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 t...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.展开更多
To cope with the problem of emitter identification caused by the radar words＇ uncertainty of measured multi-function radar emitters, this paper proposes a new identification method based on stochastic syntax-directed...To cope with the problem of emitter identification caused by the radar words＇ uncertainty of measured multi-function radar emitters, this paper proposes a new identification method based on stochastic syntax-directed translation schema（SSDTS）. This method, which is deduced from the syntactic modeling of multi-function radars, considers the probabilities of radar phrases appearance in different radar modes as well as the probabilities of radar word errors occurrence in different radar phrases. It concludes that the proposed method can not only correct the defective radar words by using the stochastic translation schema, but also identify the real radar phrases and working modes of measured emitters concurrently. Furthermore, a number of simulations are presented to demonstrate the identification capability and adaptability of the SSDTS algorithm.The results show that even under the condition of the defective radar words distorted by noise,the proposed algorithm can infer the phrases, work modes and types of measured emitters correctly.展开更多
A formal-linguistic approach for solving an entertaining task is offered in this paper. The well-known task of the Hanoi towers is discussed in relation to some concepts of formal languages and grammars. A context-fre...A formal-linguistic approach for solving an entertaining task is offered in this paper. The well-known task of the Hanoi towers is discussed in relation to some concepts of formal languages and grammars. A context-free grammar which generates an algorithm for solving this task is described. A deterministic pushdown automation which in its work imitates the work of monks in solving the task of the Hanoi towers is built.展开更多
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...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.展开更多
A type checking method for the functional language LFC is presented. A distinct feature of LFC is that it uses Context-Free (CF) languages as data types to represent compound data structures. This makes LFC a dynamica...A type checking method for the functional language LFC is presented. A distinct feature of LFC is that it uses Context-Free (CF) languages as data types to represent compound data structures. This makes LFC a dynamically typed language. To improve efficiency, a practical type checking method is presented, which consists of both static and dynamic type checking. Although the inclusion relation of CF languages is not decidable, a special subset of the relation is decidable, i.e., the sentential form relation, which can be statically checked. Moreover, most of the expressions in actual LFC programs appear to satisfy this relation according to the statistic data of experiments. So, despite that the static type checking is not complete, it undertakes most of the type checking task. Consequently the run-time efficiency is effectively improved. Another feature of the type checking is that it converts the expressions with implicit structures to structured representation. Structure reconstruction technique is presented.展开更多
A Function Definition Language (FDL) is presented. Though de-signed for describing specifications, FDL is also a general-purpose functional pro-gramming language. It uses context-free language as data type, supports p...A Function Definition Language (FDL) is presented. Though de-signed for describing specifications, FDL is also a general-purpose functional pro-gramming language. It uses context-free language as data type, supports patternmatching definition of functions, offers several function definition forms, and is exe-cutable. It is shown that FDL has strong expressiveness, is easy to use and describesalgorithms concisely and naturally. An interpreter of FDL is introduced. Experi-ments and discussion are included.展开更多
LFC is a functional language based on recursive functions defined in context-free languages. In this paper, a new pattern matching algorithm for LFC is presented, which can represent a sequence of patterns as an integ...LFC is a functional language based on recursive functions defined in context-free languages. In this paper, a new pattern matching algorithm for LFC is presented, which can represent a sequence of patterns as an integer by an encoding method. It is a rather simple method and produces efficient case-expressions for pattern matching definitions of LFC. The algorithm can also be used for other functional languages, but for nested patterns it may become complicated and further studies are needed.展开更多
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 thr...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.展开更多
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 t...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.展开更多
