Lissafi da ƙididdiga

Gwajin matrix bazuwar

Manyan matrices cike da lambobi bazuwar, ana yin diagonalise su akai-akai don nazarin ƙididdigar eigenvalues ɗinsu.

Tambayar da yake amsawa: Wane tsari eigenvalues na matrix bazuwar ke zama, kuma ya dace da sauran fannonin lissafi da fiziks?

Yana barin: Yana ɗaukar samfurin ƙaramin kusurwa ne kawai na sararin matrices marasa iyaka.

Yana gudana a: kusan 10¹² FLOPS kimanta kawai gungun kwamfutoci na jami’a yana samarwa da diagonalising matrices manya da yawaTun: 1955 Aikin farko na Wigner kan ƙididdigar eigenvalue na matrix bazuwar

Gwajin jadawali bazuwar

Jadawali da aka samar ta hanyar ƙa’ida ta bazuwar, ɗigo-ɗigo ko gefe-gefe, don ganin waɗanne siffofi, kamar haɗin kai ko tarawa, ne suke bayyana a mafi yawan lokuta.

Tambayar da yake amsawa: Yaya hanyar sadarwa ‘ta yau da kullum’ take ƙarƙashin wannan ƙa’idar ƙara nodes da gefuna?

Yana barin: Ainihin hanyoyin sadarwar duniya da wuya su kasance tsaftatattu kamar ƙa’idar da ke samar da samfurin.

Yana gudana a: kusan 10¹⁰ FLOPS kimanta kawai yana gudana a kwamfutar tebur don jadawali har zuwa miliyoyin ɗigoTun: 1959 Erdos and Renyi's random graph model

Kwaikwayon percolation

Lattice ko hanyar sadarwa da ake buɗe wurare ko haɗi a bazuwar, ana kallo don gane lokacin da hanyar haɗi ta bazu cikin dukan tsarin kwatsam.

Tambayar da yake amsawa: A wane yawa ne hanyar sadarwa ta bazuwar take haɗuwa kwatsam daga ƙarshe zuwa ƙarshe?

Yana barin: Lattice na kamala suna ɗabi’a da tsafta fiye da kowane abu mai ramuka ko hanyar sadarwa ta gaske.

Yana gudana a: kusan 10¹⁰ FLOPS kimanta kawai kwamfutar tebur don manyan binciken latticeTun: 1957 Broadbent and Hammersley's introduction of percolation theory

Binciken lissafi na gwaji

Binciken lambobi ta ƙarfin lissafi don neman tsare-tsare, misalan karyatawa ko ainihin alaƙa tsakanin lambobi, ana yin shi fiye da yadda za a iya dubawa da hannu.

Tambayar da yake amsawa: Wannan zato gaskiya ne a kowane yanayi da kowa zai iya duba, kuma wani tsari yana bayyana?

Yana barin: Babu adadin lamura da aka duba da ke zama hujja, duk yawan waɗanda aka gano suna tabbata.

Yana gudana a: kusan 10¹¹ FLOPS kimanta kawai gungun kwamfutoci na jami’a yana gudana kwanaki a kan bincike ɗayaTun: 1963 Zuwa 1963, binciken kwamfuta don alaƙar lamba da tsarin lambobin prime

Kimanta lambobi na dindindin (constants) ta Monte Carlo

Ɗaukar samfur na bazuwar da ake amfani da shi don kimanta lambar dindindin (constant) ta lissafi ko integral, kamar watsa maki don kimanta fili, a matsayin atisaye ba don samfurin zahiri ba.

Tambayar da yake amsawa: Yaya daidai ɗaukar samfuri bazuwar a makance kaɗai zai iya tantance ainihin adadin lissafi?

Yana barin: Yana haɗuwa a hankali fiye da kusan duk wata hanyar lissafi mafi inganci.

Yana gudana a: kusan 10⁹ FLOPS kimanta kawai yana gudana a kan laptop cikin daƙiƙu zuwa mintunaTun: 1946 Ra’ayin Ulam na 1946; von Neumann ya gabatar da sigar kwamfutar lantarki a Maris 1947, kuma an fara buga hanyar a 1949 tusheA bishiyar kwaikwayo: Hanyar Monte Carlo

Gudanar da samfurin mai mu’amala

Binciken ka’idar lambobi ta lissafi

Manyan lambobi da ake gwada ko su prime ne, ana rarraba su ko ana neman halaye na musamman kamar cikakkun lambobi, ta amfani da algorithms da ake gudanarwa a mizani maimakon da hannu.

Tambayar da yake amsawa: Shin wannan lamba mai girma tana da halin da muke nema, kuma har ina bincike zai iya tura rikodin?

Yana barin: Bincike mai karya rikodi yana faɗin kaɗan game da lambobin da ba wanda ya yi tunanin dubawa tukuna.

