Clusters of repetition roots: single chains (Algebraic system, Logic, Language and Related Areas in Computer Sciences II)

This work proposes a new approach towards solving an over 20 years old conjecture regarding the maximum number of distinct squares that a word can contain. To this end we look at clusters of repetition roots, that is, the set of positions where the root u of a repetition u^[l] occurs. We lay the foundation of this theory by proving basic properties of these clusters and establishing upper bounds on the number of distinct squares when their roots form a chain with respect to the prefix order

Sweep Complexity Revisited

We study the sweep complexity of DFA in one-way jumping mode answering several questions posed earlier. This measure is the number of times in the worst case that such machines have to return to the beginning of their input after having skipped some of the symbols. The class of languages accepted by these machines strictly includes the regular class and constant sweep complexity allows exactly the acceptance of regular languages. However, we show that there exist machines with higher than constant complexity still only accepting regular languages and that in general the sweep complexity of an automaton does not distinguish between accepting regular and non-regular languages. We establish separation results for asymptotic classes defined by this complexity measure and give a surprising exponential/logarithmic relation between factors of certain inputs which can be verified by such machines.Comment: 12 pages, 8 figure

Freezing 1-Tag Systems with States

We study 1-tag systems with states obeying the freezing property that only allows constant bounded number of rewrites of symbols. We look at examples of languages accepted by such systems, the accepting power of the model, as well as certain closure properties and decision problems. Finally we discuss a restriction of the system where the working alphabet must match the input alphabet.Comment: In Proceedings AFL 2023, arXiv:2309.0112

An Experiment with Ant Colony Optimization for Edge Detection in Images (Algebras, logics, languages and related areas)

Ant colony optimization (ACO) is a simulation of the natural behavior of ant species; where ants find the shortest path between its nest and food source. Image edge detection is a basic image processing task, where the outlines of the objects in an image are identified, and then extracted. We present the results of an experiment conducted with the ACO algorithm applied to the edge detection problem

Absztrakt automaták és formális nyelvek = Abstract Automata and Formal Languages

Monográfiában foglaltuk össze a véges automata hálózatok elméletének alapvető eredményeit . Megadtuk a Leticsevszkij kritérium nélküli automata-hálózatok egy új jellemzését. Megadtunk bizonyos szimbólum osztályokkal ellátott többszalagos automatákat. Megadtuk és vizsgáltuk a kutatásaink során felfedezett automataelméleti elvű új titkosítási rendszert. Új bizonyítást adtunk a Lyndon-Schützenberger tételre és a Shyr-Yu tételre. Általánosítottuk a szavak primitivitásának, illetve periodicitásának fogalmát, s megadtuk, hogy melyek azok a Marcus nyelvtanok, amelyek az adott típusú szavakból álló nyelveket képesek generálni. Sikerült találni egy iterációs lemmát azon környezetfüggetlen nyelvekre, melyek nem lineárisak. A contextuális sztringnyelvek általánosításaként bevezettük és vizsgáltuk a hypergráf contextuális nyelvek és nyelvtanok fogalmát. Automaták segítségével jellemeztük az uniómentes nyelveket. Leírtuk a különféle logikai kalkulusok és valamely levezetési rendszer szabályai szerint megadott levezetések kapcsolatait, s a különféle kalkulusok normalizálhatósági tulajdonságait. Új elvű számítási kutatásainkban az intervallum-értékű számításokat, mint új számítási modellt írtuk le. Digitális geometriai kutatásainkban digitális távolság alapján értelmezett szakaszokat, köröket, hiperbolákat és parabolákat vizsgáltunk. | We summarized in monograph the fundamental results of theory of finite automata networks. We gave a new characterization of automata-networks having no Letichevsky criteria. We gave multi-tape automata supplied by certain symbol classes. We gave and investigated a novel cryptosystem based on automata theory discovered during our research.. We gave a new proof of Lyndon-Schützenberger Theorem and Shyr-Yu Theorem. We generalized the concept of primitivity and periodicity of words and we give the Marcus gramars which are able to generate languages consisting of given type words. It succeed in finding an iteration lemma for non-linear context-free languages. As a generalization of contextual string languages, we introduced and investigated the concept of hypergraph contextual grammars and languages. We characterized the union-free languages by automata. We described the connections of derivations given by various logical calculi and certain derivation system, moreover the normalizable properties of various calculi. In our new computation principle researches we described the intervallum-value computations as new computation model In our digital geometric researches we investigated the sessions, circles, hyperbolas and parabolas defined by a digital distance

Sweep complexity revisited

We study the sweep complexity of DFA in one-way jumping mode answering several questions posed earlier. This measure is the number of times in the worst case that such machines have to return to the beginning of their input after having skipped some of the symbols. The class of languages accepted by these machines strictly includes the regular class and constant sweep complexity allows exactly the acceptance of regular languages. However, we show that there exist machines with higher than constant complexity still only accepting regular languages and that in general the sweep complexity of an automaton does not distinguish between accepting regular and non-regular languages. We establish separation results for asymptotic classes defined by this complexity measure and give a surprising exponential/logarithmic relation between factors of certain inputs which can be verified by such machines.</p

Firefly Algorithm for Uncapacitated Facility Location Problem and Number of Fireflies (Developments of Language, Logic, Algebraic system and Computer Science)

We apply the firefly algorithm to the uncapacitatcd facility location problem which is one of optimization problems and investigate the optimum number of the fireflies. The light absorption coefficient parameter $gamma$ of the firefly algorithm is examined to obtain better performance and suitable values of $gamma$ are explored for the uncapacitated facility location problem. Effectiveness of local search in the firefly algorithm is also investigated. In addition, we investigate the optimum number of fireflies for the firefly algorithm

Number of occurrences of powers in strings

We show a Θ(nlog n) bound on the maximal number of occurrences of primitively-rooted k-th powers occurring in a string of length n for any integer k, k ≥ 2. We also show a Θ(n²) bound on the maximal number of primitively-rooted powers with fractional exponent e, 1 &lt; e &lt; 2, occurring in a string of length n. This result holds obviously for their maximal number of occurrences. The first result contrasts with the linear number of occurrences of maximal repetitions of exponent at least 2