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Category: softwaresoftware

Современные программные системы

1.

Pa3pa6oTKa cucTeMBi aHaau3a 6ontmux gaHHBix o
KOMMHTaX Ha eCTeCTBeHHOM a3BIKe B git-pen03HT0pH^X
gaa K^acTepH3a^HH ya3BHMocTeM u cnoco6ax HX ucnpaBaeHua B
OTKPBITOM nporpaMMHOM o6ecneneHuu
CrapoBOHTOB HuKUTa AaeKcaHgpoBua (MarucrpaHT
HanpaBaeHua “nporpaMMHaa uH^eHepua”, accucTeHT
Ka^egpbi “npuKaagHaa MareMaruKa”)
AmTTy HM H.H. nonsyHOBa
BapHaya
2023
1/19

2.

npoeKTa
o Pa3pa6oTKa nonHocTtro aBTOMara3HpoBaHHtix MeTogoB o6pa6oTKH
Gontmux gaHHMx coo6^eHHH Ha ecTecTBeHHoM a3MKe H3 cucTeM
Kornpona Bepcnn gna OTKPMTMX peno3HTopneB c KogoM gna onpegeneHHa
Tex H3MeHeHHH, KoToptie ncnpaBnaroT paHee gony^eHHtie omn6KH,
KnacTepH3a^HH HangeHHtix omn6oK H BtiaBneHna KaroueBLix naTTepHoB
ya3BHMocTen B ucxogHoM Koge.
o OTKPMTMH HCxogHMH Kog agpa Linux 6ygeT Hcnont3oBaH gna o6yueHna
Kaaccn^HKaTopoB o6Hapy^eHna ^HKcnpyro^nx H3MeHeHnn, H ganee
BO3MO^HO 6ygeT aHanronpoBaTt nro6on peno3HTopnn o6^enpHHaTon
CHCTeMLI git.
2/19

3.

^geBaa rpynna nogb3oBaTegeM
o Pe3ygbrar MO^CT 6biTb ucnogb3oBaH ana. iimiKaMii B c^epe
HH$opMa^HOHHOH 6e3onacHOCTH nyTeM nogyneHua narrepHoB
Hau6ogee nacro BcrpenaeMbix TunoB ya3BuMocren gga pa3pa6oTKu MeTogoB
6opb6bi c HHMH, HTO6M He gonycKarb TaKoro poga omu6Ku gagee;
pa3pa6oTHHKaMH nporpaMMHoro oSecneneHHH gga o3HaKoMgeHua c
nacrbiMu omu6KaMu u conocraBgeHua U3MCHCHUH B Koge, HTO6M
nporpaMMupoBarb c gynmuM KanecrBoM, TpeHepaMH no
HH$opMa^HOHHOH 6e3onacHOcra H npenogaBaTegHMH gga Marepuaga gga
geKgun no gu^unguHaM, cBa3aHHMM c KanecrBoM xoga.
o TaKHM o6pa3oM, noTpe6uTegaMu npogyxra MoryT crarb KaK KoMnaHuu,
c^e^uagu3upyM^ueca B uH^opMaguoHHon 6e3onacHocru, KpynHbie
KoMnaHuu no pa3pa6oTKe no, KoTopMe xoTaT HagaguTb BonpocM
KanecTBa pa3pa6oTKH, a TaK^e uHguBugyagbHbie pa3pa6omuKu, KoTopMe
craBaT ce6e ^gb pa3pa6arMBarb Kog c HenoBropeHueM U3BCCTHMX
ya3BuMocren B pa3pa6oTKe.
3/19

4.

Ha3HaneHHe ripo/tyicra
PemeHHe
IlporpaMMHbffl npojyicr npcjHa maHCH TJJIH nonHOCTbio aBro\iaTHLiccKoro
aHanroa 6OJH>HIHX jaHHbix B BHJC cooGmemra o (Jimccaipra roMeHemra (KOMMHT3X)
B yKa3aHHbix git-pcnoiHTopusix c nporpaMMHbiM KOJOM
OvHKunoHa.i npcjCTaB.iJicT CO6OH o6pa6oTKy TeKCTa cooGmemra OT pa
!pa6oTLiHKOB. onpcjc.iCHnc KOMMHTOB, HcnpaBjiinoiipix OHIH6KH, BbmeneHHe
KJiaCCOB OLUHOOK MCTOjaMH K.iaCTCpH’iaUHH H BbljaHY OT LICTa 0 HanGonee THnHHHblX
OLUHOKaX B jaHHOM peiI03HT0pHH, BKJHOHaa YHSBHMOCTH
Git
CucTCMa KOHTpojiH Bepcnn - ycneiirabiH npoeicr JlnHyca
TopBa.ibjca. H maLia.ibHO co uaHa COBMCCTHOH pa3pa6oTKH
>mpa Linux, ceiraac npH\iCH;iCTc;i BO Bcex IT-KO\inaHn;ix
fljia pacnpcjc.iCHHoii pa3pa6oTKH H Kompojra npoeKTOB
4/19

