Buliyani ajebura. ajebura maganizo. Zochitika za mfundo masamu

Masiku ano ife akugwiritsa ntchito zosiyanasiyana makina ndi zipangizo. Ndipo osati pamene m'pofunika kugwiritsa ntchito mphamvu kwenikweni zoposa: kusuntha katundu kulera kuti ponyamuka, kukumba yaitali ndipo kwambiri ngalande, etc. Cars lero kusonkhanitsa maloboti, chakudya yophika Multivarki ndi kuwerengetsera pulayimale masamu kubala toŵerengera ... More ndipo nthawi zambiri timamva mau oti "Buliyani ajebura". Mwina nthawi yafika kudziwa udindo wa anthu polenga maloboti ndi makina mphamvu zothetsera osati masamu, komanso mavuto zomveka.

mfundo

Mu mfundo Greek - anatilamula dongosolo la lingaliro kuti amalenga ubale pakati pa zinthu linaperekedwa ndi limakupatsani kuti inferences zochokera maganizo ndi amanenera. Nthawi zambiri, ife kufunsana: "M'pake kuti" The reply akutsimikiza mfundo zathu kapena amazitsutsa sitima wa ganizo. Koma ndondomeko silitiletsa kumeneko: tipitirize kulankhula.

Nthawi zina chiwerengero cha zinthu (athandizira) ndi kwakukulu, ndi Kubverana kwawo ndi chisokonezo ndi zovuta kuti ubongo wa munthu sangathe "kupukusa" zonse mwakamodzi. Mungafunike mwezi kuposa lina (sabata, chaka) kwa kumvetsa zimene zikuchitika. Koma moyo wamakono sapereka ife intervals nthawi awa kusankha. Ndipo ife amachita pogwiritsa ntchito kompyuta. Ndipo izo ziri pano kuti pali ajebura ndi mfundo zomveka, ndi malamulo ake ndi katundu. Pambuyo otsitsira onse deta pachiyambi, tisalole kompyuta kuzindikira ubale onse, kuthetsa kusemphana ndi kupeza njira zogwira mtima.

Masamu ndi mfundo zomveka

Wotchuka Gotfrid Vilgelm Leybnits kukonza maganizo "mfundo masamu" imene ntchito kunali kovuta kumvetsa kokha yaing'ono bwalo la masikolala. Chidwi kwambiri ndi malangizo sanazichite, ndi pakati pa XIX m'ma maganizo masamu amadziwika ndi ochepa.

The chidwi chachikulu asayansi wachititsa pachinthu chimene England Dzhordzh Buli ananena cholinga chake chofuna kukhazikitsa nthambi ya masamu, alibe alibiretu kugwiritsa ntchito. Monga tikudziwa m'mbiri, pa nthawi imeneyi mwakhama osauka mafakitale, ife anayamba mitundu yonse ya makina wothandiza, T. E. atulukira onse sayansi anali lathu othandiza.

Poganizira, tinganene kuti Buliyani ajebura - kwambiri ntchito mu dziko lero gawo la masamu. Choncho zifukwa zanu Buhl anataya.

Dzhordzh Buli

Umunthu wa wolemba ayenera kulandira chisamaliro chapadera. Anapatsa kuti pa anthu akale anakulira pamaso pathu, komabe tisaiwale kuti mu zaka 16 wa Yohane. Buhl anaphunzitsa pa sukulu mudzi, ndipo anatsegula zaka 20 sukulu lake Lincoln. Masamu mwangwiro zinenero zisanu zakunja, komanso panthawi yake yopuma, ankawerenga ntchito za Newton ndi Lagrange. Ndipo zonse izi - pa mwana ntchito wamba ayi!

