toshkent - 2011
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B ul funksiyalar . A hamiyati va ahamiyatsiz o’zgaruvchilar . B ul funksiyalarining formulalar orqali amalga oshirilishi. T eng kuchli formulalar. Toshkent - 2011. Ma’ruzachi : Mamatov A. Reja :. Bul funksiyalar, ularning usullari. Bul funksiyalari soni. Bul algebrasi. - PowerPoint PPT PresentationTRANSCRIPT
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BBul funksiyalarul funksiyalar..AAhamiyati va ahamiyatsiz o’zgaruvchilarhamiyati va ahamiyatsiz o’zgaruvchilar..
BBul funksiyalarining formulalar orqali ul funksiyalarining formulalar orqali amalga oshirilishi. amalga oshirilishi.
TTeng kuchli formulalareng kuchli formulalar
Toshkent-2011
Ma’ruzachi: Mamatov A
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Reja:Reja:
1. Bul funksiyalar, ularning usullari. Bul funksiyalari soni. Bul algebrasi.
2. Ahamiyatli va ahamiyatsiz o’zgaruvchilar
3. Bul funksiyalarning formulalar orqali amalga oshirilishi
4. Ikkilamchi funksiyalar. Ikkilamchi prinsipi
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1-savolga javob:1-savolga javob:
Ma’lumki, mantiqiy amallar mulohazalar algebrasi nuqtai nazardan chinlik jadvallari bilan to’liq xarakterlanadi. Agarda funskiyaning jadval shaklda berilishini esga olsak, u vaqtda mulohazalar algebrasida ham funksiya tushunchasini aniqlashimiz mumkin.
Ta’rif. x1, x2, … ,xn mulohazalar algerbasining x1, x2, … ,xnargumentli f(x1, x2, … ,xn) funksiyasi deb nol va bir qiymat qabul funksiyaga aytiladi va uning x1, x2, … ,xnargumentlari ham nol va bir qiymatlar qabul qilinadi.
Ta’rif. F:{0,1}n -> {o,1} funksiya mantiqiy algebraning funksiyasi yoki Bul funksiyasi to’plami Pn orqali belgilaymiz, ya’ni
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Bir o’zgaruvchili funksiyalar 4 ta bo’lib, ular quyidagilar:
1.f0(x)=0 – aynan nolga teng funksiya yoki aynan yolg’on funksiya
2.f1(x)=x – aynan funksiya
3. - inkor funksiya4.f3(x)=1 – aynan birga teng funksiya yoki
aynan chin funksiya
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2-savolga javob:2-savolga javob:Ta’rif. Agar o’zgaruvchining shunday a1, a 2,...,ai-
1,ai,...,an qiymatlar majmuasi mavjud bo’lib, f(a1, a 2,...,ai-1,1,ai,...,an)=f(a1, a 2,...,ai-1,0,ai,...,an) munosabat bajarilsa, u vaqtda xi o’zgaruvchiga f(x1,x2,...,xn) funksiyaning nomuhim (sohta) o’zgaruvchisi, agar f(a1, a 2,...,ai-1,1,ai,...,an)≠f(a1, a 2,...,ai-1,0,ai,...,an) munosabat bajarilsa, u vaqtda xi o’zgaruvchiga f(x1,x2,...,xn) funksiyaning muhim (sohta emas) o’zgaruvchisi deb ataladi.
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3-savolga javob3-savolga javobФ={f1,f2,...,fn} Bul funksiyalar to’plami berilgan bo’lsin.Ta’rifФ to’plam ustida aniqlangan formula deb, F(Ф)=f(t1,t2,...,tn) ifodaga aytiladi, bu yerda fϵФ va tiФ ustidagi yoki o’zgaruvchi, yoki formula.Ф to’plam bazis, f tashqi funksiya, ti lar esa qism formulalar deyiladi. Har qanday F formulaga bir qiymatli biror f Bul funksiyasi mos keladi. Bu holda F formula f funksiyani ifodalaydi deyiladi va f=funcF ko’rinishida belgilanadi.Bazis funksiyalarini chinlik jadvalini bilgan holda, bu formula ifodalaydigan funksiyaning chinlik jadvalini hisoblashimiz mumkin.
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4-savolga javob:4-savolga javob:
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