Truth-table Schnorr randomness and truth-table reducible randomness

Process and truth-table characterisations of randomness

This paper uses quick process machines to provide characterisations of computable randomness, Schnorr randomness and weak randomness. The quick process machine is a type of process machine first considered in work of Levin and Zvonkin. A new technique for building process machines and quick process machines is presented. This technique is similar to the KC theorem for prefix-free machines. Usin...

Schnorr trivial sets and truth-table reducibility

We give several characterizations of Schnorr trivial sets, including a new lowness notion for Schnorr triviality based on truth-table reducibility. These characterizations allow us to see not only that some natural classes of sets, including maximal sets, are composed entirely of Schnorr trivials, but also that the Schnorr trivial sets form an ideal in the truth-table degrees but not the weak t...

On Sets Bounded Truth-Table Reducible to P-selective Sets

We show that if every NP set is polynomial time bounded truth table reducible to some P selective set then NP is contained in DTIME n O p logn In the proof we implement a recursive procedure that reduces the number of nondeterministic steps of a given nondeter ministic computation

Schnorr randomness

Truth and Light: Physical Algorithmic Randomness

This thesis examines some problems related to Chaitin’s Ω number. In the first section, we describe several new minimalist prefix-free machines suitable for the study of concrete algorithmic information theory; the halting probabilities of these machines are all Ω numbers. In the second part, we show that when such a sequence is the result given by a measurement of a system, the system itself c...