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Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 1
Author(s):  
Štěpán Křehlík ◽  
Michal Novák ◽  
Jana Vyroubalová

In this paper, we study two important problems related to quasi-multiautomata: the complicated nature of verification of the GMAC condition for systems of quasi-multiautomata, and the fact that the nature of quasi-multiautomata has deviated from the original nature of automata as seen by the theory of formal languages. For the former problem, we include several new conditions that simplify the procedure. For the latter problem, we close this gap by presenting a construction of quasi-multiautomata, which corresponds to deterministic automata of the theory of formal languages and is based on the operation of concatenation.


2021 ◽  
Vol volume 13, issue 2 ◽  
Author(s):  
Arman Darbinyan ◽  
Rostislav Grigorchuk ◽  
Asif Shaikh

For finitely generated subgroups $H$ of a free group $F_m$ of finite rank $m$, we study the language $L_H$ of reduced words that represent $H$ which is a regular language. Using the (extended) core of Schreier graph of $H$, we construct the minimal deterministic finite automaton that recognizes $L_H$. Then we characterize the f.g. subgroups $H$ for which $L_H$ is irreducible and for such groups explicitly construct ergodic automaton that recognizes $L_H$. This construction gives us an efficient way to compute the cogrowth series $L_H(z)$ of $H$ and entropy of $L_H$. Several examples illustrate the method and a comparison is made with the method of calculation of $L_H(z)$ based on the use of Nielsen system of generators of $H$.


2021 ◽  
Vol volume 13, issue 2 ◽  
Author(s):  
Arman Darbinyan ◽  
Rostislav Grigorchuk ◽  
Asif Shaikh

For finitely generated subgroups $H$ of a free group $F_m$ of finite rank $m$, we study the language $L_H$ of reduced words that represent $H$ which is a regular language. Using the (extended) core of Schreier graph of $H$, we construct the minimal deterministic finite automaton that recognizes $L_H$. Then we characterize the f.g. subgroups $H$ for which $L_H$ is irreducible and for such groups explicitly construct ergodic automaton that recognizes $L_H$. This construction gives us an efficient way to compute the cogrowth series $L_H(z)$ of $H$ and entropy of $L_H$. Several examples illustrate the method and a comparison is made with the method of calculation of $L_H(z)$ based on the use of Nielsen system of generators of $H$.


2021 ◽  
Vol 22 (4) ◽  
pp. 1-48
Author(s):  
Jiří Adámek ◽  
Liang-Ting Chen ◽  
Stefan Milius ◽  
Henning Urbat

Profinite equations are an indispensable tool for the algebraic classification of formal languages. Reiterman’s theorem states that they precisely specify pseudovarieties, i.e., classes of finite algebras closed under finite products, subalgebras and quotients. In this article, Reiterman’s theorem is generalized to finite Eilenberg-Moore algebras for a monad  T on a category  D: we prove that a class of finite T -algebras is a pseudovariety iff it is presentable by profinite equations. As a key technical tool, we introduce the concept of a profinite monad T ^ associated to the monad T , which gives a categorical view of the construction of the space of profinite terms.


Semiotica ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Vern S. Poythress

Abstract This article uses tagmemic theory as a semiotic framework to analyze symbolic logic. It attends particularly to the issue of context for meaning and the role of personal observer/participants. It focuses on formal languages, which employ no ordinary words and from one point of view have “no meaning.” Attention to the context and the theorists who deploy these languages shows that formal languages have meanings at a higher level, colored by the purposes of the analysts. In fact, there is an indefinitely ascending hierarchy of theories of theories, each of which analyzes and evaluates the theories at a lower level. By analogy with Kurt Gödel’s incompleteness theory, no level of the hierarchy can capture within formalism everything in a sufficiently complex system. The personal analysts always have to make judgments about how a formalized system is analogous to the world outside the system. Arguments in analytic philosophy can be useful in clarification, but neither clarification of terms nor clarification of the structure of arguments can eliminate the need for personal judgment.


Author(s):  
Vitalii Statkevych

We consider a Petri net for the producer/consumer problem (one of the classical synchronization problems) with the bounded buffer of size n and the regular formal languages Ln, generated by the net. The objective of this paper is to obtain a regular expression for the set difference of languages Ln \ Lm, n > m. For this purpose, we give the finite automaton which accepts the set difference of mentioned languages, and then we use the state elimination method to obtain the regular expression in the recursive form. The main result is illustrated by the examples. In an appendix, we consider the problem with two producers and two consumers with the bounded buffer of size 1. We give a reachability graph and propose the method for obtaining the regular expression. The explicit formulas are given for the problem with two producers and one consumer and also for the problem with one producer and two consumers.


2021 ◽  
Vol 25 (4) ◽  
pp. 13-22
Author(s):  
A. P. Sergushicheva ◽  
E. N. Davydova

This study aimed ro describe and determine the characteristic patterns and the word formation process of various language terms used in tourism advertisements on digital media during the COVID-19 pandemic. There are several new terms that are widely used by people all over the globe, and tourism adevertisements are no excpetion. This study used descriptive qualitative method. The data were taken from advertisements found on social media Facebook and Instagram. The thoery used in this research is the theory of language style proposed by Chaer & Agustina (2010) and theory of word formation process by Chaer (2008). It can be concluded that: (1) the characteristic pattern of the variety of languages used in tourism advertisements on social media Facebook and Instagram during the COVID-19 pandemic is a variety of non-formal languages, and (2) the variety of terms used tourism advertisements on social media Facebook and Instagram during the COVID-19 pandemic are formed from blending, abbreviations and compounding. Keywords: Language Varieties, Terms, Advertisement, COVID-19


AI Matters ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 14-17
Author(s):  
Li Dong

Language is the primary and most natural means of communication for humans. The learning curve of interacting with various services (e.g., digital assistants, and smart appliances) would be greatly reduced if we could talk to machines using human language. However, in most cases computers can only interpret and execute formal languages.


2021 ◽  
Vol 180 (1-2) ◽  
pp. 151-177
Author(s):  
Qichao Wang

Weighted restarting automata have been introduced to study quantitative aspects of computations of restarting automata. In earlier works we studied the classes of functions and relations that are computed by weighted restarting automata. Here we use them to define classes of formal languages by restricting the weight associated to a given input word through an additional requirement. In this way, weighted restarting automata can be used as language acceptors. First, we show that by using the notion of acceptance relative to the tropical semiring, we can avoid the use of auxiliary symbols. Furthermore, a certain type of word-weighted restarting automata turns out to be equivalent to non-forgetting restarting automata, and another class of languages accepted by word-weighted restarting automata is shown to be closed under the operation of intersection. This is the first result that shows that a class of languages defined in terms of a quite general class of restarting automata is closed under intersection. Finally, we prove that the restarting automata that are allowed to use auxiliary symbols in a rewrite step, and to keep on reading after performing a rewrite step can be simulated by regular-weighted restarting automata that cannot do this.


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