scholarly journals Formations of finite monoids and formal languages: Eilenberg's variety theorem revisited

2014 ◽  
Vol 26 (6) ◽  
Author(s):  
Adolfo Ballester-Bolinches ◽  
Jean-Éric Pin ◽  
Xaro Soler-Escrivà

AbstractWe present an extension of Eilenberg's variety theorem, a well-known result connecting algebra to formal languages. We prove that there is a bijective correspondence between formations of finite monoids and certain classes of languages, the formations of languages. Our result permits to treat classes of finite monoids which are not necessarily closed under taking submonoids, contrary to the original theory. We also prove a similar result for ordered monoids.

2021 ◽  
Author(s):  
Yongbing Wang ◽  
Lixia Zhang

Abstract Algrbraic properties and structures of intuitionistic L -fuzzy multiset finite automata (ILFMA) are discussed through congruences on a semigroup in this paper. Firstly,we put forward the notion of the intuitionistic L -fuzzy compatible relation, the compatible monoid associated to the intuitionistic L- fuzzy compatible relation can be effectively constructed, and we construct two finite monoids through two different congruence relations on a given ILFMA, then we also prove that they are isomorphic. Furthermore, using the quotient structure of ILFMA, algebraic properties of intuitionistic L -fuzzy multiset transformation semigroup are discussed. According to intuitionistic L -admissible relation and homomorphism of ILFMA, we show that there is a bijective correspondence between an ILFMA and the quotient structure of another ILFMA.


1994 ◽  
Vol 04 (03) ◽  
pp. 375-403 ◽  
Author(s):  
JORGE ALMEIDA ◽  
PASCAL WEIL

In this paper we investigate certain notions from the theory of free profinite groups, which we then apply to the study of certain pseudovarieties of monoids. More precisely, the profinite Cayley graphs of the free pro-H groups are H-trees for certain, so-called arborescent, pseudovarieties of groups H. For such pseudovarieties, we introduce the notion of reduced factorizations in the free pro-H groups, and we prove that these factorizations enjoy a common refinement property. This property, in turn, is used to compute joins of certain pseudovarieties of monoids with pseudovarieties of groups within the pseudovariety DS of all finite monoids in which each regular [Formula: see text]-class is a subsemigroup. We then apply our results to the theory of formal languages.


Author(s):  
Nicholas Owen

Other People’s Struggles is the first attempt in over forty years to explain the place of “conscience constituents” in social movements. Conscience constituents are people who participate in a movement but do not stand to benefit if it succeeds. Why do such people participate when they do not stand to benefit? Why are they sometimes present and sometimes absent in social movements? Why and when is their participation welcome to those who do stand to benefit, and why and when is it not? The work proposes an original theory to answer these questions, crossing discipline boundaries to draw on the findings of social psychology, philosophy, and normative political theory, in search of explanations of why people act altruistically and what it means to others when they do so. The theory is illustrated by examples from British history, including the antislavery movement, the women’s suffrage and liberation movements, labor and socialist movements, anticolonial movements, antipoverty movements, and movements for global justice. Other People’s Struggles also contributes to new debates concerning the rights and wrongs of “speaking for others.” Debates concerning the limits of solidarity—who can be an “ally” and on what terms—have become very topical in contemporary politics, especially in identity politics and in the new “populist” movements. The book provides a theoretical and empirical account of how these questions have been addressed in the past and how they might be framed today.


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.


2020 ◽  
Author(s):  
Haiyan Wang

Abstract This article develops Karl Mannheim’s theory of generations as a tool to analyze the profound changes that journalism is experiencing in the mainland of China. The article begins with a discussion of generational theory. It demonstrates that the development of critical journalism that occurred in the late 1990s and early 2000s was the result of a unique combination of circumstances. A range of factors, including the introduction of digital technologies and shifts in the political atmosphere, have restricted that kind of journalism. Young people entering journalism today confront different circumstances and their resultant views, as well as their journalistic activities, are significantly different, and less engaged, than those of their seniors. The article concludes by discussing the theoretical modifications which are essential to make the original theory more suitable for contemporary conditions.


Histories ◽  
2021 ◽  
Vol 1 (3) ◽  
pp. 108-121
Author(s):  
Satoshi Murayama ◽  
Hiroko Nakamura

Jan de Vries revised Akira Hayami’s original theory of the “Industrious Revolution” to make the idea more applicable to early modern commercialization in Europe, showcasing the development of the rural proletariat and especially the consumer revolution and women’s emancipation on the way toward an “Industrial Revolution.” However, Japanese villages followed a different path from the Western trajectory of the “Industrious Revolution,” which is recognized as the first step to industrialization. This article will explore how a different form of “industriousness” developed in Japan, covering medieval, early modern, and modern times. It will first describe why the communal village system was established in Japan and how this unique institution, the self-reliance system of a village, affected commercialization and industrialization and was sustained until modern times. Then, the local history of Kuta Village in Kyô-Otagi, a former county located close to Kyoto, is considered over the long term, from medieval through modern times. Kuta was not directly affected by the siting of new industrial production bases and the changes brought to villages located nearer to Kyoto. A variety of diligent interactions with living spaces is introduced to demonstrate that the industriousness of local women was characterized by conscience-driven perseverance.


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