Mu 1839, Buhl anatumiza Mwana wake woyamba zokhudza sayansi mu Cambridge masamu Journal. Scientist anatembenuka ndi zaka 24. ntchito Boole ali ndi chidwi a Royal Society, mu 1844 anapatsidwa Mendulo chopereka ake chitukuko cha kusanthula masamu. A ochepa lofalitsidwa mapepala imene zinthu za mfundo masamu, masamu analola achinyamata kutenga malo a pulofesa mu College of Nkhata Bay County anatchula. Kumbukirani kuti pa maphunziro Boole kwambiri sanali.

lingaliro

Mfundo Buliyani ajebura lophweka. Pali mawu (zomveka mawu), kuchokera amazionera a masamu, akhoza kumatanthauza mu mawu awiri: "oona" kapena "wabodza". Mwachitsanzo, mitengo mu kasupe pachimake - choonadi, yotentha, chisanu - bodza. Kukongola masamu kuti si mmene zinayenera ntchito manambala yekha. Pakuti ziweruzo ajebura ndithu woyenera mawu aliwonse ndi tanthauzo lapadera.

Choncho, ajebura maganizo angagwiritsidwe ntchito kwenikweni kulikonse: mu ndandanda ndi kulemba malangizo, kusanthula mfundo zotsutsana za zochitika ndi mtima wa ndondomeko ya zochita. Chinthu chofunika kwambiri - kuzindikira kuti zilibe kanthu kuti tingadziwe choonadi kapena Bodza la mawu. Anthu amenewa "mmene" ndi "chifukwa" muyenera kunyalanyaza. Kodi chofunika chokha mawu Ndipotu: choonadi ndi bodza.

Kumene, mapulogalamu ntchito yofunika kwambiri ya ajebura maganizo amene ali ndi zizindikiro zoyenera. Ndipo kuphunzira - kumatanthauza kuphunzira chinenero chakunja. Palibe chosatheka.

mfundo zikuluzikulu ndi matanthauzo

Popanda kupita mozama, timachita terminology. Choncho, Buliyani ajebura kumapereka lingaliro:

• mawu;
• zomveka ntchito;
• Nchito ndi malamulo.

Ziganizo - akuti aliyense inde kuti angathe kutanthauziridwa awiri ofunika. Zinalembedwa monga manambala (5> 3) kapena kukonza mawu bwino (njovu - ndi nyama yaikulu). Pankhaniyi, mawu akuti "khosi giraffe si" ali ndi ufulu kulibe, kokha Buliyani ajebura tanthauzo monga "bodza."

mawu onse ayenera kukhala lomveka, koma akhale maziko kapena pawiri. ntchito Recent zomveka mtolo. E. Mu ajebura mawu maweruzo pawiri popangidwa ndi Kuwonjezera ntchito pulayimale maganizo.

Buliyani ntchito ajebura

Ife kale kumbukirani kuti ntchito mu ajebura ziweruzo - zomveka. Monga ajebura a manambala ntchito ntchito masamu kuwonjezera, kuchotsera, kapena kuyerekeza manambala, masamu zinthu mfundo kulola kuti mfundo zovuta, kukana kapena kuwerengera chifukwa komaliza.

Zomveka ntchito kwa formalization ndi kuphweka anafotokoza mfundo, bwino kwa ife mu masamu. Katundu wa maikwezhoni Buliyani ajebura n'zotheka kuti alembe ndi kuwerengera osadziwika. ntchito Kukamba zambiri wolembedwa ndi tebulo choonadi. zanyengo chimatanthauza mizati ndi kompyuta ntchito imene imagwiridwa pa iwo, ndi mizere amasonyeza chifukwa cha kuwerengetsera.

Kuweta mfundo ya kanthu

Ambiri mu Buliyani ntchito ajebura ndi negation (OSATI), ndi zomveka ndi OR. Choncho n'zotheka kufotokoza pafupifupi masitepe onse ziweruzo ajebura. Tinkaphunzira mwatsatanetsatane lililonse ntchito ndi atatu.

The negation (osati) umagwiritsidwa ndi chinthu chimodzi chokha (operand). Choncho, opaleshoni amatchedwa negation unary. Kulemba mfundo "osati A" ntchito zizindikiro chotero: ¬A, kapena !. Mu mawonekedwe tabular izo zikuwoneka ngati izi:

Ntchito kukana ankaikira mawu amenewa: ngati ndi zoona, ndiye A - ndi zabodza. Mwachitsanzo, mwezi chimazungulira Lapansi - choonadi; Earth chimazungulira mwezi - bodza.

