## 355 Citations

### The Broad Conception of Computation

- Philosophy
- 1997

A myth has arisen concerning Turing's article of 1936, namely that Turing set forth a fundamental principle concerning the limits of what can be computed by machine; this supposed principle is sometimes incorrectly termed the Church-Turing thesis.

### What is Church's Thesis? An Outline*

- PhilosophyMinds and Machines
- 2004

My suspicion is that physics is easily rich enough so that E2, the functions compatable in principle given Turing’s operations and equilibriating, include non-recursive functions.

### The Church-Turing Thesis

- Philosophy
- 2006

The notion of an effective method is an informal one, and attempts to characterise effectiveness, such as the above, lack rigour, for the key requirement that the method demand no insight or…

### A Natural Axiomatization of Computability and Proof of Church's Thesis

- Computer ScienceBulletin of Symbolic Logic
- 2008

It is shown that augmenting those postulates about algorithmic computation with an additional requirement regarding basic operations gives a natural axiomatization of computability and a proof of Church's Thesis, as Gödel and others suggested may be possible.

### On mind & Turing’s machines

- PhilosophyNatural Computing
- 2006

G Gödel’s perspective on mechanical computability as articulated in his [193?], where he drew a dramatic conclusion from the undecidability of certain Diophantine propositions, namely, that mathematicians cannot be replaced by machines, is discussed.

### K-graph machines : generalizing Turing's machines and arguments

- Computer Science
- 1996

K-graph machines are introduced and used to give a detailed mathematical explication of the first two aspects of Turing's considerations for general configurations, i.e. boundedness and locality conditions and mechanical operations, which provide a significant strengthening of Turing’s argument for his central thesis.

### Turing’s Theory of Computation

- Computer Science
- 2017

This work discusses the historical and philosophical reasons that led to the widely accepted classic-computational interpretation of the Turing machine, and argues that this interpretation is wrong, because it treats the tape of a Turing machine as its internal memory, rather than as the external environment.

### On Effective Procedures

- PhilosophyMinds and Machines
- 2004

This paper presents an alternative to Turing's analysis; it unifies, refines, and extends my earlier work on this topic, and has the advantage of applying to ordinary, everyday procedures such as recipes and methods, as well as the more refined procedures of mathematics and computer science.

### Church Without Dogma: Axioms for Computability

- Computer Science
- 2008

An analysis of computability that leads to precise concepts, but dispenses with theses is presented, which leads to axioms for discrete dynamical systems (representing human and machine computations) and allows the reduction of models of theseAxioms to Turing machines.

### A Natural Axiomatization of Church's Thesis

- Philosophy
- 2007

The Abstract State Machine Thesis asserts that every classical algorithm is behaviorally equivalent to an abstract state machine. This thesis has been shown to follow from three natural postulates…

## References

SHOWING 1-7 OF 7 REFERENCES

### Finite combinatory processes—formulation

- MathematicsJournal of Symbolic Logic
- 1936

The present formulation should prove significant in the development of symbolic logic along the lines of Gödel's theorem on the incompleteness of symbolic logics and Church's results concerning…

### Abstract computability and its relation to the general purpose analog computer (some connections between logic, differential equations and analog computers)

- Computer Science, Mathematics
- 1974

This work presents a mathematical definition of an analog generable function of a real variable in terms of a simultaneous set of nonlinear differential equations possessing a "domain of generation," which includes functions generated by existing general-purpose analog computers.

### Computation Over Abstract Structures: Serial and Parallel Procedures and Friedman's Effective Definitional Schemes

- Mathematics
- 1975

### Subgroups of finitely presented groups

- MathematicsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- 1961

The main theorem of this paper states that a finitely generated group can be embedded in a finitely presented group if and only if it has a recursively enumerable set of defining relations. It…

### On computable numbers, with an application to the Entscheidungsproblem

- Computer ScienceProc. London Math. Soc.
- 1937

This chapter discusses the application of the diagonal process of the universal computing machine, which automates the calculation of circle and circle-free numbers.

### An algebraic characterization of groups with soluble word problem

- Mathematics
- 1974

The following theorem is the focal point of the present paper. It stipulates an algebraic condition equivalent, in any finitely generated group, to the solubility of the word problem. THEOREM I. A…

### ÜBER EINE BISHER NOCH NICHT BENÜTZTE ERWEITERUNG DES FINITEN STANDPUNKTES

- Mathematics, Philosophy
- 1958

Zusammenfassung
P. Bernays hat darauf hingewiesen, dass man, um die Widerspruchs freiheit der klassischen Zahlentheorie zu beweisen, den Hilbertschen flniter Standpunkt dadurch erweitern muss,…