Yana gudana a: kusan 10¹³ FLOPS kimanta kawai wani aikin lissafi na sa kai da aka rarraba a kan injuna da yawa da aka ba da gudummawaTun: 1951 Gwajin hannu na Lucas don Mersenne primes, wanda kwamfuta ta fara gudanarwa a 1951

Lissafin chaotic-attractor

Ƙaramin saitin lissafi marasa layi da ake haɗawa mataki-mataki don bayyana dogaro mai tsananin saurin amsawa ga yanayin farawa da fractal attractor.

Tambayar da yake amsawa: Me ya sa tsarin tabbatacce mai sauƙi ke zama ba za a iya hasashe ba?

Yana barin: Kusantar lambobi a lissafi (rounding) na nufin dogon tafiya ba ainihin kewayawa ba ne, sai dai wanda ke kusa da ɗaya.

Yana gudana a: kusan 10³ FLOPS kimanta kawai ƙananan lissafi, daƙiƙu a kwamfutar tafi-da-gidanka.Tun: 1963 Lorenz’s deterministic nonperiodic flow, a convection model run on a computer. tusheA bishiyar kwaikwayo: Convection mai hargitsi na Lorenz

Gwaje-gwajen lattice marasa layi

Jerin ƙullun nauyi masu maɓuɓɓugai marasa layi, an fara su a hanya ɗaya aka bi diddigin ko kuzarin yana yaɗuwa daidai, kamar yadda thermodynamics zai nuna.

Tambayar da yake amsawa: Shin sarƙa marar layi tana raba kuzarinta daidai tsakanin dukan motsinta?

Yana barin: Sakamako yana dogara da sarƙar da aka zaɓa da yanayin farko.

Yana gudana a: kusan 10³ FLOPS kimanta kawai ƙarami ne a ma’aunin yau; na asali ya yi amfani da ’yan dozin na masses.Tun: 1955 Fermi, Pasta and Ulam's studies of nonlinear problems on an early digital computer. tushe

Gwajin lissafi na soliton

Lissafin taguwa maras layi da aka warware a kan grid don kallon bugun taguwa suna ratsa juna suna riƙe siffarsu, abin da taguwa masu layi ba sa yi.

Tambayar da yake amsawa: Me ya sa wasu raƙuman ruwa marasa layi ke wucewa juna ba tare da canji ba?

Yana barin: Yana nuna rukuni ɗaya na ma’aunai, ba ɗabi’ar raƙuman ruwa marasa layi gaba ɗaya ba.

Yana gudana a: kusan 10⁴ FLOPS kimanta kawai grid mai girma ɗaya, mai sauƙi a yau.Tun: 1965 Mu’amalar solitons ta Zabusky da Kruskal a cikin plasma mara karo da sake dawowar yanayin farko. tushe

Nuna saitin fractal

Ƙa’idar da ake maimaitawa mai sauƙi da ake gwadawa a kowane wuri a fuskar lambobi masu rikitarwa don ganin ko ta tsere, tana zana iyakar saitin wurare masu kwanciyar hankali.

Tambayar da yake amsawa: Menene siffar saitin da maimaitawa mai sauƙi ke zama iyakantacce a ciki?

Yana barin: Gwajin tsere kawai yana nuna ko wuri yana cikin saitin, kuma hoton ɗiban samfur ne mai ƙudurin da ya ƙayyadu na saitin da yake da cikakken bayani mara iyaka.

Yana gudana a: kusan 10⁹ FLOPS kimanta kawai zurfafan zuƙowa suna buƙatar maimaitawa mai daidaito mai faɗaɗa a miliyoyin wurare.Tun: 1980 Mandelbrot’s fractal aspects of the iteration of z to lambda z(1-z), first computer images of the Mandelbrot set. tushe

Sandpile self-organised criticality

Ana zuba hatsi a kan grid, sai su zube idan sun yi gangare da yawa, suna haifar da zaftarewa ta kowane girma ba tare da gyara ba, a matsayin samfurin yadda tsarin ke kaiwa ga yanayin da ke bakin sauyi.

Tambayar da yake amsawa: Me ya sa zaftarewa ta kowane girma ke bayyana ba tare da daidaitawa ba?

Yana barin: Ko ainihin tsare-tsare suna da ma’aunin iri ɗaya ana jayayya.

Yana gudana a: kusan 10⁹ FLOPS kimanta kawai dogayen gudanarwa a manyan grid don ganin sikeli.Tun: 1987 Bak, Tang and Wiesenfeld's self-organised criticality: an explanation of 1/f noise. tushe

Lissafin sifilin Riemann zeta

Ana lissafa ƙimar zeta function a kan layinta mai muhimmanci don gano da ƙirga sifilinta, ana duba suna inda hasashen ya ce.

Tambayar da yake amsawa: Shin dukan sifilai marasa sauƙi (non-trivial) na aikin zeta suna kan layi ɗaya?

Yana barin: Binciken da ya ƙare, ko yaya tsawonsa, ba zai iya tabbatar da cewa babu sifili a wajen layi da ya wuce shi ba.