5.

AiciyajiBHOCTB
» CoBpeMeHHbie nporpaMMHbie CHCTCMbi crpoaTca H3 6ojn>moro HHCJia (JiaiuiOB c
HCXOflHblM KOJOM Ha OJHOM H3 HSbIKOB n p 0 T p tl \ I \ IM p 0 Btl H M H.
pa3pa60TKa BCJCTCH KOJUieKTHBOM pa3pa60THHK0B C HCn0JH>30BaHHeM
OOLHHX peno3HTopHeB KOja H noaaep>KKOH KompojiH BepcHOHHoem
9 Kaviuoc H3MeHeHHe ncxojHoro KOja ((|)HKcaun;i) ccrojHsi ocymecTBjiaeTCH
pa3pa6oTHHKaMH c yKa3aHneM TeKCTa npon sBcjCHHbix H3MeHeHHH Ha
eCTeCTBeHHOM HSbIKC
9 BojIbHIHe pen03HT0pHH HBJHHOTCH HCT0HHHK3MH 60JIbHIHX jaHHblX (big data)
06 3BOjnoiiHH nporpaMMHoro KOja
r HnoTe3a
C.TCJYCT Hcnojib30BaTb oo.ibumc jaHHbic Ha ecTecTBeHHOM
H3biKe H3 nporpaMMHbix peno3HTopHeB y jry nine HHH HX
paooTbi B TOM HHCJie fljia aHajiH3a HcnpaBjieHHbix OHIH6OK c
BbmejieHHeM HX Hanoo.icc penpe3eHTaTHBHbix KjiaccoB
5/19

6.

HMiogecIgo axooMivoorA'dx XOCM'HHO o>i;.od OXH ao>iHhxogi:dn:d
HHHorngooo cmirox t: i:ro>i ojOHroxon sun: HI: Koxuroas.nodu ajj ©
ivoro>i a aondoxns.ouod n>ixogt:dgo cooonodu axooHHcaodHS.Hxtuvoxat:
KBHiron KOxoKL'aK KHHomod HO>Iuxondoi-'iedex HOHSOHOO ®
EOTKK oJOHHoaxooxoo n>ixogt:dgo H oouops
pep naxaeirgo EH aoroxaiv BITOHH oxomurog OHHcaos.arouon xotuerourodu
x>iood[j ©
KHHsmsd ^aioamXiMHadu 9iqHiH9dX>iHO>j

7.

CymecTByioiuHe aHanorH
®
Bee pa3pa6oTKH B J3HHOH c(|icpc TpYjosaTpaTHbi H
pe3yjn>TaTbi
npcjCTaB.iCHbi
KaK
npaBHjio
BCJVLUHMH
aiaucMunccKHMn HHCTmyTHMH Ha rocyjapcTBCHHbic rpaHTbi
® IlpHMepbi HHCTHTyTOB: INRIA (Op3Hun;i). HCn PAH (POCCHH)
® B HHX ncno.ib !yK)Tc;i jpyrnc MCTOjbi no.iyLiCHn;i
KjiaccoB OHIH6OK B
OCHOBHOM, 3a CHCT CT3THLICCKOTO aHajIH3a H KOMnH.ltfUHH HCXOJHOrO
KOJ3 C nOC.3CJVK)LUHM n0.IVaBTOM3THLICCKHM aH3JlH30M
(3BTO\13THLICCK3H 06pa60TKa BbiBOja nporpaMMHbix cpcjCTB aHanroa HJIH
KOMHH.TIIHHH. pyiHOii aHanro pe3yjn>T3TOB)
a IlpHMepbi CTaTHHecKHx 3H3JiH3aTopoB: Coverity (CHIA),
PVS-Studio (POCCHH), HCH3 nojnucKH OT 10.000 USD/rcu
Hx HeAOCTaTKH
Bojibinoe BpcMH aHajiH3a, 3Hepro3arpaTbi, 33BHCHMOCTb OT KjiaccoB OHIH6OK,
KOTOpbie MOryT 6bITb BbMBJieHbl HMeiOIHHMHCH 3HajIH3aTOpaMH,
B03M05KH0CTb JI05KH0-n03HTHBHbIX Cpa6aTbIBaHHH
7/19

8.

