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AN APPLICATION OF FIRST-ORDER LOGIC TO THE STUDY OF RECOGNIZABLE LANGUAGES

PEDRO V. SILVA
2004 International journal of algebra and computation  
A variation of first-order logic with variables for exponents is developed to solve some problems in the setting of recognizable languages on the free monoid, accommodating operators such as product, bounded  ...  Restricting the operators to powers and product, analogous results are obtained for recognizable languages of an arbitrary finitely generated monoid M .  ...  by the European Comunity fund FEDER.  ... 
doi:10.1142/s0218196704001906 fatcat:e5dopznn3ze6tjmtvn2smqrwfa

Monadic Second-Order Logic for Graphs: Algorithmic and Language Theoretical Applications [chapter]

Bruno Courcelle
2009 Lecture Notes in Computer Science  
This tutorial will present an overview of the use of Monadic Second-Order Logic to describe sets of finite graphs and graph transformations, in relation with the notions of tree-width and clique-width.  ...  It will review applications to the construction of algorithms, to Graph Theory and to the extension to graphs of Formal Language Theory concepts.  ...  We first explain the role of Logic.  ... 
doi:10.1007/978-3-642-00982-2_2 fatcat:ryjvoaa7dnefrcruygfnpqso2i

MK-fuzzy Automata and MSO Logics

Manfred Droste, Temur Kutsia, George Rahonis, Wolfgang Schreiner
2017 Electronic Proceedings in Theoretical Computer Science  
We introduce an MK-fuzzy MSO logic and show the expressive equivalence of a fragment of this logic with MK-fuzzy automata, i.e., a B\"uchi type theorem.  ...  We introduce MK-fuzzy automata over a bimonoid K which is related to the fuzzification of the McCarthy-Kleene logic.  ...  We show that the strong support, related to the first component of the elements in K, of a deterministically recognizable MK-fuzzy language is a recognizable language.  ... 
doi:10.4204/eptcs.256.8 fatcat:yqoohv4pkfavvergl5jf6rvsla

Recognizable Sets of Graphs, Hypergraphs and Relational Structures: A Survey [chapter]

Bruno Courcelle
2004 Lecture Notes in Computer Science  
The general framework of this research which associates tightly algebraic notions (equational and recognizable sets) and Monadic Second-Order logic (for defining sets and transformations of graphs, hypergraphs  ...  New results on the recognizability of sets of finite graphs, hypergraphs and relational structures are presented.  ...  Hence Monadic Second-Order logic (MS logic in short) is an appropriate language for specifying sets of graphs. It can be seen as an alternative to the non-existing notion of graph automaton.  ... 
doi:10.1007/978-3-540-30550-7_1 fatcat:pkfifmamb5h5rj7u4vib2r7p7u

Graph Structure and Monadic Second-Order Logic: Language Theoretical Aspects [chapter]

Bruno Courcelle
2008 Lecture Notes in Computer Science  
tools for the construction of Fixed-Parameter Tractable algorithms and also for the extension of methods and results of Formal Language Theory to the description of sets of finite graphs.  ...  Hierarchical decompositions yielding the notions of tree-width and clique-width, expressed by terms written with appropriate graph operations and associated with Monadic Second-order Logic are important  ...  Walukiewicz for many useful comments on a first draft of this overview. The first 11 references are books and survey articles.  ... 
doi:10.1007/978-3-540-70575-8_1 fatcat:ftpcqszcb5fs5nswbqnbnmy5ja

Algebraic recognizability of languages [article]

Pascal Weil
2006 arXiv   pre-print
Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory.  ...  We would like to briefly explore why that is, and how this word-related notion extends to more complex models, such as those developed for modeling distributed or timed behaviors.  ...  Recognizability Based on the examples of words and trees, the natural language for logical definability of recognizable sets would seem to be MSO, monadic second order logic.  ... 
arXiv:cs/0609110v1 fatcat:2fnhr3gu5rdbbdugq76cqfvl4y

Algebraic Recognizability of Languages [chapter]

