225 research outputs found
Hereditarily finite sets and identity trees
AbstractSome asymptotic results about the sizes of certain sets of hereditarily finite sets, identity trees, and finite games are proven
On colouring point visibility graphs
In this paper we show that it can be decided in polynomial time whether or
not the visibility graph of a given point set is 4-colourable, and such a
4-colouring, if it exists, can also be constructed in polynomial time. We show
that the problem of deciding whether the visibility graph of a point set is
5-colourable, is NP-complete. We give an example of a point visibility graph
that has chromatic number 6 while its clique number is only 4
On vertex coloring without monochromatic triangles
We study a certain relaxation of the classic vertex coloring problem, namely,
a coloring of vertices of undirected, simple graphs, such that there are no
monochromatic triangles. We give the first classification of the problem in
terms of classic and parametrized algorithms. Several computational complexity
results are also presented, which improve on the previous results found in the
literature. We propose the new structural parameter for undirected, simple
graphs -- the triangle-free chromatic number . We bound by
other known structural parameters. We also present two classes of graphs with
interesting coloring properties, that play pivotal role in proving useful
observation about our problem. We give/ask several conjectures/questions
throughout this paper to encourage new research in the area of graph coloring.Comment: Extended abstrac
An Exponential Lower Bound for the Latest Deterministic Strategy Iteration Algorithms
This paper presents a new exponential lower bound for the two most popular
deterministic variants of the strategy improvement algorithms for solving
parity, mean payoff, discounted payoff and simple stochastic games. The first
variant improves every node in each step maximizing the current valuation
locally, whereas the second variant computes the globally optimal improvement
in each step. We outline families of games on which both variants require
exponentially many strategy iterations
Synchronization Problems in Automata without Non-trivial Cycles
We study the computational complexity of various problems related to
synchronization of weakly acyclic automata, a subclass of widely studied
aperiodic automata. We provide upper and lower bounds on the length of a
shortest word synchronizing a weakly acyclic automaton or, more generally, a
subset of its states, and show that the problem of approximating this length is
hard. We investigate the complexity of finding a synchronizing set of states of
maximum size. We also show inapproximability of the problem of computing the
rank of a subset of states in a binary weakly acyclic automaton and prove that
several problems related to recognizing a synchronizing subset of states in
such automata are NP-complete.Comment: Extended and corrected version, including arXiv:1608.00889.
Conference version was published at CIAA 2017, LNCS vol. 10329, pages
188-200, 201
The Wonder of Colors and the Principle of Ariadne
The Principle of Ariadne, formulated in 1988 ago by Walter Carnielli
and Carlos Di Prisco and later published in 1993, is an infinitary principle that is independent of the Axiom of Choice in ZF, although it can be consistently added to
the remaining ZF axioms. The present paper surveys, and motivates, the foundational importance of the Principle of Ariadne
and proposes the Ariadne Game, showing that the Principle of Ariadne,
corresponds precisely
to a winning strategy for the Ariadne Game. Some relations to other
alternative. set-theoretical principles
are also briefly discussed
Coexistence of Anomalous Hall Effect and Weak Net Magnetization in Collinear Antiferromagnet MnTe
Anomalous Hall effect (AHE) plays important role in the rapidly developing
field of antiferromagnetic spintronics. It has been recently discussed that it
can be a feature of not only uncompensated magnetic systems but also in
altermagnetic materials. Hexagonal MnTe belongs to this appealing group of
compounds exhibiting AHE and is commonly perceived as magnetically compensated.
Here, we demonstrate that bulk form of MnTe exhibits small but detectable
magnetic moment correlating with hysteretic behaviour of the AHE. We formulate
a phenomenological model which explains how this feature allows to create a
disbalance between states with opposite N\'eel vector and prevent the AHE
signal from averaging out to zero. Moreover, we show how the dependence of AHE
on the N\'eel vector arises on microscopical level and highlight the
differences in Berry curvature between magnetically compensated and
uncompensated systems
The combinatorics of the Baer-Specker group
Denote the integers by Z and the positive integers by N.
The groups Z^k (k a natural number) are discrete, and the classification up
to isomorphism of their (topological) subgroups is trivial. But already for the
countably infinite power Z^N of Z, the situation is different. Here the product
topology is nontrivial, and the subgroups of Z^N make a rich source of examples
of non-isomorphic topological groups. Z^N is the Baer-Specker group.
We study subgroups of the Baer-Specker group which possess group theoretic
properties analogous to properties introduced by Menger (1924), Hurewicz
(1925), Rothberger (1938), and Scheepers (1996). The studied properties were
introduced independently by Ko\v{c}inac and Okunev. We obtain purely
combinatorial characterizations of these properties, and combine them with
other techniques to solve several questions of Babinkostova, Ko\v{c}inac, and
Scheepers.Comment: To appear in IJ
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