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

Language complexity of rotations and Sturmian sequences

AbstractGiven a rotation of the circle, we study the complexity of formal languages that are generated by the itineraries of interval covers. These languages are regular iff the rotation is rational. In the case of irrational rotations, our study reduces to that of the language complexity of the corresponding Sturmian sequences. We show that for a large class of irrationals, including e, all quadratic numbers and more generally all Hurwitz numbers, the corresponding languages can be recognized by a nondeterministic Turing machine in linear time (in other words, belongs to NLIN)

On Factor Universality in Symbolic Spaces

The study of factoring relations between subshifts or cellular automata is central in symbolic dynamics. Besides, a notion of intrinsic universality for cellular automata based on an operation of rescaling is receiving more and more attention in the literature. In this paper, we propose to study the factoring relation up to rescalings, and ask for the existence of universal objects for that simulation relation. In classical simulations of a system S by a system T, the simulation takes place on a specific subset of configurations of T depending on S (this is the case for intrinsic universality). Our setting, however, asks for every configurations of T to have a meaningful interpretation in S. Despite this strong requirement, we show that there exists a cellular automaton able to simulate any other in a large class containing arbitrarily complex ones. We also consider the case of subshifts and, using arguments from recursion theory, we give negative results about the existence of universal objects in some classes

Topological properties of cellular automata on trees

We prove that there do not exist positively expansive cellular automata defined on the full k-ary tree shift (for k>=2). Moreover, we investigate some topological properties of these automata and their relationships, namely permutivity, surjectivity, preinjectivity, right-closingness and openness.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

Program schemes with deep pushdown storage.

Inspired by recent work of Meduna on deep pushdown automata, we consider the computational power of a class of basic program schemes, TeX, based around assignments, while-loops and non- deterministic guessing but with access to a deep pushdown stack which, apart from having the usual push and pop instructions, also has deep-push instructions which allow elements to be pushed to stack locations deep within the stack. We syntactically define sub-classes of TeX by restricting the occurrences of pops, pushes and deep-pushes and capture the complexity classes NP and PSPACE. Furthermore, we show that all problems accepted by program schemes of TeX are in EXPTIME

Self-administration of the Parish in Utraquism

Předkládaná práce analyzuje samosprávné prvky v řízení utrakvistické farnosti. Vychází ze středověkého právního uspořádání a sleduje, jak se proměňovalo vlivem husitské a později reformační ekleziologie i vlivem světského vývoje v 16. století. Kromě úvah o volbě faráře se soustřeďuje na laickou správu farního majetku, zabývá se postavením a vlivem zádušních úředníků. Vzhledem k dochovanosti pramenů je těžištěm situace v českých královských městech kolem roku 1600. Práce dochází k závěru, že rozhodujícím faktorem pro uplatnění laického prvku byly světské právní zvyklosti, nikoliv konfesijní vývoj. Powered by TCPDF (www.tcpdf.org)This thesis analyzes self governing elements in administration of the Utraquist parishes. It is based on of medieval legal order and shows, how it was changed under the influence of Hussite and later reformational ecclesiology and by secular developments in the 16th Century. Besides the election of the parish priest it focuses mainly on lay administration of parish property, it deals with position and authority of chantry officials. Regarding the state of sources, the focus is on the situation in Bohemian Royal towns around 1600. The thesis concludes that the most important factor for penetration of the lay element into the administration was the secular law usage, not the confessional evolution. Powered by TCPDF (www.tcpdf.org)Evangelická teologická fakultaProtestant theological facultyEvangelická teologická fakultaProtestant Theological Facult

Epigeic spiders from lowland oak woodlands in the south Moravia region (Czech Republic)

This paper presents spider faunistics from abandoned coppice oak forest stands located along the South Moravia region. Spiders were collected from May to July 2012 by pitfall trapping at eight different localities. We collected 1945 adult spiders representing 20 families, 53 genera, and 90 species. More than one-third of all the species are known to be xerothermophilous with ecological restrictions to open and partly shaded habitats such as forest-steppe and sparse forests which belong to endangered habitats along central Europe. The most abundant species were Pardosa alacris, P. lugubris and Arctosa lutetiana from the family Lycosidae. In the surveyed area, 24 species were found listed in the Red List of Threatened Species in the Czech Republic (CR - 1 species, EN - 2 species, VU - 15 species, LC - 6 species). In general, we discovered a substantially diversified spider community with a large presence of rare and endangered species characteristic for open and xeric habitats.O