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Is the Halting probability . . .
"... ... Marcus identify eight stages in the development of the concept of a mathematical proof in support of an ambitious conjecture: we can express classical mathematical concepts adequately only in a mathematical language in which both truth and provability are essentially unverifiable. In this essay ..."
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we show, first, that the concepts underlying their thesis can, however, be interpreted constructively; and, second, that an implicit thesis in the authors’ arguments implies that the Halting problem is solvable, but that, despite this, the probability of a given Turing machine halting on a random
An algebraic characterization of the halting probability
 FUNDAMENTA INFORMATICAE
, 2007
"... 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. Our proof closely follows a 1978 formulation of Post’s work by M. Davis. The proof is selfcontained and not very complicat ..."
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Cited by 2 (2 self)
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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. Our proof closely follows a 1978 formulation of Post’s work by M. Davis. The proof is selfcontained and not very
Relativizing Chaitin’s halting probability
 J. Math. Log
"... Abstract. As a natural example of a 1random real, Chaitin proposed the halting probability Ω of a universal prefixfree machine. We can relativize this example by considering a universal prefixfree oracle machine U. Let Ω A U be the halting probability of U A; this gives a natural uniform way of p ..."
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Cited by 34 (9 self)
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Abstract. As a natural example of a 1random real, Chaitin proposed the halting probability Ω of a universal prefixfree machine. We can relativize this example by considering a universal prefixfree oracle machine U. Let Ω A U be the halting probability of U A; this gives a natural uniform way
The halting probability in von Neumann architectures
 Proceedings of the 9th European Conference on Genetic Programming, volume 3905 of Lecture
, 2006
"... Abstract. Theoretical models of Turing complete linear genetic programming (GP) programs suggest the fraction of halting programs is vanishingly small. Convergence results proved for an idealised machine, are tested on a small T7 computer with (finite) memory, conditional branches and jumps. Simulat ..."
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Cited by 14 (4 self)
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Abstract. Theoretical models of Turing complete linear genetic programming (GP) programs suggest the fraction of halting programs is vanishingly small. Convergence results proved for an idealised machine, are tested on a small T7 computer with (finite) memory, conditional branches and jumps
Leibniz, Randomness & the Halting Probability
, 2004
"... to the Entscheidungsproblem marks a dramatic turning point in modern mathematics. On the one hand, the computer enters center stage as a major mathematical concept. On the other hand, Turing establishes a link between mathematics and physics by talking about what a machine can accomplish. It is amaz ..."
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to the Entscheidungsproblem marks a dramatic turning point in modern mathematics. On the one hand, the computer enters center stage as a major mathematical concept. On the other hand, Turing establishes a link between mathematics and physics by talking about what a machine can accomplish
A generalization of Chaitin’s halting probability Ω and halting selfsimilar sets
 Hokkaido Math. J
, 2002
"... We generalize the concept of randomness in an infinite binary sequence in order to characterize the degree of randomness by a real number D> 0. Chaitin’s halting probability Ω is generalized to Ω D whose degree of randomness is precisely D. On the basis of this generalization, we consider the deg ..."
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Cited by 36 (14 self)
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We generalize the concept of randomness in an infinite binary sequence in order to characterize the degree of randomness by a real number D> 0. Chaitin’s halting probability Ω is generalized to Ω D whose degree of randomness is precisely D. On the basis of this generalization, we consider
HELEN HAlt
"... JUD'TH A;%ANC E RQNEY tjEL.m.,,JA r 4 R SHERRY wjC " E SANDRA K 'DTEvvAqT!Ecd.Es, tnYonk) ..."
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JUD'TH A;%ANC E RQNEY tjEL.m.,,JA r 4 R SHERRY wjC " E SANDRA K 'DTEvvAqT!Ecd.Es, tnYonk)
Halting probability amplitude of quantum computers
 Journal of Universal Computer Science
, 1995
"... The classical halting probability to quantum computations. introduced by Chaitin is generalized Chaitin's [1,2,3] is a magic number. It is a measure for arbitrary programs to take a nite number of execution steps and then halt. It contains the solution for all halting problems, and hence to que ..."
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Cited by 9 (7 self)
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The classical halting probability to quantum computations. introduced by Chaitin is generalized Chaitin's [1,2,3] is a magic number. It is a measure for arbitrary programs to take a nite number of execution steps and then halt. It contains the solution for all halting problems, and hence
Results 1  10
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1,973,592