Yana gudana a: kusan 10¹⁸ FLOPS kimanta kawai shekaru goma-goma na lokacin CPU a manyan bincike.Tun: 1953 Lissafin Turing na Riemann zeta function. tushe

Lambobin pi ta kwamfuta

Ana tara jerin pi zuwa adadin lambobi masu yawa tare da ainihin lissafi, yana gwada lambar da na’urar.

Tambayar da yake amsawa: Shin lambobin pi suna kama da bazuwar, kuma za a iya amincewa da na’urar a wannan girman?

Yana barin: Lambobin ba su amsa wata tambaya buɗaɗɗiya ba, kuma bincike yana kama kuskuren kayan aiki ne kawai idan hanyar ta kasance mai zaman kanta.

Yana gudana a: kusan 10¹⁷ FLOPS kimanta kawai watanni a kan uwar garke don ɗaruruwan tiriliyoyin lambobi.Tun: 1950 Reitwiesner’s ENIAC determination of pi and e to more than 2000 decimal places (published 1950, reprinted in Pi: A Source Book). tushe

Gano zato da AI take jagoranta

Koyon na’ura a kan manyan teburori na abubuwan lissafi yana gano waɗanne halaye ne ke da alaƙa, don ba da shawarar zato da masana lissafi daga nan suke ƙoƙarin tabbatarwa.

Tambayar da yake amsawa: Wace alaƙa da ba a gani tsakanin waɗannan adadin lissafi ta cancanci a tabbatar?

Yana barin: Yana ba da shawarar tsare-tsare kawai, ba ya tabbatar da komai da kansa, kuma wasu daidaituwa a bayanan na iya zama kurakurai na yadda aka yi bayanan.

Yana gudana a: kusan 10¹⁵ FLOPS kimanta kawai kwanaki a GPU kaɗan a kowane saitin bayanai.Tun: 2021 Davies and colleagues' advancing mathematics by guiding human intuition with AI. tushe

Neman algorithm da gini da aka koya

Tsarin wasa ko samfurin harshe yana neman sababbin hanyoyi ko abubuwan lissafi, kwamfuta tana duba daidaiton kowane ɗan takara.

Tambayar da yake amsawa: Shin shiri zai iya gano algorithm mafi sauri ko babban misali fiye da yadda mutane suka samu?

Yana barin: Kowane sakamako misali sabo ne ɗaya, kuma bincike yana rufe nau’ikan abubuwa da masu ƙira suka tsara a matsayin wasa ne kawai.

Yana gudana a: kusan 10¹⁷ FLOPS kimanta kawai kwanaki zuwa makonni a gungun na’urorin hanzari.Tun: 2022 Fawzi and colleagues' AlphaTensor, discovering faster matrix multiplication algorithms with reinforcement learning. tushe

Duba samfuri

Kowane yanayin da za a iya kaiwa ga tsari mai iyaka, kamar yarjejeniya ko ƙirar da’ira, ana lissafa shi ta kwamfuta don duba cewa hali yana riƙe a dukansu.

Tambayar da yake amsawa: Akwai wani yanayi da ake iya kaiwa inda wannan ƙira ke karya ƙa’idodinta?

Yana barin: Adadin yanayin da ake iya samu yana ƙaruwa fiye da abin da za a iya dubawa, don haka ana sauƙaƙa ainihin ƙira da farko.

Yana gudana a: kusan 10¹² FLOPS kimanta kawai gungun kwamfutoci na jami’a yana bincika kowane yanayi a cikin babban fili mai iyakaTun: 1981 Clarke and Emerson's introduction of model checking

Binciken hujjar ka’ida ta atomatik

Bincike ta sarƙoƙin hujjar mantiki, kwamfuta tana samar da su mataki-mataki, tana neman hujja ko karyata bayanin lissafi.

Tambayar da yake amsawa: Shin akwai ingantacciyar sarƙar matakan mantiki daga axioms zuwa wannan magana?

Yana barin: Yana gano hujjoji da babu ɗan Adam da zai zaɓa, wani lokaci ma babu ko ɗaya a iya isa.

Yana gudana a: kusan 10¹¹ FLOPS kimanta kawai gungun kwamfutoci na jami’a yana bincike awanni zuwa kwanakiTun: 1956 Logic Theorist, farkon shirin neman hujja ta atomatik

SAT da warware ƙuntatawa

Miliyoyin haɗin ƙimomin gaskiya ko ƙarya da ake nema bisa tsari don gamsar da babban saitin ƙuntatawa na mantiki, ana amfani da su don tsarawa, hanya ko tabbatar da ƙira.

Tambayar da yake amsawa: Akwai wani rabon ƙimomi da ke gamsar da duk waɗannan iyakoki lokaci guda?

Yana barin: Wasu misalai suna da wuya sosai har babu mai warwarewa, komai kyawunsa, da ke gamawa a kan lokaci.