Kukamba chulutsa ndi Kuwonjezera

Kukamba ndi ntchito amatchedwa molumikizana. Kodi zikutanthauza chiyani? Choyamba, kuti ingagwiritsidwe ntchito operands awiri, mwachitsanzo, ine - .. bayinare ntchito. Kachiwiri, si mu nkhani ya choonadi cha operands onse (onse A ndi B) ndi woona ndi mawu yokha. Mwambi, "Kuleza ndi chidwi" akusonyeza kuti zinthu ziwiri zokha zingathandize munthu kupirira mavuto.

zizindikiro ntchito kujambula: A∧B, A⋅B kapena A && B.

Molumikizana ndi ofanana chulutsa mu masamu. Nthawi zina ndi kunena - zomveka chulutsa. Ngati inu kuchulukitsa zinthu za mizere pa tebulo, ife chifukwa ofanana ya kulingalira.

Disjunction ndi zomveka OR ntchito. Nzowona ngati chimodzi mwa ziganizo ziri zoona (kapena A kapena B). Kwalembedwa monga izi: A∨B, A + B kapena A || B. choonadi tebulo ntchito ndi awa:

Disjunction ofanana Kuwonjezera masamu. zomveka Kuwonjezera ntchito ali chinthu chimodzi chokha: 1 + 1 = 1. Koma tiyenera kukumbukira kuti mu mtundu digito okha kuti mfundo masamu 0 ndi 1 (kumene 1 - choonadi, 0 - wabodza). Mwachitsanzo, mawu "mu nyumbayi mukhoza kuona mwaluso kapena kupeza amakhalidwe abwino" kumatanthauza mukhoza kuona mwaluso ndi n'zotheka kukumana ndi munthu chidwi. Pa nthawi yomweyo, si kulamulira zingatheke kukwaniritsidwa munthawi yomweyo zochitika zonse.

Nchito ndi malamulo

Kotero, ife tikudziwa kale zimene zomveka opareshoni ntchito Buliyani ajebura. Nchito pofotokoza katundu zonse zam'mwamba maganizo masamu, ndi kulola ife kuti musinthe mawu ovuta pawiri. Kwambiri bwino ndi losavuta zikuwoneka kukana chuma cha ntchito ofanana nawo. Ndi ena ofanana akuoneka XOR, tionetsa ndi pazikhala kufanana. Monga tawerenga okha ndi ntchito zazikulu, kenako chuma ndi kokha amawaona.

Associativity zikusonyeza kuti mawu monga "onse A ndi B, ndi B 'zinayendera ndandanda wa operands si kanthu. Ndondomeko kwalembedwa motere:

(A∧B) ∧V = A∧ (B∧V) = A∧B∧V,

(A∨B) ∨V = A∨ (B∨V) = A∨B∨V.

Monga mukuonera, ichi silili molumikizana koma disjunction.

Commutativity ananena kuti chifukwa cha akamaimba kapena disjunction sikudalira zimene item ankaona poyamba paja:

A∧B = B∧A; A∨B = B∨A.

Distributivity amalola kuulula m'mabokosi mawu ovuta zomveka. Malamulo ofanana ndi kutsegula zolemba mu chulutsa ndi Kuwonjezera mu ajebura:

A∧ (B∨V) = A∧B∨A∧V; A∨B∧V = (A∨B) ∧ (A∨V).

katundu Unit ndi zikande, amene akhoza kukhala mmodzi wa operands komanso ofanana chulutsa algebraic ndi ziro kapena wina, ndi Kuwonjezera amodzi:

A∧0 = 0, A∧1 = A; A∨0 = A, A∨1 = 1.

Idempotency limatiuza kuti ngati ndi awiri operands ofanana chifukwa cha ntchito ali yemweyo, mungathe "kutaya" ndi muyeso kusokoneza maganizo operands. Ndipo molumikizana ndi disjunction ntchito ndi idempotent.

B∧B = B; B∨B = B.

