Results 1 
8 of
8
Characteristics of discrete transfinite time Turing machine models: halting times, stabilization times, and . . .
, 2008
"... ..."
On the transfinite action of 1 tape Turing machines
 Computational Paradigms: Proceedings of CiE2005
, 2005
"... Abstract. • We produce a classification of the pointclasses of sets of reals produced by infinite time turing machines with 1tape. The reason for choosing this formalism is that it apparently yields a smoother classification of classes defined by algorithms that halt at limit ordinals. • We conside ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Abstract. • We produce a classification of the pointclasses of sets of reals produced by infinite time turing machines with 1tape. The reason for choosing this formalism is that it apparently yields a smoother classification of classes defined by algorithms that halt at limit ordinals. • We consider some relations of such classes with other similar notions, such as arithmetical quasiinductive definitions. • It is noted that the action of ω many steps of such a machine can correspond to the double jump operator (in the usual Turing sense): a−→ a ′ ′. • The ordinals beginning gaps in the “clockable ” ordinals are admissible ordinals, and the length of such gaps corresponds to the degree of reflection those ordinals enjoy. 1
Arithmetical quasiinductive definitions and the transfinite action of one tape Turing machines
, 2003
"... • We produce a classification of the pointclasses using infinite time turing machines with 1tape. The reason for choosing this formalism is that it apparently yields a smoother classification of classes defined by algorithms that halt at limit ordinals. • We consider some relations of such classes ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
• We produce a classification of the pointclasses using infinite time turing machines with 1tape. The reason for choosing this formalism is that it apparently yields a smoother classification of classes defined by algorithms that halt at limit ordinals. • We consider some relations of such classes with other similar notions, such as arithmetical quasiinductive definitions. • It is noted that the action of ω many steps of such a machine can correspond to the double jump operator (in the usual Turing sense): a− → a ′ ′. • The ordinals beginning gaps in the “clockable” ordinals are admissible ordinals, and the length of such gaps corresponds to the degree of reflection those ordinals enjoy.
P^f ≠ NP^f for almost all f
, 2002
"... We discuss the question of RalfDieter Schindler whether for in nite time Turing machines P can be true for any function f from the reals into ! 1 . We show that \almost everywhere" the answer is negative. ..."
Abstract
 Add to MetaCart
We discuss the question of RalfDieter Schindler whether for in nite time Turing machines P can be true for any function f from the reals into ! 1 . We show that \almost everywhere" the answer is negative.
Transfinite Machine Models
, 2011
"... In recent years there has emerged the study of discrete computational models which are allowed to act transfinitely. By ‘discrete ’ we mean that the machine models considered are not analogue machines, but compute by means of distinct stages or in units of time. The paradigm of such models is, of co ..."
Abstract
 Add to MetaCart
(Show Context)
In recent years there has emerged the study of discrete computational models which are allowed to act transfinitely. By ‘discrete ’ we mean that the machine models considered are not analogue machines, but compute by means of distinct stages or in units of time. The paradigm of such models is, of course, Turing’s original
Discrete Transfinite Computation
"... We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have longer tapes than the standard model, or that work on ordinals r ..."
Abstract
 Add to MetaCart
(Show Context)
We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have longer tapes than the standard model, or that work on ordinals rather than numbers. We outline the connections between such models and the older theories of recursion in higher types, generalized recursion theory, and recursion on ordinals such as αrecursion. We conclude that, in particular, polynomial time computation on ωstrings is well modelled by several convergent conceptions. 1