Theories of Computability
Cambridge University Press, 28.05.1997 - 251 Seiten
Broad in coverage, mathematically sophisticated, and up to date, this book provides an introduction to theories of computability. It treats not only "the" theory of computability (the theory created by Alan Turing and others in the 1930s), but also a variety of other theories (of Boolean functions, automata and formal languages) as theories of computability. These are addressed from the classical perspective of their generation by grammars and from the more modern perspective as rational cones. The treatment of the classical theory of computable functions and relations takes the form of a tour through basic recursive function theory, starting with an axiomatic foundation and developing the essential methods in order to survey the most memorable results of the field. This authoritative account, written by one of the leading lights of the subject, will be required reading for graduate students and researchers in theoretical computer science and mathematics.
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0-preserving algebraic arguments automata belongs Boolean functions called clone closure conditions closure system co-clone Compl(A complement complete comprises construct contains context-free grammar context-free languages contradiction corresponding Cyl(A define definition denote deterministic automaton dyadic element empty word encoding equivalence classes exists family of languages finite number finite set function g grammar G homomorphism implies infinite recursively enumerable Lang(G Lemma letters logical expression machine monadic monadic recursive function monoid n-adic natural numbers non-deterministic finite automaton obtained occurrences one-to-one operations pair partial function partial recursive function primitive recursion productions programs proof Proposition prove rational cone real numbers recognizable language Recursion Theorem recursive isomorphism recursive permutation recursively enumerable sets reflexive class regular expression regular languages respectively result semigroup sequence smallest stage Suppose symbol Syn(L T-complete T-degree theory total function transition variables