Yana gudana a: kusan 10¹¹ FLOPS kimanta kawai kwamfutar aiki zuwa gungun kwamfutoci, gwargwadon girman matsalarTun: 1962 tsarin Davis-Putnam don neman gamsuwa

Samfurin harin cryptographic

Tsarin code ko musayar maɓalli da aka kai wa hari miliyoyin lokuta a kwaikwayo, ta ƙarfin lissafi kawai, ta karkacewar ƙididdiga ko ta raunin da aka yi samfurinsa, don auna ainihin ƙoƙarin da ake buƙata wajen karya shi.

Tambayar da yake amsawa: Ayyuka nawa zai ɗauka a gaske don karya wannan, kuma har yanzu wannan adadin yana da girma sosai don a ji aminci?

Yana barin: Yana gwada hare-haren da mai bincike ya yi tunanin yi wa samfuri kawai, ba wanda kowa bai gano ba tukuna.

Yana gudana a: kusan 10¹⁴ FLOPS kimanta kawai gungun kwamfutoci da aka rarraba na injuna da yawa suna gudanar da gwajin hariTun: 1976 Zuwa 1976, nazarin kwamfuta na ƙarfin cipher da musayar maɓalli

Kwaikwayon zubewar side-channel

Ana yin samfurin amfani da wuta, lokaci ko fitar da lantarki-maganadisu na na’ura yayin da take gudanar da aikin cryptographic, don ganin abin da mai saurare daga waje zai koya daga gare ta.

Tambayar da yake amsawa: Nawa daga maɓallin sirri ke zubewa ta ɗabi’ar zahiri ta na’urar, ba lissafi ba?

Yana barin: Yanayin dakin gwaji yana kama sigina masu tsabta fiye da abin da na’ura mai hayaniya ta gaske ke bayarwa yawanci.

Yana gudana a: kusan 10¹⁰ FLOPS kimanta kawai kwamfutar aiki tana yin samfurin wutar lantarki ko rubutun lokaci na na’ura ɗayaTun: 1996 Nunin Kocher na hare-haren lokaci a kan aiwatar da cryptography

Tabbatar da yarjejeniyar tsaro

Kowane saƙo da maharin zai iya aikawa, maimaitawa ko ƙirƙira a yarjejeniyar sadarwa, ana lissafa shi ta kwamfuta don duba ko za a iya tilasta sirri ko shaida daga ciki.

Tambayar da yake amsawa: Shin kowane jerin saƙonni zai iya yaudarar wannan yarjejeniya ta bayyana sirri ko karɓar shaidar ƙarya?

Yana barin: Yana tabbatar da yarjejeniyar kamar yadda aka bayyana, ba gajerun hanyoyin da ainihin aiwatarwa ke ɗauka ba.

Yana gudana a: kusan 10¹¹ FLOPS kimanta kawai kwamfutar aiki zuwa gungun kwamfutoci suna duba filin saƙo na yarjejeniya ɗayaTun: 1989 Samfurin Dolev-Yao, tushen tabbatar da yarjejeniya

Hujja da kwamfuta ke taimaka wa ta duba kowane lamari

Wata ka’idar lissafi da aka mayar zuwa ƙayyadadden jerin lamura, kowanne an tabbatar da shi ta shirin kwamfuta, saboda babu ɗan Adam da zai iya duba su duka.

Tambayar da yake amsawa: Shin za a iya kammala hujja ta na’ura tana duba kowane lamari?

Yana barin: Amincewa tana komawa ga shirin, kayan aiki da hujjar rage lamura.

Yana gudana a: kusan 10⁹ FLOPS kimanta kawai kusan awanni dubu a kan mainframe don na asali; kaɗan sosai yanzu.Tun: 1977 Appel and Haken's proof that every planar map is four-colourable, using computer-checked reducibility. tushe

Lissafin da aka tabbatar

Lissafin da ake yi da iyakoki tabbatattu, don sakamakon lamba ya tabbatar da maganar lissafi, kamar wanzuwar chaotic attractor.

Tambayar da yake amsawa: Shin za a iya tabbatar da amsar da aka lissafa daidai ne, ba kawai mai yiwuwar daidai ba?

Yana barin: Iyakoki na iya fashewa a dogon lokaci, yana iyakance hujjoji ga gajerun matsaloli ko masu kyakkyawar hali.

Yana gudana a: kusan 10⁹ FLOPS kimanta kawai lissafin tazara yana ninka lissafin da ake buƙata da ƙaramin adadi.Tun: 2002 Mai warware ODE mai tsauri na Tucker da matsala ta 14 ta Smale, suna tabbatar da cewa Lorenz attractor yana wanzuwa. tushe

Ƙirga na’urar Turing

Kowane ƙaramin shiri na na’ura mafi ƙanƙanta ana gudanar da shi don ganin wanne yake tsayawa wanne yake gudana har abada, don gano mafi dogon gudu mai tsayawa na kowane girma.

Tambayar da yake amsawa: Har yaushe ƙaramin shiri zai iya aiki kafin ya tsaya?