We consider context-free grammars of the form G = {f → f^b1＋b2＋1g^a1＋a2, g → f^b1 g^a1＋1},where ai and bi are integers sub ject to certain positivity conditions. Such a grammar G gives rise to triangular arrays...We consider context-free grammars of the form G = {f → f^b1＋b2＋1g^a1＋a2, g → f^b1 g^a1＋1},where ai and bi are integers sub ject to certain positivity conditions. Such a grammar G gives rise to triangular arrays {T（n, k）}0≤k≤n satisfying a three-term recurrence relation. Many combinatorial sequences can be generated in this way. Let Tn （x） =∑k=0^n T（n, k）x^k. Based on the differential operator with respect to G, we define a sequence of linear operators Pn such that Tn＋1（x） = Pn（Tn（x））. Applying the characterization of real stability preserving linear operators on the multivariate polynomials due to Borcea and Br？ndén, we obtain a necessary and sufficient condition for the operator Pn to be real stability preserving for any n. As a consequence, we are led to a sufficient condition for the real-rootedness of the polynomials defined by certain triangular arrays, obtained by Wang and Yeh.Moreover, as special cases we obtain grammars that lead to identities involving the Whitney numbers and the Bessel numbers.展开更多
Stochastic context-free grammars （SCFGs） have been applied to predicting RNA secondary structure. The prediction of RNA secondary structure can be facilitated by incorporating with comparative sequence analysis. How...Stochastic context-free grammars （SCFGs） have been applied to predicting RNA secondary structure. The prediction of RNA secondary structure can be facilitated by incorporating with comparative sequence analysis. However, most of existing SCFG-based methods lack explicit phylogenic analysis of homologous RNA sequences, which is probably the reason why these methods are not ideal in practical application. Hence, we present a new SCFG-based method by integrating phylogenic analysis with the newly defined profile SCFG. The method can be summarized as： 1） we define a new profile SCFG, M, to depict consensus secondary structure of multiple RNA sequence alignment; 2） we introduce two distinct hidden Markov models, λ and λ＇, to perform phylogenic analysis of homologous RNA sequences. Here, λ＇ is for non-structural regions of the sequence and λ＇ is for structural regions of the sequence; 3） we merge λ and λ＇ into M to devise a combined model for prediction of RNA secondary structure. We tested our method on data sets constructed from the Rfam database. The sensitivity and specificity of our method are more accurate than those of the predictions by Pfold.展开更多
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 ...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.展开更多
In this paper, an interactive learning algorithm of context-free language is presented. This algorithm is designed especially for system SAQ, which is a system for formal specification acquisition and verification. A...In this paper, an interactive learning algorithm of context-free language is presented. This algorithm is designed especially for system SAQ, which is a system for formal specification acquisition and verification. As the kernel of concept acquisition subsystem (SAQ/CL) of SAQ, the algorithm has been implemented on SUN SPARC workstation. The grammar to be obtained can represent sentence structure naturally.展开更多
基金the Special Funds for the Major State Basic Research Projects.
文摘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.
基金supported by the National Natural Science Foundation of China (No. 61002026)
文摘To cope with the problem of emitter identification caused by the radar words＇ uncertainty of measured multi-function radar emitters, this paper proposes a new identification method based on stochastic syntax-directed translation schema（SSDTS）. This method, which is deduced from the syntactic modeling of multi-function radars, considers the probabilities of radar phrases appearance in different radar modes as well as the probabilities of radar word errors occurrence in different radar phrases. It concludes that the proposed method can not only correct the defective radar words by using the stochastic translation schema, but also identify the real radar phrases and working modes of measured emitters concurrently. Furthermore, a number of simulations are presented to demonstrate the identification capability and adaptability of the SSDTS algorithm.The results show that even under the condition of the defective radar words distorted by noise,the proposed algorithm can infer the phrases, work modes and types of measured emitters correctly.
文摘A formal-linguistic approach for solving an entertaining task is offered in this paper. The well-known task of the Hanoi towers is discussed in relation to some concepts of formal languages and grammars. A context-free grammar which generates an algorithm for solving this task is described. A deterministic pushdown automation which in its work imitates the work of monks in solving the task of the Hanoi towers is built.
文摘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.
文摘A type checking method for the functional language LFC is presented. A distinct feature of LFC is that it uses Context-Free (CF) languages as data types to represent compound data structures. This makes LFC a dynamically typed language. To improve efficiency, a practical type checking method is presented, which consists of both static and dynamic type checking. Although the inclusion relation of CF languages is not decidable, a special subset of the relation is decidable, i.e., the sentential form relation, which can be statically checked. Moreover, most of the expressions in actual LFC programs appear to satisfy this relation according to the statistic data of experiments. So, despite that the static type checking is not complete, it undertakes most of the type checking task. Consequently the run-time efficiency is effectively improved. Another feature of the type checking is that it converts the expressions with implicit structures to structured representation. Structure reconstruction technique is presented.
