Filters








18,177 Hits in 8.6 sec

Formalism and intuition in computability

R. I. Soare
2012 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
In 1936, Turing and in 1944, Post introduced more intuitive models of Turing machines and generational systems.  ...  A third wave of intuition has arisen from 1996 to the present with a return to the original meaning of computability in the sense of Turing and Gödel, and a return of 'recursive' to its original meaning  ...  The grant is Computability theory and applications, funded by the Simons Foundation Program for Mathematics and the Physical Sciences.  ... 
doi:10.1098/rsta.2011.0335 pmid:22711859 fatcat:z2ae3dac65dmfmijd2sylefawq

Page 4018 of Mathematical Reviews Vol. , Issue 2003f [page]

2003 Mathematical Reviews  
Baer (Mill Valley, CA) 2003f:03053 03D15 03F30 68Q05 68Q15 Gordeew, Lew (D-TBNG-ILS; Tiibingen) Proof theory and Post-Turing analysis.  ...  Summary: “Traditional proof theory and post-Turing computabil- ity are parts of discrete mathematics, whereas traditional analysis deals with non-discrete objects like real numbers and related topo- logical  ... 

Book Review: Complexity theory of real functions

Marian Boykan Pour-El
1993 Bulletin of the American Mathematical Society  
analysis, functional analysis, and physical theory.  ...  (For example, the Post production, a rule for manipulating strings of symbols, played a role in the theory of programming languages, the work of Noam Chomsky on the grammatical analysis of language, and  ... 
doi:10.1090/s0273-0979-1993-00417-8 fatcat:tb6vc2k5lzhmznp3p3hmkf3cnq

Page 2279 of Mathematical Reviews Vol. , Issue 87e [page]

1987 Mathematical Reviews  
The uniform version of the Post-Turing thesis, i.e. Je B Vz(Bp(x) U(e,z)) is inconsistent.  ...  2279 Sieg, Wilfried (1-CLMB-Q) Reductions of theories for analysis. Foundations of logic and linguistics (Salzburg, 1983), 199-231, Plenum, New York-London, 1985.  ... 

Review of 'Computation: Finite and Infinite Machines' (Minsky, Marvin; 1967)

M. Arbib
1968 IEEE Transactions on Information Theory  
This is a beautifully written and produced introduction to finite automata, Turing machines, Post symbol-manipulation systems, and related topics in computability.  ...  Giving the proofs due to himself and to J.  ... 
doi:10.1109/tit.1968.1054133 fatcat:rriovgno5jbdtl5akbzcy6azo4

The History and Concept of Computability [chapter]

Robert I. Soare
1999 Studies in Logic and the Foundations of Mathematics  
Post 1944 explicitly added the empty set as an r.e. set (see [11, p. 308]), which Church and Kleene had omitted.  ...  since then, except for the term "computably enumerable," recently introduced, because Turing and Gödel did not explicitly introduce a term for these corresponding sets, but just for the computable functions  ...  A theory of such machines was given by Turing 1936 and in less detail by Post 1936."  ... 
doi:10.1016/s0049-237x(99)80017-2 fatcat:j23jinkxfrg57fy55nn3nx3jcy

Turing oracle machines, online computing, and three displacements in computability theory

Robert I. Soare
2009 Annals of Pure and Applied Logic  
, analysis, model theory, algorithmic complexity and many more.  ...  Post gave no hint of a universal Turing machine. Most important, Post gave no analysis, as did Turing, of why the intuitively computable functions are computable in his formal system.  ... 
doi:10.1016/j.apal.2009.01.008 fatcat:66vngrvfhfcr3c2rq36p2pbaeq

Computability and Recursion

Robert I. Soare
1996 Bulletin of Symbolic Logic  
After a careful historical and conceptual analysis of computability and recursion we make several recommendations in section §7 about preserving the intensional differences between the concepts of "computability  ...  We consider the informal concept of "computability" or "effective calculability" and two of the formalisms commonly used to define it, "(Turing) computability" and "(general) recursiveness".  ...  A theory of such machines was given by Turing 1936 and in less detail by Post 1936 ."  ... 
doi:10.2307/420992 fatcat:yq5vicyjf5aq7ercdrg2jql6zm