Yana barin: Rashin yiwuwar yanke hukunci na nufin wasu na’urori ba za a taɓa rarraba su ba, komai tsawon gudanarwarsu.

Yana gudana a: kusan 10¹⁵ FLOPS kimanta kawai biliyoyin injuna, tare da hujjoji ga waɗanda ba sa tsayawa.Tun: 1965 Nazarin kwamfuta na Lin da Rado na matsalolin Turing-machine. tushe

Duba samfuri ta ƙididdiga

Tsarin da ke da hali na bazuwar ana kwaikwayonsa sau da yawa don kiyasin da tabbaci yiwuwar keta wani hali.

Tambayar da yake amsawa: Yaya yiwuwar tsarin bazuwar ya karya ƙa’idar aminci?

Yana barin: Gudanarwa ta ƙididdiga tana ba da yiwuwa tare da matakin tabbaci, ba hujja ba, kuma gazawa ba kasafai ba na buƙatar samfurin muhimmanci.

Yana gudana a: kusan 10⁹ FLOPS kimanta kawai dubbai zuwa miliyoyin aiwatarwa da aka ɗauki samfur.Tun: 2002 Tabbatar da yiwuwa na Younes da Simmons na tsarin abubuwan da suka bambanta ta amfani da acceptance sampling. tushe

Fuzz testing

Ana ciyar da shirin da lambobi masu yawa na shigarwa na bazuwar ko canzawa don nemo waɗanda suke sa shi ya daina aiki, a aikace yana kwaikwayon duniya mai ƙiyayya ko rashin kulawa.

Tambayar da yake amsawa: Wane shigarwa ne zai sa wannan software ta kasa?

Yana barin: Yana gano gazawar da shigarwar bazuwar ke kaiwa kawai, kuma shiri na iya wucewa shekaru yana ɓoye kuskure a bayan wani lamari da ba kasafai ba.

Yana gudana a: kusan 10¹⁴ FLOPS kimanta kawai shekarun na’ura na lokacin CPU don babban tushen lambar.Tun: 1990 Binciken gwaji na Miller, Fredriksen da So na amincin kayan aikin UNIX. tushe

Aiwatarwa ta alama

Ana gudanar da shirin da shigarwar da ba a sani ba da aka rubuta a matsayin alamomi, ana tattara sharuɗɗan kowace hanya, sannan mai warwarewa ya gano ƙimomin da suke ɗaukar kowane reshe.

Tambayar da yake amsawa: Waɗanne shigarwa ne ke sa kowace hanya ta wannan shirin ta yi aiki, kuma wata ta kai ga kwaro?

Yana barin: Adadin hanyoyi yana ƙaruwa ninkin-ninkin tare da girman shirin, don haka manya ana rufe su ne ɓangare kawai.

Yana gudana a: kusan 10¹² FLOPS kimanta kawai sa’o’i na lokacin mai warware matsala ga kowane shiri, suna ƙaruwa sosai da adadin hanyoyi.Tun: 1976 King’s symbolic execution and program testing. tushe

Fassarar abstract

Ana gudanar da shirin a kan saitin ƙimomi masu yiwuwa, kamar tazara, maimakon ƙima ɗaya, don tabbatar da halaye da suke riƙe ga kowace shigarwa.

Tambayar da yake amsawa: Shin wannan shirin zai iya raba da sifili ko ya cika, ga kowace shigarwa?

Yana barin: Kimanta mai aminci yana haifar da ƙararrawar ƙarya, don haka dole mutane su ci gaba da duba kowane gargaɗi.

Yana gudana a: kusan 10¹¹ FLOPS kimanta kawai sa’o’i a kan kwamfutar aiki don babban tushen lambar jirgin sama.Tun: 1977 Cousot and Cousot's abstract interpretation, a unified lattice model for static analysis of programs. tushe

Duba samfuri mai iyaka

Halin ƙira har zuwa takamaiman adadin matakai ana rubuta shi a matsayin dabarar mantiki kuma a miƙa wa mai warware gamsuwa don nemo kowace gajeriyar hanya zuwa kwaro.

Tambayar da yake amsawa: Shin wannan da’ira ko shiri zai iya kai yanayin kuskure cikin matakai da aka bayar?

Yana barin: Ba ya tabbatar da komai fiye da iyakar mataki sai idan wata hujja dabam ta nuna cewa ya isa.

Yana gudana a: kusan 10¹³ FLOPS kimanta kawai sa’o’i a kan uwar garke ga kowane kadara.Tun: 1999 Biere, Cimatti, Clarke and Zhu's symbolic model checking without BDDs. tushe

Gwajin bazuwar bisa halaye (property-based)

Ana bayyana ƙa’ida da ya kamata ta riƙe koyaushe, kwamfuta tana samar da misalai da yawa na bazuwar tana rage kowace kasawa zuwa ƙaramin misali mai karyatawa.

Tambayar da yake amsawa: Shin wannan code yana bin bayanin da aka rubuta masa a kan shigarwa iri-iri?

