Computing halting probabilities from other halting probabilities
نویسندگان
چکیده
منابع مشابه
Computing halting probabilities from other halting probabilities
The halting probability of a Turing machine is the probability that the machine will halt if it starts with a random stream written on its one-way input tape. When the machine is universal, this probability is referred to as Chaitin’s omega number, and is the most well known example of a real which is random in the sense of Martin-Löf. Although omega numbers depend on the underlying universal T...
متن کاملDifferences of halting probabilities
The halting probabilities of universal prefix-free machines are universal for the class of reals with computably enumerable left cut (also known as left-c.e. reals), and coincide with the Martin-Löf random elements of this class. We study the differences of Martin-Löf random left-c.e. reals and show that for each pair of such reals α, β there exists a unique number r > 0 such that qα − β is a M...
متن کاملRandomness and halting probabilities
We consider the question of randomness of the probability ΩU [X] that an optimal Turing machine U halts and outputs a string in a fixed set X. The main results are as follows: • ΩU [X] is random whenever X is Σn-complete or Π 0 n-complete for some n ≥ 2. • However, for n ≥ 2, ΩU [X] is not n-random when X is Σn or Π 0 n. Nevertheless, there exists ∆n+1 sets such that ΩU [X] is n-random. • There...
متن کاملNatural Halting Probabilities, Partial Randomness, and Zeta Functions
We introduce the zeta number, natural halting probability and natural complexity of a Turing machine and we relate them to Chaitin’s Omega number, halting probability, and program-size complexity. A classification of Turing machines according to their zeta numbers is proposed: divergent, convergent and tuatara. We prove the existence of universal convergent and tuatara machines. Various results...
متن کاملHalting the Allergic March
The prevalence of childhood allergic diseases, such as allergic asthma, allergic rhinitis, and atopic dermatitis, has increased exponentially. In Singapore, the prevalence of asthma at all ages exceeds 20%, and around 50% of Singaporean children show features of an underlying allergy. The exact environmental causes for the increase of allergic diseases have not yet been identified, but most res...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2017
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2016.11.013