View source for Universal algorithm

''for a given class of algorithms''

An [[Algorithm|algorithm]] depending on an input parameter <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095640/u0956401.png" /> which for different admissible values of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095640/u0956402.png" /> models the work of any algorithm of a given class. Different formalizations of computability correspond to different refinements of the notion of a universal algorithm: for recursive functions (cf. [[Recursive function|Recursive function]]) it is the universal partial recursive function (cf. [[Universal function|Universal function]]), for Turing machines it is the universal [[Turing machine|Turing machine]], for normal algorithms it is the [[Universal normal algorithm|universal normal algorithm]], etc.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  V.A. Uspenskii,   "Leçons sur les fonctions calculables" , Hermann  (1966)  (Translated from Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  A.I. Mal'tsev,   "Algorithms and recursive functions" , Wolters-Noordhoff  (1970)  (Translated from Russian)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  H. Rogers jr.,   "Theory of recursive functions and effective computability" , McGraw-Hill  (1967)  pp. 164–165</TD></TR></table>