Yana barin: Lamura na bazuwar ba za su taɓa kaiwa yanayi mai wuya ba, kuma halayen da aka rubuta ba lallai ne su ne masu muhimmanci ba.

Yana gudana a: kusan 10⁹ FLOPS kimanta kawai mintuna a kan laptop don dubban lamura.Tun: 2000 Claessen and Hughes' QuickCheck, a lightweight tool for random testing of Haskell programs. tushe

Tabbatar da hanyar sadarwar jijiyoyi

Masu warware ƙuntatawa suna tabbatar da cewa ga kowace shigarwa a yanki, fitowar neural network tana zama cikin iyaka, maimakon gwada samfura.

Tambayar da yake amsawa: Shin ƙaramin canji ga shigarwa zai iya sa hanyar sadarwa ta ba da amsa mara daidai?

Yana barin: Hujjoji suna yiwuwa ne a kan ƙananan hanyoyin sadarwa kawai, kuma tarin damuwar da za a iya dubawa kunkuntar ne.

Yana gudana a: kusan 10¹³ FLOPS kimanta kawai sa’o’i zuwa kwanaki a kan uwar garke don ƙaramar hanyar sadarwa.Tun: 2017 Reluplex na Katz da abokan aikinsa, mai warware SMT don tabbatar da hanyoyin sadarwar jijiyoyi masu zurfi. tushe

Kwaikwayon tsarin kwamfuta

Layin sarrafa umarni na na’urar sarrafawa da aka ba da shawara, caches da mai hasashen reshe, ana yin samfurinsu umarni bayan umarni, don kiyasin saurin guntu kafin a gina shi.

Tambayar da yake amsawa: Yaya sauri wannan ƙirar processor za ta gudanar da ainihin shirye-shirye, kafin a yanka silicon?

Yana barin: Yana sauƙaƙa isasshen guntu na gaske har silicon na ƙarshe koyaushe ya bambanta kaɗan da samfurin.

Yana gudana a: kusan 10¹¹ FLOPS kimanta kawai gungun kwamfutoci na jami’a yana gudanar da shirye-shiryen benchmark ta samfurinTun: 1990 Zuwa 1990, na’urorin kwaikwayon na’ura mai sarrafawa daidai zagaye don binciken tsari

Kwaikwayon tsarin rarrabawa da yarjejeniya

Kwamfutoci da yawa da aka yi wa samfuri suna aika saƙonni ga juna da jinkiri, ɓacewa da gazawa, don gwada ko algorithm da aka rarraba har yanzu yana yarda a kan amsar da ta dace.

Tambayar da yake amsawa: Shin wannan algorithm har yanzu yana kai ga yarjejeniya daidai lokacin da saƙonni suka ɓace, suka yi jinkiri ko ɗigo suka rushe?

Yana barin: Gazawar da aka shigar su ne waɗanda mai ƙira ya yi tsammani, ba waɗanda ke tasowa ba zato ba tsammani a samarwa ba.

Yana gudana a: kusan 10¹⁰ FLOPS kimanta kawai gungun kwamfutoci yana kwaikwayon ɗaruruwan ɗigon kama-da-waneTun: 1978 Aikin farko na Lamport kan tsari da gazawa a tsarin rarrabawa

Kwaikwayon tsarin ajiya

Diski, faifan ajiya da tsarin fayiloli da aka yi samfuri don yadda suke shimfiɗa bayanai, kasawa da murmurewa, don gwada ƙirar ajiya kafin a sayi a cika ainihin faifai.

Tambayar da yake amsawa: Yaya wannan tsarin ajiya ke aiki da tsira daga gazawa, a mizanin da ya yi tsada a gwada da farko a gaske?

Yana barin: Ainihin faifai suna gazawa ta hanyoyi masu ruɗani da alaƙa fiye da adadin gazawar bazuwar na samfurin.

Yana gudana a: kusan 10¹⁰ FLOPS kimanta kawai kwamfutar aiki zuwa ƙaramin gungun kwamfutoci suna yin samfurin jerin ajiyaTun: 1988 Zuwa 1988, samfuran kwaikwayo na amincin jerin diski

Kwaikwayon mai tsara tsarin aiki

Rafin ayyukan lissafi da ake yin samfurin zuwansu da gasar neman na’ura mai sarrafawa, ana gudanar da shi a kan ƙa’idojin tsarawa daban-daban don ganin wanne ne mafi adalci ko sauri.

Tambayar da yake amsawa: Wace hanyar tsara jerin ayyuka ke yin aiki mafi yawa, ko ta fi adalci ga kowane aiki?

Yana barin: Ayyukan wucin gadi ba kasafai suke dacewa da gaurayen ayyuka marasa tsari da ainihin na’ura ke fuskanta ba.

