13,566 research outputs found
Bell's Theorem from Moore's Theorem
It is shown that the restrictions of what can be inferred from
classically-recorded observational outcomes that are imposed by the no-cloning
theorem, the Kochen-Specker theorem and Bell's theorem also follow from
restrictions on inferences from observations formulated within classical
automata theory. Similarities between the assumptions underlying classical
automata theory and those underlying universally-unitary quantum theory are
discussed.Comment: 12 pages; to appear in Int. J. General System
Automata theory in nominal sets
We study languages over infinite alphabets equipped with some structure that
can be tested by recognizing automata. We develop a framework for studying such
alphabets and the ensuing automata theory, where the key role is played by an
automorphism group of the alphabet. In the process, we generalize nominal sets
due to Gabbay and Pitts
Advances and applications of automata on words and trees : executive summary
Seminar: 10501 - Advances and Applications of Automata on Words and Trees. The aim of the seminar was to discuss and systematize the recent fast progress in automata theory and to identify important directions for future research. For this, the seminar brought together more than 40 researchers from automata theory and related fields of applications. We had 19 talks of 30 minutes and 5 one-hour lectures leaving ample room for discussions. In the following we describe the topics in more detail
A Fibrational Approach to Automata Theory
For predual categories C and D we establish isomorphisms between opfibrations
representing local varieties of languages in C, local pseudovarieties of
D-monoids, and finitely generated profinite D-monoids. The global sections of
these opfibrations are shown to correspond to varieties of languages in C,
pseudovarieties of D-monoids, and profinite equational theories of D-monoids,
respectively. As an application, we obtain a new proof of Eilenberg's variety
theorem along with several related results, covering varieties of languages and
their coalgebraic modifications, Straubing's C-varieties, fully invariant local
varieties, etc., within a single framework
A state of a dynamic computational structure distributed in an environment: a model and its corollaries
Currently there is great interest in computational models consisting of
underlying regular computational environments, and built on them distributed
computational structures. Examples of such models are cellular automata,
spatial computation and space-time crystallography. For any computational model
it is natural to define a functional equivalence of different but related
computational structures. In the finite automata theory an example of such
equivalence is automata homomorphism and, in particular, automata isomorphism.
If we continue to stick to the finite automata theory, a fundamental question
arise, what a state of a distributed computational structure is. This work is
devoted to particular solution of the issue.Comment: 11 pages, 5 figure
Languages, machines, and classical computation
3rd ed, 2021. A circumscription of the classical theory of computation building up from the Chomsky hierarchy. With the usual topics in formal language and automata theory
A Cellular Automata Model with Probability Infection and Spatial Dispersion
In this article, we have proposed an epidemic model by using probability
cellular automata theory. The essential mathematical features are analyzed with
the help of stability theory. We have given an alternative modelling approach
for the spatiotemporal system which is more realistic and satisfactory from the
practical point of view. A discrete and spatiotemporal approach are shown by
using cellular automata theory. It is interesting to note that both size of the
endemic equilibrium and density of the individual increase with the increasing
of the neighborhood size and infection rate, but the infections decrease with
the increasing of the recovery rate. The stability of the system around the
positive interior equilibrium have been shown by using suitable Lyapunov
function. Finally experimental data simulation for SARS disease in China and a
brief discussion conclude the paper
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