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1
Content available remote Dwa spojrzenia na nieskończoność
Samulewicz Alicja, Starosolski Andrzej
MINUT Matematyka i Informatyka na Uczelniach Technicznych
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2021
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Nr 3
52-60
PL
Z nieskończonością spotykamy się bardzo często w wielu działach matematyki. Celem tego artykułu jest przybliżenie Czytelnikowi, czym właściwie jest ta nieskończoność, a raczej czym są te nieskończoności.
2
Content available remote A New Proof for Undecidability of the Bi-Infinite Post Correspondence Problem
Halava V., Harju T., Sahla E.
Fundamenta Informaticae
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2017
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Vol. 154, nr 1/4
167--176
EN
We give a new simplified proof for undecidability of the Bi-Infinite Post Correspondence Problem (ℤPCP). We reduce the special case of the word problem of semi-Thue systems to ℤPCP.
3
Content available remote The paths of mathematics in Lithuania: bishop Baranauskas (1835‒1902) and his research in number theory
Banionis J., Marchertaitė J.
Czasopismo Techniczne. Nauki Podstawowe
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2015
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Y. 112, iss. 2-NP
5--12
EN
Bishop Antanas Baranauskas is a prominent personality in the history of the Lithuanian culture. He is well known not only as a profound theologian, a talented musician creating hymns, a literary classicist and an initiator of Lithuanian dialectology, but also as a distinguished figure in the science of mathematics. The author of this article turns his attention to the mathematical legacy of this prominent Lithuanian character and aspires to reveal the circumstances that encouraged bishop Antanas Baranauskas to undertake research in mathematics, to describe the influence of his achievements in the science of mathematics, to show the incentives that encouraged him to pursue mathematical research in Lithuania as well as to emphasize his search for a connection between mathematics and theology.
PL
Biskup Antoni Baranowski (Antanas Baranauskas) należy do prominentnych osobistości w historii kultury litewskiej. Znany jest jako istotny teolog, utalentowany muzyk tworzący hymny, literacki klasyk i inicjator dialektologii Litwy; zajmował się również matematyką. W artykule przedstawiono okoliczności, w związku z którymi biskup A. Baranowski zajął się badaniami matematycznymi. Zarysowane zostało znaczenie jego wyników w rozwoju badań matematycznych na Litwie. Podkreślono również związki pomiędzy matematyką i teologią.
4
Content available Persistent Sequences with Effective Random Access and Support for Infinity
Grzanek K.
Journal of Applied Computer Science Methods
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2014
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Vol. 6 No. 1
67--80
EN
Persistent sequences are the core data structure in functional programming style. Their typical implementations usually allow creating infinite streams of objects. Unfortunately, asking for length of an infinite data structure never ends or ends with a run-time error. Similarly, there is no default way to make an effective, O[1] or logarithmic access to an arbitrarily chosen sequence element, even when the nature of the correlation between index value and the sequence element is known. This paper presents a Clojure library that meets these limitations and offers an enhanced version of sequences with a support for effective random access and the ability to ask for an infinite length.
5
Content available remote Probabilistic Constructions of Computable Objects and a Computable Version of Lovász Local Lemma
Rumyantsev A., Shen A.
Fundamenta Informaticae
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2014
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Vol. 132, nr 1
1--14
EN
A nonconstructive proof can be used to prove the existence of an object with some properties without providing an explicit example of such an object. A special case is a probabilistic proof where we show that an object with required properties appears with some positive probability in some random process. Can we use such arguments to prove the existence of a computable infinite object? Sometimes yes: following [8], we show how the notion of a layerwise computable mapping can be used to prove a computable version of Lovász local lemma.
6
Content available remote Epichristoffel Words and Minimization of Moore Automata
Castiglione G., Sciortino M.
Fundamenta Informaticae
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2014
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Vol. 134, nr 3/4
319--333
EN
This paper is focused on the connection between the combinatorics of words and minimization of automata. The three main ingredients are the epichristoffel words, Moore automata and a variant of Hopcroft’s algorithm for their minimization. Epichristoffel words defined in [14] generalize some properties of circular sturmian words. Here we prove a factorization property and the existence of the reduction tree, that uniquely identifies the structure of the word. Furthermore, in the paper we investigate the problem of the minimization of Moore automata by defining a variant of Hopcroft’s minimization algorithm. The use of this variant makes simpler the computation of the running time and consequently the study of families of automata that represent the extremal cases of the minimization process. Indeed, such a variant allows to use the above mentioned factorization property of the epichristoffel words and their reduction trees in order to find an infinite family of Moore automata such that the execution of the algorithm is uniquely determined and tight.
7
Content available remote Checking MTL Properties of Discrete Timed Automata via Bounded Model Checking
Woźna-Szcześniak B., Zbrzezny A.
Fundamenta Informaticae
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2014
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Vol. 135, nr 4
553--568
EN
We investigate a SAT-based bounded model checking (BMC) method for MTL (metric temporal logic) that is interpreted over linear discrete infinite time models generated by discrete timed automata. In particular, we translate the existential model checking problem for MTL to the existential model checking problem for a variant of linear temporal logic (called HLTL), and we provide a SAT-based BMC technique for HLTL. We show how to implement the BMC technique for HLTL and discrete timed automata, and as a case study we apply the technique in the analysis of GTPP, a Generic Timed Pipeline Paradigm modelled by a network of discrete timed automata.
8
Content available remote Reachable sets concept - a general abstract analysis
Terlikowski T.
Control and Cybernetics
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2003
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Vol. 32, no 4
803-817
EN
A control problem over the infinite time horizon for periodical system is considered. Our aim is to analyze a special concept of solving problems of this type, based on the known idea of reachable sets. We try to consider this concept in a more general manner than it was done in earlier works and to find what is really essential in it. The algorithm corresponding to the proposed general description is presented.
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