Introduction to Theoretical Computer Science
The contents of this book are self-sufficient in the sense that no preliminary knowledge other than elementary set theory is needed and there are no complicated mathematical theorems in the book. A must for those entering the field.
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CHAPTERS ALGEBRAIC FUNCTIONS AND ALGEBRAIC FUNCTIONALS
THE LEAST FIXPOINT THEORY
CHAPTERS RECURSIVE FUNCTIONS
COMPUTABLE AND LISTABLE SETS
abstract computer algebraic form algebraic function atom axiom basic functions binary tree C-F-expression coding function completes the proof computable total function COND CONST constant functional Corollary decision function domain function empty function example exists a computable exists a total fixpoint of 9 formal solution func function g function is called given identity functional input isomorphic least fixpoint least upper bound Lemma length Let g Let n>0 listable set listp mathematical monotonic sequence n-ary functions natural number notation obtain one-one mapping otherwise p,ci pair list primitive recursive functions Problem procedure property Q recursive definition recursive domain regarded S-expression sequence of functions sequential computer set equation set is listable Show smallest solution stack structural induction structure-recursive definition subset termination function Theoretical Computer Science theory tion total computable function Turing machines unary computable undefined unique fixed point word