HaynHaa H0BH3Ha
o npoeKT 6a3upyeTca Ha HOBOM npHMeHeHHH MeToga KgaCTepu3a^uu K
noucKy OCHOBHMX KgaccoB omu6oK u ya3BHMocreH B nporpaMMHHx
peno3UTopuax
o npegnogaraeTca caMocroaTegbHaa peagroa^a Heo6xoguMbix agropuTMoB
KgacTepu3a^uu, HTO6M He 3aBuceTb OT cropoHHux nporpaMMHbix
6u6guoTeK
8/19

9.

HaynHaa H0BH3Ha
o BeKToproa^a $pa3M, “MemoK caoB”, KOCHHycHoe paccmaHHe
D(si, S2) := D((W1,1, w 1,2, • •, Wl,n),
(W2,1, W2,2,
W2,n)) =
En
i=1 W1,i ■ W2,i
W
i=1 W1,i
■E:i=1 2,i
(1)
2
nepecraHOBKH caoB B $pa3e He H3MeHaroT ee cogep^aHHa
9/19

10.

HaynHaa H0BH3Ha
o TF-IDF Hcno^b3yeTca gas H3MeHeHHa BecoB caoB c “cngbHMMH
KOMnoHeHTaMH^:
Ecau MM o6o3HanHM nw KaK KoanaecTBO Bxo^geHHH caoBa w B coo6^eHHH
KOMMHTa m G M, nw KaK o6^ee KoanaeCTBO caoB, a \M\ KaK o6^ee
KoanaecTBO coo6^eHHH, Torga:
tf-idf(w, m, M)
tf(w, m) x idf(w,M) =
nw , _ \M\
J2knk X og \{ mi G M \ w G d }\
(2)
10/19

11.

HaynHaa H0BH3Ha
o ^eMMaTH3a^HH ngn HopMaflH3a^HH ieMM Hcno^b3yeTca gga
nogyneHHa ^opMbi OCHOBM gga Ka^goro cgoBa:
fix
fix
fixed
fixed
fixes
fixes
fixes
fixing
fix
fix
fix
fix
fix
fix
fix
fix
$N$
$V+0$
$V+ed$
$V+en$
$N+s$
$N+s$
$V+s$
$V+ing$
11/19

12.

HaynHaa H0BH3Ha
o AaropuTM KaacTepu3a^uu npegcTaBaaeT CO6OH ^yH^uro X ^ Y, KOTopaa
npucBauBaeT ugemu^uKaTop KaacTepa y G Y aro6oMy oG^eKiy x e X
o HeKoTopMMH nonyaapHMMH aaropuTMaMu KaacTepu3a^uu aBaaroTca
K-cpegHue, DBSCAN u uepapxrnecKaa KaacTepu3a^ua
o npu uepapxuaecKon KaacTepu3a^uu CTpouTca gepeBo (geHgporpaMMa) OT
aucrteB go KopHa. H3HaaaatHo Ka^gtiH oG^eKT cogep^uTca B CBoeM
KaacTepe. flaaee npoucxoguT uTepa^uoHHMH npo^cc oG^eguHeHua gByx
6au^anmux KaacTepoB go Tex nop, noKa Bce KaacTepti He oG^eguHaTca B
oguH, au6o He 6ygeT HangeHo Heo6xoguMoe KoauaecTBo KaacTepoB
12/19

13.

