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» Randomness and halting probabilities
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JSYML
2006
43views more  JSYML 2006»
13 years 7 months ago
Randomness and halting probabilities
Verónica Becher, Santiago Figueira, Serge G...
FUIN
2002
109views more  FUIN 2002»
13 years 7 months ago
Another Example of Higher Order Randomness
We consider the notion of algorithmic randomness relative to an oracle. We prove that the probability
Verónica Becher, Gregory J. Chaitin
CORR
2008
Springer
70views Education» more  CORR 2008»
13 years 7 months ago
Every Computably Enumerable Random Real Is Provably Computably Enumerable Random
We prove that every computably enumerable (c.e.) random real is provable in Peano Arithmetic (PA) to be c.e. random. A major step in the proof is to show that the theorem stating ...
Cristian S. Calude, Nicholas J. Hay
FUIN
2007
100views more  FUIN 2007»
13 years 7 months ago
An Algebraic Characterization of the Halting Probability
Using 1947 work of Post showing that the word problem for semigroups is unsolvable, we explicitly exhibit an algebraic characterization of the bits of the halting probability Ω....
Gregory J. Chaitin
EUROGP
2006
Springer
112views Optimization» more  EUROGP 2006»
13 years 11 months ago
The Halting Probability in Von Neumann Architectures
Abstract. Theoretical models of Turing complete linear genetic programming (GP) programs suggest the fraction of halting programs is vanishingly small. Convergence results proved f...
William B. Langdon, Riccardo Poli