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Characteristics of discrete transfinite time Turing machine models: halting times, stabilization times, and . . .
, 2008
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P f �= NP f for almost all f
 Mathematical Logic Quarterly 49 (2003
"... We discuss the question of RalfDieter Schindler whether for infinite time Turing machines P f = NP f can be true for any function f from the reals into ω1. We show that “almost everywhere ” the answer is negative. 1 ..."
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Cited by 6 (4 self)
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We discuss the question of RalfDieter Schindler whether for infinite time Turing machines P f = NP f can be true for any function f from the reals into ω1. We show that “almost everywhere ” the answer is negative. 1
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 ..."
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Cited by 4 (1 self)
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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 ..."
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Cited by 2 (1 self)
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• 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. ..."
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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 ..."
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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