HaynHaa H0BH3Ha
o ,3,ga ogeHKu KanecTBa Kgacreproaguu u Bbi6opa onraMagbHoro MeToga
npegnogaraeTca npoBecru uccgegoBaHueM npuMeHHMo CTH pa3guHHMx
MeTogoB B TOM Hucge u HenpoHHbix ceTen, B Hacma^ee BpeMa noKa ecTb
runoTe3a o npuMeHHMocTu MeToga uepapxHHecKon KgacTeproaguu, Korga
HecKogbKo BeKTopoB, HgeHTH^ugupyw^ue coo6^eHua nocTeneHHo
cguBaroTca
o OgHaKo, TyT Tpe6yeTca peagroagua ^BpHCTHKH, Bo3Bpa^aro^en nopor
paccToaHua Me^gy BeKTopaMH, npu KOTOPOM BeKTopa cnuTaroTca
oKoHHaTegbHo pa3guHHMMMu, HTO Tpe6yeT gonogHuTegbHbix
uccgegoBaHun
o KpoMe Toro, gaa pemeHua nocraBgeHHMx 3agan Heo6xoguMo
npoaHagu3upoBaTb pa6oTbi B c$epe co3gaHua Kgaccu^uKaropoB gga
KOMMHTOB KaK no coo6^eHuaM TaK u no H3MeHeHuax B rpa^e ynpaBgeHua
u peagrooBarb co6crBeHHMH Kgaccu^uKarop Ha ocHoBe MeTogoB
MamuHHoro o6yneHua, HTO no3BoguTb oTgunarb KOMMUTM c
ucnpaBgeHueM omu6oK OT Bcex KOMMUTOB B pe^o3HTopHH, BKgKraro^ux,
HanpuMep, go6aBgeHue HOBOH ^yHKguoHagbHocru, HTO Hac He
uHTepecyeT
13/19

14.

HayHHBiM 3ageg
o B 2023 rogy aBTopoM 3aaBKH cgegaH goKgag Ha Me^gyHapogHoM
KoggoKBHyMe no nporpaMMHOH HH^eHepuu, opraHH30BaHHMM
HHcTrnyTOM cncreMHoro nporpaMMHpoBaHHa PAH: Towards methods to
automatically identify the most common errors in Linux by analyzing git commit
messages.
http://syrcose.ispras.ru/2023/submissions/SYRCoSE_2023_paper_9521.pdf
o B gaHHOH pa6oTe paccMorpeHbi ocHOBHMe pa6ora B grou o6gacTH,
peagu30BaH0 pemeHue c Hcnogb30BaHueM paccmaHua .HeBeHmTeHHa
Me^gy coo6meHHHMH KOMMHTOB, a TaK^e cgegaH mar K KgacTepH3a^HH
TaKux coo6meHHH
o Pa6oTOcnoco6HOCTb noKa3aHa Ha He6ogbmoM peno3HTopuH Koga pa6ora c
aganTepaMH Thunderbolt B agpe Linux, H no peno3HTopuro c KogoM 6bigu
onpegegeHM omu6KH, cooTBeTcTByrnmne H3BecTHbiM B guTeparype
ya3BHMocraM gga TaKux aganTepoB
o Pa6oTa noKa3aga Ba*Hocrb npoBegeHua oTgegbHbix o6mupHbix
uccgegoBaHHH B c$epe KgacrepH3auHH TeKcroB omu6oK H co3gaHHa
Kgaccu^HKaropoB gga pemeHua, aBgaeTca gu Ka^gbiu KOMMHT
HcnpaBgammHM ugu HeT
14/19

15.

KoMMep^uagu3a^ua
r> npeggaraeTca peagu3oBarb nporpaMMHbm npogyKT u npogeMoHcrpupoBarb
ero pa6oTy Ha pa3Hbix nacTax agpa Linux
^ Hanarb noucK napTHepoB cpegu KOMnaHHH no pa3pa6oTKe HT pemeHHH,
KOTopbie MoryT 3aKa3arb aHagu3 CBOUX peno3UTopueB c BbiganeH
geTagbHbix OTneTOB, reHepupyeMbix nporpaMMon no KoMMuraM
BO3MO*HO TaK^e npegocraBgeHue KoHcagTuHroBbix ycgyr KoMnaHuaM no
pa3pa6oTKe no nyTeM geTagbHoro aHagu3a BbiaBgeHHbix KgroneBbix
omu6oK B uHTepecyM^ux ux peno3uTopuax c npuBa3Kon K ucxogHoMy Kogy.
P) ngaHupyeTca 3apa6arbiBarb Ha ycgyrax, KoTopbie nogynaroTca nyTeM
npuMeHeHHa npeggaraeMon nporpaMMbi Ha gaHHbix OT KgueHToB
Pa3Mep noTeHguagbHon ongara 3a oTneT no peno3uTopuro Mo^eT 3aBuceTb
OT KogunecTBa ^uKcupyro^ux KOMMUTOB, Ha ypoBHe geHbi CTarugecKoro
aHagu3aTopa gga KoMnaHuu TaKoro *e ypoBHa
^ TaK^e BO3MO*HM uHguBugyagbHMe pemeHua no BcrpauBaHuro nporpaMMHoro
npogyKra B npogeccbi CI/CD (npogeccbi HenpepbiBHon uHTerpaguu c
pa3BepTMBaHueM Koga) KoMnaHuu
15/19

16.

