A probabilistic anytime algorithm for the halting problem

Computability ◽  
2018 ◽  
Vol 7 (2-3) ◽  
pp. 259-271 ◽  
Author(s):  
Cristian S. Calude ◽  
Monica Dumitrescu
Keyword(s):  
Halting Problem ◽  
Anytime Algorithm

A statistical anytime algorithm for the Halting Problem

Computability ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 155-166
Author(s):  
Cristian S. Calude ◽  
Monica Dumitrescu
Keyword(s):  
Halting Problem ◽  
Anytime Algorithm

scholarly journals Anytime Algorithms for Non-Ending Computations

2015 ◽  
Vol 26 (04) ◽  
pp. 465-475 ◽  
Author(s):  
Cristian S. Calude ◽  
Damien Desfontaines
Keyword(s):  
Stopping Time ◽  
General Setting ◽  
Anytime Algorithms ◽  
Halting Problem ◽  
Anytime Algorithm

A program which eventually stops but does not halt “too quickly” halts at a time which is algorithmically compressible. This result — originally proved in [4] — is proved in a more general setting. Following Manin [11] we convert the result into an anytime algorithm for the halting problem and we show that the stopping time (cut-off temporal bound) cannot be significantly improved.

scholarly journals Anytime Algorithms for Non-Ending Computations

2017 ◽  
Author(s):  
Cristian S. Calude ◽  
Damien Desfontaines
Keyword(s):  
Stopping Time ◽  
General Setting ◽  
Anytime Algorithms ◽  
Halting Problem ◽  
Anytime Algorithm

A program which eventually stops but does not halt “too quickly” halts at a time which is algorithmically compressible. This result—originally proved in [4]—is proved in a more general setting. Following Manin [11] we convert the result into an anytime algorithm for the halting problem and we show that the stopping time (cut-off temporal bound) cannot be significantly improved

Incompleteness and the Halting Problem

Studia Logica ◽  
2021 ◽  
Author(s):  
Cristian S. Calude
Keyword(s):  
Halting Problem

A proof of Beigel's cardinality conjecture

1992 ◽  
Vol 57 (2) ◽  
pp. 677-681 ◽  
Author(s):  
Martin Kummer
Keyword(s):  
Complexity Theory ◽  
Structural Complexity ◽  
Halting Problem ◽  
Parallel Queries

In 1986, Beigel [Be87] (see also [Od89, III.5.9]) proved the nonspeedup theorem: if A, B ⊆ ω, and as a function of 2n variables can be computed by an algorithm which makes at most n queries to B, then A is recursive (informally, 2n parallel queries to a nonrecursive oracle A cannot be answered by making n sequential (or “adaptive”) queries to an arbitrary oracle B). Here, 2n cannot be replaced by 2n − 1. In subsequent papers of Beigel, Gasarch, Gill, Hay, and Owings the theory of “bounded query classes” has been further developed (see, for example, [BGGOta], [BGH89], and [Ow89]). The topic has also been studied in the context of structural complexity theory (see, for example, [AG88], [Be90], and [JY90]).If A ⊆ ω and n ≥ 1, let . Beigel [Be87] stated the powerful “cardinality conjecture” (CC): if A, B ⊆ ω, and can be computed by an algorithm which makes at most n queries to B, then A is recursive. Owings [Ow89] verified CC for n = 1, and, for n 1, he proved that A is recursive in the halting problem. We prove that CC is true for all n.

The Halting Problem and Formal Proofs

1993 ◽  
pp. 121-138
Author(s):  
Jan L. A. Snepscheut
Keyword(s):  
Formal Proofs ◽  
Halting Problem

Formalization of the Undecidability of the Halting Problem for a Functional Language

2018 ◽  
pp. 196-209 ◽  
Author(s):  
Thiago Mendonça Ferreira Ramos ◽  
César Muñoz ◽  
Mauricio Ayala-Rincón ◽  
Mariano Moscato ◽  
Aaron Dutle ◽  
...  
Keyword(s):  
Functional Language ◽  
Halting Problem
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