On the Complexity of Limit Sets of Cellular Automata Associated with Probability Measures

We study the notion of limit sets of cellular automata associated with probability measures (mu-limit sets). This notion was introduced by P. Kurka and A. Maass. It is a refinement of the classical notion of omega-limit sets dealing with the typical long term behavior of cellular automata. It focuses on the words whose probability of appearance does not tend to 0 as time tends to infinity (the persistent words). In this paper, we give a characterisation of the persistent language for non sensible cellular automata associated with Bernouilli measures. We also study the computational complexity of these languages. We show that the persistent language can be non-recursive. But our main result is that the set of quasi-nilpotent cellular automata (those with a single configuration in their mu-limit set) is neither recursively enumerable nor co-recursively enumerable

Turing degrees of limit sets of cellular automata

Cellular automata are discrete dynamical systems and a model of computation. The limit set of a cellular automaton consists of the configurations having an infinite sequence of preimages. It is well known that these always contain a computable point and that any non-trivial property on them is undecidable. We go one step further in this article by giving a full characterization of the sets of Turing degrees of cellular automata: they are the same as the sets of Turing degrees of effectively closed sets containing a computable point

Cellular Automata Models of Road Traffic

In this paper, we give an elaborate and understandable review of traffic cellular automata (TCA) models, which are a class of computationally efficient microscopic traffic flow models. TCA models arise from the physics discipline of statistical mechanics, having the goal of reproducing the correct macroscopic behaviour based on a minimal description of microscopic interactions. After giving an overview of cellular automata (CA) models, their background and physical setup, we introduce the mathematical notations, show how to perform measurements on a TCA model's lattice of cells, as well as how to convert these quantities into real-world units and vice versa. The majority of this paper then relays an extensive account of the behavioural aspects of several TCA models encountered in literature. Already, several reviews of TCA models exist, but none of them consider all the models exclusively from the behavioural point of view. In this respect, our overview fills this void, as it focusses on the behaviour of the TCA models, by means of time-space and phase-space diagrams, and histograms showing the distributions of vehicles' speeds, space, and time gaps. In the report, we subsequently give a concise overview of TCA models that are employed in a multi-lane setting, and some of the TCA models used to describe city traffic as a two-dimensional grid of cells, or as a road network with explicitly modelled intersections. The final part of the paper illustrates some of the more common analytical approximations to single-cell TCA models.Comment: Accepted for publication in "Physics Reports". A version of this paper with high-quality images can be found at: http://phdsven.dyns.cx (go to "Papers written"

String Transformation for n-Dimensional Image Compression

Image compression and manipulation by weighted finite automata exploit similarities in the images in order to obtain notable compression ratios and manipulation tools. The investigations are often based on two-dimensional images. A natura

Vrtić u srednjem vijeku

Interes djece, ako ga prepoznamo kao potencijal budućeg projekta, može pokrenuti prava mala istraživanja koja će djeci, ali i roditeljima i odgajateljima, otkriti nove svjetove, proširiti znanja i omogućiti im smisleno učenje. Odgajateljica Željka Čulik na više je primjera opisala kako djeci omogućiti da u procesu učenja stvaraju vlastite pretpostavke, samostalno ih istražuju i potom dolaze do novih zaključaka

Rozhovor Britských listů 151. Odchod ČR z EU by byla katastrofa [Britské listy interview 151. The departure of the Czech Republic from the EU would be a catastrophe]

As a result of the general election in October 2017, the Czech Republic has moved towards authoritarian rule. As a result of the re-election of the populist extreme right wing president Miloš Zeman in January 2018, the Czech Republic has moved even further towards authoritarian rule. The Czech Republic is one of the most eurosceptic countries in the EU and since the October 2017 general election, right wing extremists in Czech parliament have demanded a referendum about Czexit from the EU. In this interview, Jan Čulík speaks to Jiří Pehe, Director of New York University (Prague) and a well-known global expert on Czech and Central European affairs about the possible impact of the Czech Republic leaving the European Union. The interview was broadcast by the Czech cable TV station Regionalnitelevize.cz from Friday 9th February 2018

Rozhovor Britských listů 149. Společným jmenovatelem zemanovského tábora je strach [Britské listy interview 149. Fear is the common denominator of the camp of Zeman's supporters]

Jan Čulík interviews Jiří Pehe, the well known global political scientist and director of New York University in Prague, about the reasons why the extreme right wing, populist president Miloš Zeman won the Czech Presidential election in January 2018, and about what impact his re-election might mean for Czech and Central European politics. The interview was broadcast by the Czech cable TV station Regionalnitelevize.cz from Friday 2nd February 2018

Rozhovor Britských listů 165. Byl jsem v uprchlickém táboře v Kurdistánu [Britské listy Interview 165. I have been to a refugee camp in Kurdistan]

Jan Čulík interviews Daniel Veselý, a foreign affairs analyst working for Czech public service radio and for Britské listy, about his recent stay in Kurdistan in Turkey and in Iraq