61/91
HJVEXHJVJVOM
XH mvooa oo xnuiq edrii aoxHOHOimoa cloivuclutm ivoron o Hudoxus ouod oumarog
axcaodwunmi: oxoHgooono tmuxoxodu ojomonuoged Kuncs urcoj ©
HHdoxHtonod
a KHHOtngooo oiaHaoHOO HL'KL'acxorodu OHanxcxHOS.oduod oorogntm taooeoi oiaHHOh
/rou ragoxh >n:x ‘aoxodon HMHodxorou H unlit:;.udoxocL'M eaxoohoi roiHOlio
HOMOOiiHxcivoxat: Ktrli HMuxondae. aoroxoiv Klim:;.ureod H eaxogedny ©
aoxmvivoM HIVHH o xiaHHBEKao H HHHOlngooo aoooeoi xiaHaoHOO KHHOiroliodno
oiaron o HivKHHOtngooo o aodoxaoa HHrn:;.Hdoxot:oi
aoivxudojL't: t:>ixogt:d;.t:d H eroxoiv oJOHanaviixiio dogiaa 'iunmy ©
(EHHOlngooo erod OJOMIU I:H x ta H H t:a od H; . H I v HXU o) aoHdoxw.ouod-iiS
0 (X'CXHIVIVOM) HHH3H3IW.H XKHHB3>IH([) 0 HHHOlngOOO XiaaOX3>I3X
HHllBEHdOXaOa H HHlmHXBIMIMOir aoivxudojL't: KHllBEHITBOd H Oixoged'c ty ©
:utut [
HHllBeHir^sd HBITJJ

17.