Yana gudana a: kusan 10⁹ FLOPS kimanta kawai yana gudana a kan laptop ko kwamfutar aiki cikin daƙiƙu zuwa mintunaTun: 1968 Zuwa 1968, nazarin kwaikwayo na manufofin tsara na’urar sarrafawa

Bincike na ingantawa na compiler da shiri

Ana gwada ƙananan bambance-bambance masu yawa na code ana aunawa, ana neman mafi sauri ko mafi gajarta da har yanzu yake yin aikin iri ɗaya.

Tambayar da yake amsawa: Daga cikin dukkan hanyoyin da ke da ma’ana iri ɗaya na rubuta wannan ƙaramin yanki na code, wace ce mafi sauri a gaske?

Yana barin: Shirye-shiryen da aka samu wani lokaci suna da ban mamaki sosai har babu bayani na dalilin da ya sa suke aiki.

Yana gudana a: kusan 10¹⁰ FLOPS kimanta kawai gungun kwamfutoci yana bincike a cikin babban fili na bambance-bambancen codeTun: 2006 Zuwa 2006, binciken superoptimisation a kan gajerun jerin umarni

Gwajin aunawa na aikin algorithm

Ana gudanar da algorithm sau dubbai a kan shigarwar da aka samar bazuwar ko ta duniya ta gaske da girmansu yake ƙaruwa, ana auna yadda lokacin gudunsa yake girma maimakon tabbatar da shi a takarda.

Tambayar da yake amsawa: Yaya lokacin aikin wannan algorithm ke ƙaruwa a gaske, a kan bayanan da zai gani a zahiri?

Yana barin: Yanayi mafi muni da ba ya cikin shigarwar gwaji yana kasancewa ba a gano shi ba har sai ya faru.

Yana gudana a: kusan 10⁹ FLOPS kimanta kawai yana gudana a kwamfutar aiki a kan shigarwar gwaji da yawa da aka samarTun: 1970 Zuwa 1970, gwajin aunawa na tsari na lokutan gudun algorithm

Aiwatar da shirin samfurin harshe

Samfurin harshe yana rubuta yanayin tsakiya mataki-mataki yayin da yake bin abin da shirin zai lissafa.

Tambayar da yake amsawa: Shin samfurin harshe zai iya kwaikwayon gudanar da code?

Yana barin: Ba a tabbatar da cewa fitarwa daidai ne ba, kuma dogayen shirye-shirye suna gazawa.

Yana gudana a: kusan 10¹⁴ FLOPS kimanta kawai Hasashe ga kowace tambayaTun: 2021 Show your work: scratchpads for intermediate computation with language models (2021) tushe

Kwaikwayon yarjejeniyar blockchain

Hanyar sadarwa ta ɗigo da ke samarwa da raba tubalan a jinkiri, don gwada yadda girman tubala, lokaci da maharan suke shafar tsaro da ƙarfin sarrafawa.

Tambayar da yake amsawa: Yaya tsaro da saurin blockchain a ƙarƙashin jinkirin hanyar sadarwa da hari?

Yana barin: Ainihin ɗabi’ar ɗigo da tsarin hanyoyin sadarwa ana auna su ne a ɓangare kawai.

Yana gudana a: kusan 10⁸ FLOPS kimanta kawai gudun dubban ɗigo da abubuwan da suke faruwa ke tuƙawa.Tun: 2016 Gervais and colleagues' security and performance analysis of proof-of-work blockchains with a simulator. tushe

Kwaikwayon al’amura daban-daban masu tafiya a lokaci guda

Ana raba kwaikwayon abubuwan da suke faruwa a lokaci a kan na’urorin sarrafawa da yawa kowanne yana ci gaba da agogonsa yana komawa baya idan ɗaya ya iso a makare.

Tambayar da yake amsawa: Yaya babban kwaikwayo mai tafiya bisa abubuwan da ke faruwa, kamar hanyar sadarwa ko fagen yaƙi, zai iya gudana da sauri a kan kwamfutoci da yawa?

Yana barin: Komawa baya na iya biyo juna a jere, kuma saurin ƙaruwa yana dogara sosai da yadda al’amuran suke da haɗin kai.

Yana gudana a: kusan 10¹⁴ FLOPS kimanta kawai sa’o’i a kan babbar kwamfuta don biliyoyin al’amura.Tun: 1985 Lokacin kama-da-wane na Jefferson, tsarin Time Warp don daidaitawa mai fata. tushe

Kwaikwayon tsarin na’urar sarrafa hotuna

Ana yin samfurin cores, warps da ƙwaƙwalwar na’urar sarrafa hotuna zagaye bayan zagaye, tana gudanar da shirye-shirye na gaske don tantance ƙira kafin gini.

Tambayar da yake amsawa: Yaya canjin ƙira zai shafi saurin shirye-shirye masu aiki a lokaci guda a kan guntun hotuna?

Yana barin: Bayanan ainihin guntu sirri ne ko ba a sani ba, don haka samfurin yana dacewa da lambobin ƙirar da ake da su kimanta kawai.

