril

Qz

4nil

Qa

q2bn

Qs

OcraHou

19s

EYxra

JI

n

C

lDr

Bseuruufi

lS"

a,'r$arur

]

.

lSo

lq'

BHyrpeuHrfi

lo.

a.n$arnr

1

..

(cocroruur)

lr;

"

Ko,qorar

rpynua

l0l

1001

10001

100001-

4 xo,rr

I

loo00ool-6ro,rer

I

HerHoe

I

qncro

Horefi,

|

6on"*.

10...01

-2(k

+l) notett)

qer\t

2

1000001-

5

uorcit

I

Heueruoe

_

100000001-?

ro,ren

I

qHcno

HoneH'

|

6omue

|

'rertr

3

10...01

-

2(n

+l) +lnoaeil)

L B xa'recrse

KoAoBhrx

rpynrr

r4cno^b3yroTct

3 *

k

*

m

pa3/\l4rlHblx

cAoB

Br4Aa

100 ... 0

1

(rrrex<4y eAuHlrrtraMu

-

norrra)

,

r4e

k

-

quc/\o

clIM-

Bo oB

BHeurHero

a,LQaaura;

m

-

quc^o

cocroqHHll

yctporictra

yu'

paB./\eHI1f.

flpn

erou

pas6uara crpoK

Ha

KoAoBbIe

rpyrrubl

npol'I3BoAl4Tcff

oA-

HO3HaTIHbIM

O6paSOu

IIyTeM

BbIAeAeHnf

IIOCAeAoBaTenlnOCrefi

HOleIi,

3aKATOqeHHEIX

MeX(Ay

AByMfl

eAI4HI{rIaMr4.

2. CouocrasleHHe

KoAoBbrx

rpynfl

c

r4cxoAHbrMIA

CUMBOAaMI4

BHeIII-

Hero

r{ BHyrpeHHero

aaQaautoB

ocyulecTB^_seTcfl

cor^acHo

c^eAyro-

u1eri

ra6araqe

KoAI4PoBanrrf

:

Taxru o6pasor'r,

ec,rru KaKar-ara6o

MarrrraHa

Trropunra

{.

peuraer-

HeKoropyrc

3aAaary, To H

ynr{BepcalbHan

Malur.rHa TrrcpuHra

T,

cno-

co6ua

pe[rr{Tb

3ry

saAarry uptr

ycloBr.rr4r

qro

KpoMe KoAoB

r{cxoArrbrx

AaHHhrx

grori gaAa.ru

Ha

ee lterrry

6y4er [oAaH

KoA nporpaMMbr

Marrru-

Hrr

4.

3a4aaaa

yHr4Bepca

bnori r"rarur.lne

TrropnHra

I lrso6pa:xenue

nporpaMMbr ,rro6ori

4aHuorl

MatuHHbr

TrropuHra

I

u uso6pa)KeHHe

ruo6oro

ee

BxoAHoro

cloBa X", uorryvrarrl

uso6paxeHr.re

BbrxoAHoro

cloBa

\,

a xoropoe

MarrrlrHa

?l nepeaogur

c,rroao X,.

Ecau x<e

aLLroprrrM,

pea

r,rgyeMbrri

r"raurnHori

{,

aeupuueHrrM

K clo-

ay Xn, ro

a ropr.rrM,

pea

r.r3yeMbrft

ynr,rsepcaarnorl

praurr.trori

I rar-

xe

He[prirMeHrrM

K c^oBy, o6pasoeannoMy

r43

nso6paxreHuaXnunpo-

rpaMMbr

uaruunrr

[.

Taxalr

o6pa3oM, Maruuna

Taropunra

I

rnroxter

paccMarpr4Barbcfl

KaK

OAHa H3 uporpaMM

A^-ff

yHr4BepCarr.suorl

ruarur.firu

I,.