,^eMOHCTpa^Hfl pa6oTBi
HaH/lCHHhIH BeKTOp II3
KJIIOMeBblX CJIOB
■BjiicKaftiuiie COO6IHCHII>T 06
11CIIpaBJIC H11H X II IIX X'jllHI
/(iLHHbiii HiiSop naii,'iei[iiLix cooGmemiH IIOJIHOCIUKI opiieunipoBmi mi iicnpiiariemie HS
«ciiCKy;utiitBHOu ar;iKou», KOTopaa uosBOJiaer 2JioyMbtiujiCHIIIIKUM iicuojibMBaTb 4
4IIIO CUCKyjIHTlIBHOro BbUIOJIHCHUJt COBpCMCKHblX lipOUCCCOpOB
JUU JOC'l'yilil f 1 KpCMfl HCKJ1 lO'lLtlll II II 11 pCpiiliicUI IIII. HTOfibl
;iociy11. Biopoc itcnpaBJieHitc anajioriiNHO, HO OHO KOHKPCTHO sacaciOI CHCTCMHUX B&I
liptVlOrBp.lllilb HCCilHKUHOHHpOBilH HblK
3anycKa 32-OIIIHUX npioiojucHHii B 04-fnmioH CKCTCMC, II iicnpaBJiCHiic onuuaer peniCTpu, iicnanbiycMbic BO BpeMsi 3THX cucrcMitbix BW30BOB, uiofibi iipejoiBpaiiii
•iKciuiyaranHR) ,'iaiinoft yjnBHMOCTM. Tperbe iieiipaBJieiiHe ycrpaHser OIIJHOKV. irpii Koropofi UMIP fibui BbBbtBatt c6oii GP B oiipejicjiaiiiibix cirryamiax. KOTopue Moiyt 6hiib
HCiiOjIb-iOBiiibi inoyMMlUJlCKHHKilM H. UMIP — TiO ((jyiujunx SoiOnaciiOCiH, KOiopax npCflOTBpaniACT BMIIOJIHCHIIC onpe.«CJieHHblX ItHCTpy KIIHH B
n0Jlb30BaTfcirbCKt)M pOsiiMC. McTBcproe iicnpaBjioiiiie iicpoMCuiaor oopaooi'in KM iipepuBaHiifi APlC B tkuiee SeaonacHoe MBCTO B HOMSTH, (notjbi npi'.ioI npa miL
OKCiuiyaiauiuo. HiiKOtieu, IIOCJICAHCC iioiipaBJicmic ucpciiMCKOBbiBacT uapaMcrp Kom|miypamin napa II yciuiiaa'iHBaer a'isi HCH> Jimeuitc no yMOjriaiiino «HCI», no6bi
iipcaoiBpaiiiib iicuoia-aoBaKiic ■jjiOyMbiiujiCH mi Ka MII (JtyiiKUHM VM 86, KOrOpaa nO'iBOjiaCT 16-6HTHUM iipHJiOjKCKiuiM aaiiyCKaibCH B BH prya JI biiOM pCaaiMC 8086. Ii
a ijiv it KU MX OcuibuiC HC iiy* na B COspexteiiHbix
3KCnepTHbIH TCKCT
\aHaJiii3a OUIHSOK H
C 8 76 2e5 0928 28
c3 (bdde80 7da0
7e17
3 c 67 Qd £7 7 £i)
yaaiiHMOCTeii no HaftfleHHblM
COo6llJ,eHll5IM
JaHHUH iiaOop iiciipaBJieHiift IIOCBHUIEH HcnpaBJicumo ysnBiiMOCTCH B iiftacHCTCMax KVM, ritncpBH-Jope Xcn, AMD Secure Virual Machine it Virtual Machine Interface.
3TH Aocryna K KOHtJiHjiCHuiiajibHoit itHi)H>pMaunn. OBHOBACHHS suiioiaioT orpaHHHCHHC npoBcpcx Koaa OIUH6KH AJIH PFERR_NESTED_GUEST_PAGE TOJIIKO ;uia rocra
ncpBoro
ypOBHSI, ILClipa BJICHILC BblACHCHIfH C'ip:lHI(H ,VliL 11 ap:LB Itp i y IL11 Q ItpOBtl HHbIX raGjIltU OipillKlip POOtllblCH HC lUVbtep^Kb 11 AOItOJIHHTCJIbHbJX
KQJJOB O III 11 (it) K, CB5I-SBIL H bl K C OI11IIOKIIMK
17/19

18.

n^aH peagu3a^uu
2 gran:
Pa3pa6oTKa agropuTMoB Kgaccu^uKaguu Tuna KoMMuTa
(ucnpaBgeHue/go6aBgeHue) MeTogaMu MamuHHoro o6yneHua c gegbro
TOHHOIO BbiaBgeHua uMeHHO KOMMUTOB c omu6KaMu
^ OnraMroagua Bcex pa3pa6oTaHHbix agropuTMoB u BHyTpeHHen apxuTeKiypbi
npugo^eHHH
Peagu3agua BMBoga ygo6onuTaeMoro pe3ygbTaTa pa6oTM nporpaMMM, c
BMHBgeHHMMu KgaccaMu omu6oK u ya3BuMocTen, CBa3aHHMMu
KOMMuTaMu, pe^epaTuBHaa cnpaBKa no TeKCTaM HangeHHbix
KOMMuTax, gpyraa guarHOCTHnecKaa uH^opMagua, noge3Haa gga
aHaguTuKa
^oKyMeHTupoBaHue npoeKTa
nogana 3aaBKu Ha perucTpaguro npaB Ha pe3ygbTaTM uHTeggeKTyagbHon
geaTegbHocTu, npoxo^geHue npeaxcegepaguoHHon nporpaMMM, gopo^Haa
KapTa pa3BuTua npoeKTa
18/19

19.

Pa3pa6oTKa cucTeMBi aHaau3a 6ontmux gaHHBix o
KOMMHTaX Ha eCTeCTBeHHOM a3BIKe B git-pen03HT0pH^X
gaa K^acTepH3a^HH ya3BHMocTeM u cnoco6ax HX ucnpaBaeHua B
OTKPBITOM nporpaMMHOM o6ecneneHuu
CrapoBOHTOB HuKUTa AaeKcaHgpoBua (MarucrpaHT
HanpaBaeHua “nporpaMMHaa uH^eHepua”, accucTeHT
Ka^egpbi “npuKaagHaa MareMaruKa”)
AmTTy HM H.H. nonsyHOBa
BapHaya
2023
19/19
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