by Cristian S. Calude, Michael A. Stay – Inform. and Comput. 2006
“. We introduce the zeta number, natural halting probability and natural complexity in the Turing machine and then we relate individuals to Chaitin’s Omega number, halting probability, and program-size complexity. A classification of Turing machines based on their zeta figures is suggested: divergent, convergent. “
We introduce the zeta number, natural halting probability and natural complexity in the Turing machine and then we relate individuals to Chaitin’s Omega number, halting probability, and program-size complexity. A classification of Turing machines based on their zeta figures is suggested: divergent, convergent and tuatara. We prove the presence of universal convergent and tuatara machines. Various results on (algorithmic) randomness and partial randomness are proven. For instance, we show the zeta amount universal tuatara machine is c.e. and random. A totally new kind of partial randomness, asymptotic randomness, is introduced. Finally we show rather of classical (algorithmic) randomness—which cannot be naturally characterised in relation to plain complexity—asymptotic randomness admits this sort of characterisation. 1
by Cristian S. Calude A, Michael A. Stay B. 2006
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This information was printed within the journal printed by Elsevier, along with the attached copy is supplied by Elsevier for the author’s benefit along with the advantage of the author’s institution, for non-commercial research and academic use including without limitation utilized in instruction within the institution, delivering it to specific colleagues you understand, and supplying a replica for that institution’s administrator.
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by C. S. Calude, M. A. Stay, Cristian S. Calude, Michael A. Stay, Cristian S. Calude. 2005
“. We introduce the zeta number, natural halting probability and natural complexity in the Turing machine and then we relate individuals to Chaitin’s Omega number, halting probability, and program-size complexity. A classification of Turing machines based on their zeta figures is suggested: divergent, convergent. “
We introduce the zeta number, natural halting probability and natural complexity in the Turing machine and then we relate individuals to Chaitin’s Omega number, halting probability, and program-size complexity. A classification of Turing machines based on their zeta figures is suggested: divergent, convergent and tuatara. We prove the presence of universal convergent and tuatara machines. Various results on (algorithmic) randomness and partial randomness are proven.
For instance, we show the zeta amount universal tuatara machine is c.e. and random. A totally new kind of partial randomness, asymptotic randomness, is introduced. Finally we show rather of classical (algorithmic) randomness—which cannot be naturally characterised in relation to plain complexity—asymptotic randomness admits this sort of characterisation.
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