Kupeza komanso amatilola wosalira anthu aone kuti pali. Mayamwidwe limanena kuti mawu umagwiritsidwa ntchito operand wina, opaleshoni ina ndi chinthu chomwecho zotsatira za operand ndi kungolandira ntchito.

A∧B∨B = B; (A∨B) ∧B = B.

ndondomeko ya ntchito

The ndondomeko ya ntchito ndi zofunika kwambiri. Kwenikweni, ngati masamu ameneŵa, pali patsogolo ntchito imene amagwiritsa ajebura Buliyani. Mitunduyi akhoza wosalira nkhani yekha tanthauzo la ntchito ya. Lolemekezeka la lofunika kwambiri kwa negligible timapeza akuyambira zotsatirazi:

1. Kukana.

2. Cholumikizira.

3. disjunction, XOR.

4. tionetsa, pazikhala kufanana.

Monga mukuonera, koma negation wa molumikizana ndi mulibe patsogolo ofanana. A patsogolo kwa disjunction ndi XOR ofanana, komanso zinthu za tionetsa ndi pazikhala kufanana.

Nchito ya tionetsa ndi pazikhala kufanana

Monga tanena kale, kuwonjezera zofunika ntchito zomveka, masamu logic ndi chiphunzitso cha ma aligorivimu ntchito ofanana nawo. Ndi nthawi zambiri asadafe ndi pazikhala kufanana.

Asadafe kapena zomveka zotsatira - mawu awa, amene zochita ndi chikhalidwe, ndi zina - zotsatira za kukhazikitsa. M'mawu ena, maganizo ichi ndi malingaliro a "ngati ... ndiye". "Pambuyo chakudya pakubwera aweruze." E. Pakuti galimoto kuti omangika pa phiri sled. Ngati palibe kufunitsitsa kusamukira kutsika pa phiri, ndiyeno kokani sled Sikuti. Kwalembedwa kuti: A → B kapena A⇒B.

Pazikhala kufanana zikutanthauza kuti zotsatira ukonde kumachitika kokha pamene operands onse ali woona. Mwachitsanzo, usiku agonjera ku tsiku ndiye (kenako okha), pamene dzuwa limatuluka pa kaja. M'chilankhulo cha mfundo masamu mawu awa analembedwa A≡B, A⇔B, A == B.

malamulo ena a ajebura Buliyani

Ajebura chiweruzo zingachitike ndipo ambiri asayansi chidwi zopanga malamulo atsopano. Wotchuka amaonedwa postulates Scottish masamu O. De Morgan. Anaona ndipo anapereka tanthauzo la katundu monga negation pafupi, Kuwonjezera ndi iwiri negative.

Close kukana zikusonyeza kuti pamaso pa zolemba Sitingatsutse: ayi (A kapena B) = osati A kapena B. OSATI

Pamene operand ndi adakana, mosasamala mtengo wake, kunena za Kuwonjezera:

B∧¬B = 0; B∨¬B = 1.

Ndipo potsiriza, negation iwiri yokha compensates. Ie nkuti negation operand Mwamsanga kapena amakhalabe chimodzi chokha.

Mmene angathetsere mayesero

Zomveka zikutanthauza zosabvuta anakonzeratu maikwezhoni. Monga mu Bodza ajebura, m'pofunika maximally atsogolere chikhalidwe choyamba (kuchotsa ntchito yovuta athandizira, ndi iwo), ndiye kuyamba kufunafuna yankho lolondola.

Kodi kuchita wosalira zambiri? Sinthani opangidwa kuchokera zonse mu ntchito yosavuta. Ndiye kuvumbulutsa zachisinsi m'mabokosi onse (kapena mosinthanitsa, kuti m'mabokosi kuchepetsa mchitidwe uwu). Chotsatira ayenera kugwiritsa ntchito Buliyani ajebura katundu kuchita (katundu mayamwidwe ziro ndi chimodzi, ndipo T.).

Pomaliza pake, aone kuti pali ayenera zigwirizana mlingo wa unknowns, pamodzi ndi ntchito yosavuta. Chophweka njira kuyang'ana njira ngati inu kupanga ambiri zoipa pafupi. Ndiye yankho adzakhala tumphuka ngati palokha.