文摘A Function Definition Language (FDL) is presented. Though de-signed for describing specifications, FDL is also a general-purpose functional pro-gramming language. It uses context-free language as data type, supports patternmatching definition of functions, offers several function definition forms, and is exe-cutable. It is shown that FDL has strong expressiveness, is easy to use and describesalgorithms concisely and naturally. An interpreter of FDL is introduced. Experi-ments and discussion are included.
基金the National Natural Science Foundation (No.69873042), the National'863' High-Tech Programme (No. 863- 306- 05-04- 1 ), and th
文摘LFC is a functional language based on recursive functions defined in context-free languages. In this paper, a new pattern matching algorithm for LFC is presented, which can represent a sequence of patterns as an integer by an encoding method. It is a rather simple method and produces efficient case-expressions for pattern matching definitions of LFC. The algorithm can also be used for other functional languages, but for nested patterns it may become complicated and further studies are needed.
文摘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.
基金supported by National Natural Science Foundation of China(Grant No.11401083)Natural Science Foundation of Hebei Province(Grant No.A2017501007)+1 种基金the Fundamental Research Funds for the Central Universities(Grant No.N152304006)Taiwan “National” Science Council(Grant No.104-2115-M-001-010)
文摘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.
基金Supported by the 973 Projectthe PCSIRT Project+1 种基金the Doctoral Program Fund of the Ministry of Educationthe National Science Foundation of China
文摘We consider context-free grammars of the form G = {f → f^b1＋b2＋1g^a1＋a2, g → f^b1 g^a1＋1},where ai and bi are integers sub ject to certain positivity conditions. Such a grammar G gives rise to triangular arrays {T（n, k）}0≤k≤n satisfying a three-term recurrence relation. Many combinatorial sequences can be generated in this way. Let Tn （x） =∑k=0^n T（n, k）x^k. Based on the differential operator with respect to G, we define a sequence of linear operators Pn such that Tn＋1（x） = Pn（Tn（x））. Applying the characterization of real stability preserving linear operators on the multivariate polynomials due to Borcea and Br？ndén, we obtain a necessary and sufficient condition for the operator Pn to be real stability preserving for any n. As a consequence, we are led to a sufficient condition for the real-rootedness of the polynomials defined by certain triangular arrays, obtained by Wang and Yeh.Moreover, as special cases we obtain grammars that lead to identities involving the Whitney numbers and the Bessel numbers.
基金the National Natural Science Foundation of China under Grant No.60673018
文摘Stochastic context-free grammars （SCFGs） have been applied to predicting RNA secondary structure. The prediction of RNA secondary structure can be facilitated by incorporating with comparative sequence analysis. However, most of existing SCFG-based methods lack explicit phylogenic analysis of homologous RNA sequences, which is probably the reason why these methods are not ideal in practical application. Hence, we present a new SCFG-based method by integrating phylogenic analysis with the newly defined profile SCFG. The method can be summarized as： 1） we define a new profile SCFG, M, to depict consensus secondary structure of multiple RNA sequence alignment; 2） we introduce two distinct hidden Markov models, λ and λ＇, to perform phylogenic analysis of homologous RNA sequences. Here, λ＇ is for non-structural regions of the sequence and λ＇ is for structural regions of the sequence; 3） we merge λ and λ＇ into M to devise a combined model for prediction of RNA secondary structure. We tested our method on data sets constructed from the Rfam database. The sensitivity and specificity of our method are more accurate than those of the predictions by Pfold.
文摘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.
基金Supported by the National "863" Hi-Tech Programme and the National Natural Science Foundation of China, and the National 'Ninth-
文摘In this paper, an interactive learning algorithm of context-free language is presented. This algorithm is designed especially for system SAQ, which is a system for formal specification acquisition and verification. As the kernel of concept acquisition subsystem (SAQ/CL) of SAQ, the algorithm has been implemented on SUN SPARC workstation. The grammar to be obtained can represent sentence structure naturally.