1936: Post, Turing and 'a kind of miracle' in mathematical logic

G. T. Q. Hoare
2004 Mathematical Gazette  
In the 1930s several mathematicians, principally Alonzo Church (1903-1995), Stephen Kleene (1909-1994), Emil Post (1897-1954) and Alan Turing (1912-1954), began investigating the notion of effective calculability  ...  Acknowledgements I am indebted to the referee for making helpful suggestions on the first draft and to Becky Carter who typed it.  ...  Independently of Turing but aware of Church's Thesis, Post gives an analysis of the computing process very similar to that given by Turing but there is a subtle difference.  ... 
doi:10.1017/s0025557200174170 fatcat:echz27tckzegjf52yco6b5izna

Page 6526 of Mathematical Reviews Vol. , Issue 2003i [page]

2003 Mathematical Reviews  
It is a lucid and insightful combination of conceptual analysis and historical exegesis of the work of pioneers like Church, Kleene, Post, Gédel and, above all, Turing.  ...  Instead, the analysis produces rigorous axiomatizations of the key notions, and allows proofs that the intuitive notions are coextensive with each other and with Turing computability, (general) recursiveness  ... 

Definable degrees and automorphisms of $\mathcal {D}$

Leo Harrington, Richard A. Shore
1981 Bulletin of the American Mathematical Society  
The analysis of the structure V of these degrees has been a central topic in recursion theory beginning with the papers of Post [1944] and Kleene and Post [1954].  ...  If the Turing degree x is not hyperarithmetic and x, 0 < t then there is a degree s such that t is a minimal cover of s and x ^ s. PROOF.  ...  The analysis of the structure V of these degrees has been a central topic in recursion theory beginning with the papers of Post [1944] and Kleene and Post [1954] .  ... 
doi:10.1090/s0273-0979-1981-14871-0 fatcat:oac6v2hkjbe27oygxvbt7cysqi

Book Review: Recursively enumerable sets and degrees: A study of computable functions and computably generated sets

Marian Boykan Pour-El
1988 Bulletin of the American Mathematical Society  
This is obviously true of the work of Post and Turing referred to earlier. It is equally true of very recent work.  ...  The Post Production, a rule for manipulating strings of symbols, found its way into programming languages, the work of Noam Chomsky on the grammatical analysis of language, and other topics.  ...  In this volume the modern conceptions and ramifications of manifolds are treated. Perhaps no other concept in modern mathematics has been so  ... 
doi:10.1090/s0273-0979-1988-15624-8 fatcat:qi44akcymvblddnoohditudh7a

Degrees of Unsolvability [chapter]

Klaus Ambos-Spies, Peter A. Fejer
2014 Handbook of the History of Logic  
We finish our history by quoting Gerald Sacks, who through his own work and the work of his students (including, Harrington, Robinson, Shore, Simpson, Slaman, and Thomason) shaped degree theory throughout  ...  a good part of its existence: "Farewell to higher recursion theory, but not to recursion theory; there is no way to say good-bye to recursion theory" ( [Sacks, 1999] ).  ...  Kleene's real interests were in generalized recursion theory and [Kleene and Post, 1954] is his only paper in the Turing degrees.  ... 
doi:10.1016/b978-0-444-51624-4.50010-1 fatcat:clf7varewrh6lc4jq2c2sp6pgy

The jump is definable in the structure of the degrees of unsolvability

S. Barry Cooper
1990 Bulletin of the American Mathematical Society  
The structural analysis of the partial ordering 3 has been a major area of research in recursion theory since the pioneering paper of Kleene and Post [14] .  ...  Recursion theory deals with computability on the natural numbers.  ...  The structural analysis of the partial ordering 3 has been a major area of research in recursion theory since the pioneering paper of Kleene and Post [14] .  ... 
doi:10.1090/s0273-0979-1990-15923-3 fatcat:d3g7bx5i6neufhcr5b5i32okie

Incomputability after Alan Turing [article]

S. Barry Cooper
2013 arXiv   pre-print
Incomputability as a mathematical notion arose from work of Alan Turing and Alonzo Church in the 1930s.  ...  This article takes a Turing centenary look at how the interface between the computable world and the incomputable formed a central theme in Turing's work - from the early establishment of the standard  ...  On the one hand, we have numerical analysis and scientific computation; on the other hand, we have the tradition of computation theory arising from logic and computer science.  ... 
arXiv:1304.6363v1 fatcat:nh5lsf23pvedleymkatyjksivi
« Previous Showing results 1 — 15 out of 18,177 results