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Several variants of the Dumont differential system and permutation statistics

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Science China Mathematics 2019年第10期62卷 2033-2052页

作者： Shi-Mei Ma Toufik Mansour David GLWang Yeong-Nan Yeh School of Mathematics and Statistics Northeastern University at QinhuangdaoQinhuangdao066000 Department of Mathematics University of HaifaHaifa3498838 School of Mathematics and Statistics Beijing Institute of TechnologyBeijing102488 Institute of Mathematics Academia SinicaTaipei10617

The Dumont differential system on the Jacobi elliptic functions was introduced by Dumont(1979)and was extensively studied by Dumont, Viennot, Flajolet and so on. In this paper, we first present a labeling scheme for the cycle structure of permutations. We then introduce two types of Jacobi pairs of differential equations. We present a general method to derive the solutions of these differential equations. As applications,we present some characterizations for several permutation statistics.

关键词： Jacobi elliptic functions Dumont differential system permutation statistics context-free grammars

A complexity analysis of the elementary cellular automaton of rule 122

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Chinese Science Bulletin 2001年第7期46卷 600-603页

作者： JIANG ZhisongMathematics Department, Suzhou University, Suzhou 215006, China Mathematics Department Suzhou University Suzhou China

S. Wolfram initiated the use of formal languages and automata theory in study of cellular automata (CAs). By means of extensive experiments with computer, he classified all CAs into four classes and conjectured that the limit languages of the third class of CAs, which produce chaotic aperiodic behavior, are not regular. Using symbolic dynamics and formal languages, we prove that the limit language of the elementary CA of rule 122 is neither regular nor context-free.

关键词： cellular automaton formal language complexity limit language regular language context-free language.

LR(K) Parser Construction Using Bottom-up Formal Analysis

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Journal of Software Engineering and Applications 2012年第1期5卷 21-28页

作者： Nazir Ahmad Zafar 不详

Design and construction of an error-free compiler is a difficult and challenging process. The main functionality of a compiler is to translate a source code to an executable machine code correctly and efficiently. In formal verification of software, semantics of a language has more meanings than the syntax. It means source program verification does not give guarantee the generated code is correct. This is because the compiler may lead to an incorrect target program due to bugs in itself. It means verification of a compiler is much more important than verification of a source program. In this paper, we present a new approach by linking context-free grammar and Z notation to construct LR(K) parser. This has several advantages because correctness of the compiler depends on describing rules that must be written in formal languages. First, we have defined grammar then language derivation procedure is given using right-most derivations. Verification of a given language is done by recursive procedures based on the words. Ambiguity of a language is checked and verified. The specification is analyzed and validated using Z/Eves tool. Formal proofs are presented using powerful techniques of reduction and rewriting available in Z/Eves.

关键词： Compiler Construction LR(K) Parser context-free Grammar Z Specification Correctness Verification

A Grammatical Approach of Multi-Localization of GUIs: Application to the Multi-Localization of the Checkers Game GUI

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Journal of Software Engineering and Applications 2018年第11期11卷 552-567页

作者： Maurice Tchoupé Tchendji Freddy-Viany Tatou Ahoukeng Department of Mathematics and Computer Science Faculty of Sciences University of Dschang Dschang Cameroon

By proposing tools that help for the accomplishment of tasks in almost all sectors of activities, computer science has revolutionized the world in a general way. Nowadays, it addresses the peculiarities of peoples through their culture in order to produce increasingly easy-to-use software for end users: This is the aim of software localization. Localizing a software consists among other things, in adapting its GUI according to the end user culture. We propose in this paper a generic approach allowing accomplishing this adaptation, even for multi-user applications like gaming applications, collaborative editors, etc. Techniques of functional interpretations of abstracts structures parameterized by algebras, constitute the formal base of our approach.

关键词： GUIs context-free Grammars Multi-Localization Abstract Syntax Tree and Its Interpretations XML GUI Description Language Haskell

Interrelation of Languages of Colored Petri Nets and Some Traditional Languages

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Open Journal of Modelling and Simulation 2013年第3期1卷 27-29页

作者： Goharik R. Petrosyan Andrey M. Avetisyan Lilit A. Ter-Vardanyan Faculty of Mathematics Physics and Informatics Armenian State Pedagogical University after Kh. Abovyan Yerevan Armenia Seismology Institute of Geophysics and Engineering Seismology after A. Nazarov of NAS RA Gyumri Armenia

The article studies the interrelation of Languages of Colored Petri Nets and Traditional formal languages. The author constructed the graph of Colored Petri Net, which generates L* context-free language. This language may not be modeled using standard Petri Nets [1]. The Venn graph and diagram that the author modified [1], show the interrelation between languages of Colored Petri Nets and some Traditional languages. Thus the class of languages of Colored Petri Nets is supposed to include an entire class of context-free languages.

关键词： Petri Nets Colored Petri Nets context-free Languages context-Sensitive Languages Regular Languages