Topics on Combinatorial Semigroups
Description
By combinatorial semigroups, we mean a general term of concepts, facts and methods which are produced in investigating of algebraic and combinatorial properties, constructions, classifications and interrelations of formal languages and automata, codes, finite and infinite words by using semigroup theory and combinatorial analysis. The main research objects in this field are the elements and subsets of the free semigroups and monoids and many combinatorial properties of these objects, which are closely related to algebraic theory of semigroups.
This book first introduces some basic concepts and notations in combinatorial semigroups. Since many contents involving the constructions of (generalized) disjunctive languages and regular languages are closely related to the algebraic theory of codes, some selected topics are introduced in the following chapter, including the method of defining codes by using dependence systems, the maximality and completeness of codes, and the detailed discussion of some special kinds of codes such as convex codes, semaphore codes and solid codes. Then the remaining chapters present the main topics of the book - regular languages, disjunctive languages, and their various kinds of generalizations.
This book might be useful to researchers in mathematics who are interested in combinatorial semigroups.
Reviews / Votes
"The organizational structure of the present book is highly methodical and it consists of eight chapters. . Throughout the book, the authors nicely elaborate and sketch all the theories and methodologies with suitable examples. Moreover, at the end of the book, a brief bibliographical account of relevant references and also an index are nicely incorporated." (Sanjib Kumar Datta, zbMATH 1548.20001, 2024)
More details
Other editions
Additional editions
Persons
Prof. Yun Liu graduated from Sun Yat-sen University in 2006. He has worked in Department of Mathematics of Yuxi Normal University since July 2003 and was promoted to Professor in 2012. Now he is a Young and Middle-aged Academic and Technical Leader of Yunnan and Yuxi, a member of the Mathematics Teaching Steering Committee of Yunnan colleges and universities, a director of Mathematics Society of Yunnan, an executive director of Applied Statistics Society of Yunnan. He has presided two projects of National Natural Science Foundation of China and published more than twenty academic papers.
Prof. Shoufeng Wang graduated from Southwest University in 2010. He has worked in Schoolof Mathematics of Yunnan Normal University since July 2005 and was promoted to Professor in 2017. He has presided three projects of National Natural Science Foundation of China and published more than 40 academic papers. He has been a master supervisor of Yunnan Normal University since 2014.
Content
Preface.- Basic Concepts and Notations.- Some Common-Used Codes.- Regular Languages.- Disjunctive Languages.- F-Disjunctive Languages.- Relatively Disjunctive (Regular) Languages.- Generalized Disjunctive Languages.- PS-Regular Languages.