FIpn usyreunn

uo4eaeri BbrrrucleHr,rft

o6H.rHo rrpoBo4aT pa3lnrrue

MeXAy

AeTepMHHHpoBaHHbIMI{

LI HeAeTepMu

HHpOBaHHbIMn

MaIUI,IHaIMII

Trrcpunra, B

p,erepuunrapoaannoli

Marur{He Tuopraura

o6rquli xoA Bbr-

.Il.{cleauri

uolHocrbro

o[peAelsercfl

uaurranoli

Trrcpr{Hra

(uporparvrrr,rori),

HalraIAbHbrM

cr{MBoAoM r4 Harrat

bnbrMr{

BBoAaMH

c Aerrrhr. B

He4erepuu-

Hupoaannori

Marur.rHe TrrcpnHra

rra

xax<4oli

cragu srr.rucleHurl

cytqe-

cl'Byror

itlbrepHarzBbr,

T.

e, oua Mox(er

pa6orarr

B

oAir{oM r,r3 HecKoA.b-

KHx ocHoBHbrx

pe)Kr,tMoa.

llpn

sroM Klacc

3aAaq,

peuraeMb[x

Ha

Aerep-

MIlHIapoBaHHLlf,x Marrrl,IHitx

TrtopuHra

ga

rro^i4HoMr{rra1bHoe

Bpewr,

Hagbr-

Baror K arccolr

P, a K arcc 3aAaq,

peuraeMbrx

Ha

HeAepreMIrHI,rpoBaHHbLx

Marrruuax Trropunra

3a

norruHoMnua,rbuoe

BpeMsr

-

K accoM

NP

I2l.

ConpeueHuble

gleKTpoHHhre

BLrrrI{c

r{Te^bHbIe

Marur{Hbl

crpoqrcfl

KaK

yauBepcarlbHbre:

B

3arroMaHarou{ee ycrpofrcrao

HaprAy

c r{cxoA-

HhrMr{

AaHHITMH

rrocraBleHHorl

aa4aura

BBoAraTcfi TaK)Ke

r.r

uporpaMMa

ee

peureHr.rff.

o4naxo B

oT^-Ltllfie

oT

MaulnHhr

TrropraHra,

a xoropotl

BHeruHflfl rraMtrb

(aeHra)

6ecxone.rna, a

ruo6ori

pea.ruaofi

Bbrrrrrcl]r-

rearHotl Matur.rHe

oHa KogerrHa.

f4n

cpaaneHr.rr

crpyKTyp

pa3lrlrrHbrx

Marrrr,rH n

or{eHKH nx

c,rlox-

HOCTLT uC[OA;3yIoT

npOI,I3BeAeHI4e

qncla

CUMBOAOB

Bneurxero

a

Oa-

BI,ITa I{a

qucrr'o

BHyfpeHHrlx

cocroflHr4li,

ora.r,tvHsrx

or 3aK rorluTe^b-

noro. B

gToM

cMbrcle rrpeAcraBllrer

r4nTepec

3aAaqa fiocrpoeur{s

yHr.r-

BepcirabHbrx Marrrr,rx

Trropuu ra MrHr{MirlbHoft

c.rr,o:rnocrr.

34ecr

ue

-

o6xop,unro orMerurb reopeMbr

Barana6e

o cyrqecrBoBaHr{r{ yHr.rBep-

ca.,rrHori

MaITJI4HbI

c

5 cnNreo.[auu u 6

cocTotHHflMl.r,

Muucxoro

o cy-

qecrBoBaulrr,r

Marur4ubr

c

4

craIvrso.llaMu a 7

cocrosHuflv'yru

reopeMy

Tpumepa o

cyulecrBoBanr.ru

yHuBepca

bnori uaurrnsr

c 4

crausonaur.r

r 6 cocrosnnfrv'vr.

Tax,

4^"a

Matur4rrbr

Trropranra,

nepepa6arrraaroulei

c^oBo

bcadc

s

c1oBo

bcdcc

(crrl.

puc.

5.5),

BxoAHoe

c1oBo

B

yHlrBepca

bnoi

Uaruraue

TtropuHra

c

AaHHbrM

KoAOM

6y4er

npe4cTaB^eHo

crreAyrouterl

crpoxofi:

10000001

1000000001

100001

100000000001

1000000001'

rae

100001

-

o, 10000001

-

b,

1000000001

-

c,

100000000001

-

d'

Bca

nporpauua

6Y4er

IrMerb

BLIA:

(qobqobJI)

(qocqocJD

@pqpJD

(qdzqzcII)

(q2aq5dII)

1000001

10000001

1000001

10000001

l0l

t000001

1000000001

1000001

1000000001

l0l

1000001

100001

100000001

100001

101

100000001

100000000001

10000000001

1000000001

10001

r0000000001

100001

100000000000001

100000000001

10001

196

t97

Акулов О.А., Медведев Н.В. Информатика. Базовый курс

Подождите немного. Документ загружается.