137 research outputs found
On the incomputability of computable dimension
Using an iterative tree construction we show that for simple computable
subsets of the Cantor space Hausdorff, constructive and computable dimensions
might be incomputable
Projection lemmas for Ï-languages
AbstractThe paper presents projection lemmas relating the infinite behaviour of deterministic and unboundedly branching nondeterministic infinite automata
Subspaces of GF(q)Ï and convolutional codes
The present paper is a self-contained treatment of subspaces of the space GF(q)Ï of all semi-infinite strings over GF(q). Some necessary and sufficient conditions which characterize those subspaces of GF(q)Ï are derived which are convolutional codes, and the classes of subspaces defined by one or more of them are investigated. Moreover structural parameters of convolutional codes such as block length, rate, delay, and constraint length are considered as parameters of subspaces rather than parameters of an encoding device. As a conclusion it is obtained that for error-control purposes none of the investigated superclasses of the class of convolutional codes is better suited than the class of convolutional codes itself
The entropy of Ćukasiewicz-languages
The paper presents an elementary approach for the calculation of the entropy
of a class of languages. This approach is based on the consideration of
roots of a real polynomial and is also suitable for calculating the
Bernoulli measure. The class of languages we consider here is a
generalisation of the Ćukasiewicz language
Topologies for the set of disjunctive Ï-words
An infinite sequence (Ï-word) is referred to as disjunctive provided it contains every finite word as infix (factor). As JĂŒrgensen and Thierrin [JT83] observed the set of disjunctive Ï-words, D, has a trivial syntactic monoid but is not accepted by a finite automaton. In this paper we derive some topological properties of the set of disjunctive Ï-words. We introduce two non-standard topologies on the set of all Ï-words and show that D fulfills some special properties with respect to these topologies. In the first topology - the so-called topology of forbidden words - D is the smallest nonempty GÎŽ-set, and in the second one D is the set of accumulation points of the whole space as well as of itself
Randomness Relative to Cantor Expansions
Imagine a sequence in which the first letter comes from a binary alphabet,
the second letter can be chosen on an alphabet with 10 elements, the third
letter can be chosen on an alphabet with 3 elements and so on. When such a
sequence can be called random? In this paper we offer a solution to the above
question using the approach to randomness proposed by Algorithmic Information
Theory.Comment: several small change
How to Go Beyond Turing with P Automata: Time Travels, Regular Observer !-Languages, and Partial Adult Halting
In this paper we investigate several variants of P automata having in nite
runs on nite inputs. By imposing speci c conditions on the in nite evolution of the
systems, it is easy to nd ways for going beyond Turing if we are watching the behavior
of the systems on in nite runs. As speci c variants we introduce a new halting variant for
P automata which we call partial adult halting with the meaning that a speci c prede ned
part of the P automaton does not change any more from some moment on during the
in nite run. In a more general way, we can assign !-languages as observer languages
to the in nite runs of a P automaton. Speci c variants of regular !-languages then, for
example, characterize the red-green P automata
On the incomputability of computable dimension
Using an iterative tree construction we show that for simple computable
subsets of the Cantor space Hausdorff, constructive and computable dimensions
might be incomputable
Separation of Test-Free Propositional Dynamic Logics over Context-Free Languages
For a class L of languages let PDL[L] be an extension of Propositional
Dynamic Logic which allows programs to be in a language of L rather than just
to be regular. If L contains a non-regular language, PDL[L] can express
non-regular properties, in contrast to pure PDL.
For regular, visibly pushdown and deterministic context-free languages, the
separation of the respective PDLs can be proven by automata-theoretic
techniques. However, these techniques introduce non-determinism on the automata
side. As non-determinism is also the difference between DCFL and CFL, these
techniques seem to be inappropriate to separate PDL[DCFL] from PDL[CFL].
Nevertheless, this separation is shown but for programs without test operators.Comment: In Proceedings GandALF 2011, arXiv:1106.081
Exploring the Developmental Overnutrition Hypothesis Using ParentalâOffspring Associations and FTO as an Instrumental Variable
Using parental-offspring associations and theFTO gene as an instrumental variable for maternal adiposity, Debbie Lawlor and colleagues found that greater maternal BMI during offspring development does not appear to have a marked effect on offspring fat mass at age 9-11
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