Titlebook: How the World Computes; Turing Centenary Con S. Barry Cooper,Anuj Dawar,Benedikt Löwe Conference proceedings 2012 Springer-Verlag Berlin He

sultry

Ordinal Analysis and the Infinite Ramsey Theorem,th ... The upper bound is obtained by means of cut elimination and the lower bound by extending the standard well-ordering proofs for ACA.. There is a proof of this result due to McAloon [6], using model-theoretic and combinatorial techniques. According to [6], another proof appeared in an unpublished paper by Jäger.

植物学

A Note on Ramsey Theorems and Turing Jumps,d this approach to ..′ using a characterization of this system in terms of preservation of well-orderings due to Marcone and Montalbán. We finally discuss how to apply this method to . using an extension of Ramsey’s Theorem for colouring relatively large sets due to Pudlàk and Rödl and independently to Farmaki.

Nibble

美丽的写

On Mathias Generic Sets,es the jump property .. = .′ ⊕ ∅ .. We prove that every such . has generalized high degree, and so cannot have even Cohen 1-generic degree. On the other hand, we show that ., together with any bi-immune . ≤ . ∅ ., computes a Cohen .-generic.

Flinch

AMITY

,Turing’s Normal Numbers: Towards Randomness,ments of Turing are largely unknown because his manuscript remained unpublished until its inclusion in his Collected Works in 1992. The present note highlights Turing’s ideas for the construction of normal numbers. Turing’s theorems are included with a reconstruction of the original proofs.

反话

An Undecidable Nested Recurrence Relation,re . means that for every . ≥ 0, either .(.) is an initial condition or the calculation of .(.) involves only invocations of . on arguments in .. We show that the recurrence relation .is undecidable by showing how it can be used, together with carefully chosen initial conditions, to simulate Post 2-tag systems, a known Turing complete problem.

恫吓

Connecting Partial Words and Regular Languages,lity and computational-hardness results, are presented. Finally, we define a hierarchy of classes of languages of partial words, by grouping together languages that can be connected in strong ways to regular languages, and derive their closure properties.

CLAM

0302-9743 ntenary Conference and the 8th Conference on Computability in Europe, CiE 2012, held in Cambridge, UK, in June 2012. .The 53 revised papers presented together with 6 invited lectures were carefully reviewed and selected with an acceptance rate of under 29,8%. The CiE 2012 Turing Centenary Conference

induct

Curiouser and Curiouser: The Link between Incompressibility and Complexity,for example, we interpret “.” to be “the class of problems that are .-Turing reducible to ., no matter which universal machine we use in defining Kolmogorov complexity”. The lecture will survey the body of work (some of it quite recent) that suggests that, when interpreted properly, the conjectures may actually be true.