翻訳と辞書 Words near each other ・ Grzanka, Masovian Voivodeship ・ Grzawa ・ Grzbiet Lasocki ・ Grzebielin ・ Grzebienie ・ Grzebienie-Kolonia ・ Grzebieniec, Pomeranian Voivodeship ・ Grzebienisko ・ Grzebień, Łódź Voivodeship ・ Grzeboszowice ・ Grzebowilk, Gmina Siennica ・ Grzebsk ・ Grzechotki ・ Grzechynia ・ Grzeczna Panna ・ Grzegorczyk hierarchy ・ Grzegorz Adam Urbanowski ・ Grzegorz Antoni Ogiński ・ Grzegorz Arłukowicz ・ Grzegorz Baran ・ Grzegorz Bargiel ・ Grzegorz Bartczak ・ Grzegorz Bociek ・ Grzegorz Bolesław Frąckowiak ・ Grzegorz Bonin ・ Grzegorz Branicki ・ Grzegorz Braun ・ Grzegorz Bronowicki ・ Grzegorz Błaszczyk ・ Grzegorz Ciechowski Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Grzegorczyk hierarchy ： ウィキペディア英語版 Grzegorczyk hierarchy The Grzegorczyk hierarchy (pronounced: ), named after the Polish logician Andrzej Grzegorczyk, is a hierarchy of functions used in computability theory (Wagner and Wechsung 1986:43). Every function in the Grzegorczyk hierarchy is a primitive recursive function, and every primitive recursive function appears in the hierarchy at some level. The hierarchy deals with the rate at which the values of the functions grow; intuitively, functions in lower level of the hierarchy grow slower than functions in the higher levels. == Definition == First we introduce an infinite set of functions, denoted ''Ei'' for some natural number ''i''. We define $E\_0(x,y)=x+y$ and $E\_1(x)=x^2+2$. I.e., ''E0'' is the addition function, and ''E1'' is a unary function which squares its argument and adds two. Then, for each ''n'' greater than 1, we define $E\_n(x)=E^\_(2)$, i.e. the ''x''-th iterate of $E\_$ evaluated at 2. From these functions we define the Grzegorczyk hierarchy. $\backslash mathcal^n$, the ''n''-th set in the hierarchy, contains the following functions: # ''Ek'' for ''k'' < ''n'' # the zero function (''Z''(''x'') = 0); # the successor function (''S''(''x'') = ''x'' + 1); # the projection functions ($p\_i^m(t\_1,\; t\_2,\; \backslash dots,\; t\_m)\; =\; t\_i$); # the (generalized) compositions of functions in the set (if ''h'', ''g''1, ''g''2, ... and ''g''m are in $\backslash mathcal^n$, then $f(\backslash bar)\; =\; h(g\_1(\backslash bar),\; g\_2(\backslash bar),\; \backslash dots,\; g\_m(\backslash bar))$ is as well)〔; and # the results of limited (primitive) recursion applied to functions in the set, (if ''g'', ''h'' and ''j'' are in $\backslash mathcal^n$ and $f(t,\; \backslash bar)\; \backslash leq\; j(t,\; \backslash bar)$ for all ''t'' and $\backslash bar$, and further $f(0,\; \backslash bar)\; =\; g(\backslash bar)$ and $f(t+1,\; \backslash bar)\; =\; h(t,\backslash bar,f(t,\backslash bar))$, then ''f'' is in $\backslash mathcal^n$ as well)〔 In other words, $\backslash mathcal^n$ is the closure of set $B\_n\; =\; \backslash$ with respect to function composition and limited recursion (as defined above). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Grzegorczyk hierarchy」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.