Yana gudana a: kusan 10¹² FLOPS kimanta kawai sa’o’i zuwa kwanaki na lokacin mai masauki ga kowane daƙiƙa na aiwatarwar da aka yi wa kwaikwayo.Tun: 2009 Bakhoda and colleagues' analysis of CUDA workloads using a detailed GPU simulator. tushe

Kwaikwayon tsari da aka hanzarta ta FPGA

Ana ɗora tsarin guntu a kan da’irori da yawa masu iya sake tsarawa waɗanda suke gudanar da shi daidai kowane zagaye da saurin megahertz, suna kwaikwayon sabobi gabaɗaya da hanyoyin sadarwarsu.

Tambayar da yake amsawa: Yaya wannan processor da gungunsa za su ɗabi’anta wajen aiwatar da ainihin software, kafin a ƙera shi?

Yana barin: Yana da jinkiri fiye da ainihin guntu, kuma ƙira da ba ta dace da da’irori ba ba za a iya gudanar da ita ba.

Yana gudana a: kusan 10¹⁵ FLOPS kimanta kawai kwanaki a gajimaren ɗaruruwan da’irori masu sake tsarawa.Tun: 2018 FireSim na Karandikar da abokan aikinsa, kwaikwayon tsarin da aka faɗaɗa mai daidaito a kowane zagaye a girgijen jama’a, wanda FPGA ke gaggautawa. tushe

Kwaikwayon cikakken tsari

Cikakkiyar kwamfuta, mai na’urorin sarrafawa, ƙwaƙwalwa, diski da katin hanyar sadarwa, ana kwaikwayo ta da kyau har ta tada tsarin aiki da ba a canza ba ta gudanar da shirye-shiryensa.

Tambayar da yake amsawa: Yaya ainihin software ke ɗabi’a a na’urar da ba ta wanzu tukuna, ko wadda za a iya tsayarwa a sake kunnawa yadda ake so?

Yana barin: Ana ƙiyasta lokaci don sauri, don haka ba zai iya ba da ainihin aiki ba, halin aiki kawai.

Yana gudana a: kusan 10¹¹ FLOPS kimanta kawai kusan lokaci na gaske a kan uwar garke ga kowace na’urar kwaikwayo.Tun: 2002 Simics na Magnusson da abokan aikinsa, dandalin kwaikwayon cikakken tsari. tushe

Kwaikwayon hanyar sadarwa mai sauƙi

Dozin ko ɗaruruwan masu masauki da switches na kama-da-wane suna gudanar da ainihin software na hanyar sadarwa a kwamfutar tafi-da-gidanka ɗaya, da aka haɗa ta igiyoyi da aka kwaikwaya masu saurin da jinkiri da aka saita.

Tambayar da yake amsawa: Shin wannan shirin sarrafa hanyar sadarwa zai yi aiki a dukan topology kafin a tura shi?

Yana barin: Mai sarrafa mai masaukin kansa ana raba shi tsakanin dukan nodes na kama-da-wane, don haka haɗin sauri suna raguwa.

Yana gudana a: kusan 10¹⁰ FLOPS kimanta kawai lokaci na gaske a kan kwamfutar aiki ɗaya.Tun: 2010 Lantz, Heller and McKeown’s ‘A network in a laptop’, rapid prototyping for software-defined networks. tushe

Simulated annealing

Kwamfuta tana sanyaya samfurin atom ko ƙira a hankali, tana karɓar tsare-tsare marasa kyau a wasu lokuta, don nemo mafita mai kyau ga matsalar ingantawa mai wuya.

Tambayar da yake amsawa: Menene tsari ko jadawali kusan mafi kyau tsakanin yiwuwar da suka kai adadin taurari?

Yana barin: Ba ya ba da tabbacin mafi kyawun amsa, kuma sakamakon ya dogara da jadawalin sanyaya.

Yana gudana a: kusan 10¹² FLOPS kimanta kawai sa’o’i a kan kwamfutar aiki don sanya guntu.Tun: 1983 Kirkpatrick, Gelatt and Vecchi’s optimisation by simulated annealing. tushe

Approximate Bayesian computation

Ana gudanar da na’urar kwaikwayo da ƙimomin sigogi na gwaji da yawa, kuma waɗanda suke samar da bayanai kusa da bayanan da aka lura ana riƙe su, don ba da hoton waɗanne ƙimomi ne masu yiwuwa.

Tambayar da yake amsawa: Waɗanne saitunan samfuri mai sarƙaƙiya za su iya samar da bayanan da muke lura da su?

Yana barin: Sakamakon ya dogara da waɗanne taƙaitattun bayanai ake amfani da su da kusancin daidaito da ake buƙata don a ƙirga.

Yana gudana a: kusan 10¹³ FLOPS kimanta kawai miliyoyin gudanarwar na’urar kwaikwayo a kan gungun kwamfutoci.Tun: 1997 Tavaré da abokan aiki sun ƙiyasta lokutan haɗuwa daga bayanan jerin DNA ta amfani da kwaikwayo. tushe