Pascal Weil
2004 Lecture Notes in Computer Science  
In the beginning was the Word. . . Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory.  ...  Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory.  ...  Recognizability Based on the examples of words and trees, the natural language for logical definability of recognizable sets would seem to be MSO, monadic second order logic.  ... 
doi:10.1007/978-3-540-28629-5_8 fatcat:5el7wd3umvgdzhw4dxukeugoci

Page 7076 of Mathematical Reviews Vol. , Issue 99j [page]

1999 Mathematical Reviews  
- tion of the Ehrenfeucht-Fraissé game technique and some of its applications concerning first-order logic in formal language the- ory.  ...  Temporal logics and fixed-point logics took the role of the specification languages (replacing first-order and monadic second-order logic), and more efficient transformations from logic formulas to automata  ... 

Monadic Second-Order Logic over Rectangular Pictures and Recognizability by Tiling Systems

Dora Giammarresi, Antonio Restivo, Sebastian Seibert, Wolfgang Thomas
1996 Information and Computation  
The proof is based on the Ehrenfeucht Fra@ sse technique for first-order logic and an implementation of"threshold counting" within tiling systems. ]  ...  It is shown that a set of pictures (rectangular arrays of symbols) is recognized by a finite tiling system iff it is definable in existential monadic second-order logic.  ...  Formulas are built up from atomic formulas by means of the Boolean connectives c, 7, 6, Ä, W and the quantifiers _, \, applicable to first-order as well as to second-order variables.  ... 
doi:10.1006/inco.1996.0018 fatcat:wftquihpyjd5jojgjhqff3tlum

Logical definability on infinite traces

Werner Ebinger, Anca Muscholl
1996 Theoretical Computer Science  
The main results of the present paper are the equivalence of definability by monadic secondorder logic and recognizability for real trace languages, and that first-order definable, star-free, and aperiodic  ...  This generalizes results on infinite words and on finite traces to infinite traces. It closes an important gap in the different characterizations of recognizable languages of infinite traces.  ...  We also thank the anonymous referees from ICALP and especially from Theoretical Computer Science for the valuable comments which helped improving the presentation of this paper.  ... 
doi:10.1016/0304-3975(95)00130-1 fatcat:4qsekf35zvftjbxixwoot2ie6y

Recognizability in the Simply Typed Lambda-Calculus [chapter]

Sylvain Salvati
2009 Lecture Notes in Computer Science  
Using intersection types, we generalize the notions of automata for strings and trees so as to grasp recognizability for λ-terms.  ...  We then expose the closure properties of this notion and present some of its applications.  ...  As we wish to use this notion of recognizability so as to describe particular sets of λ-terms, it would be nice to obtain a connection with some logic. First-order logic would be a first step.  ... 
doi:10.1007/978-3-642-02261-6_5 fatcat:z2n4kdoccrbuvdojryja5ag7ma

Towards a Higher-Dimensional String Theory for the Modeling of Computerized Systems [chapter]

David Janin
2014 Lecture Notes in Computer Science  
In this invited paper, we will provide a guided tour of this emerging theory both as an abstract theory and with a view to concrete applications.  ...  Recent modeling experiments conducted in computational music give evidence that a number of concepts, methods and tools belonging to inverse semigroup theory can be attuned towards the concrete modeling  ...  the support, encouragement and knowledge of true  ... 
doi:10.1007/978-3-319-04298-5_2 fatcat:swpsgjcys5bsrczextmvelnqba

On labeled birooted tree languages: Algebras, automata and logic

David Janin
2015 Information and Computation  
With an aim to developing expressive language theoretical tools applicable to inverse semigroup languages, that is, subsets of inverse semigroups, this paper explores the language theory of finite labeled  ...  This notion is shown to capture the class of languages that are definable in Monadic Second Order Logic and upward closed with respect to the natural order defined in the inverse monoid structure induced  ...  Acknowledgment The author wishes to express his gratitude to the anonymous referees for providing many helpful comments on earlier versions of this work.  ... 
doi:10.1016/j.ic.2014.12.016 fatcat:gg4tea6z3jffxbx5jqcxky4rxe

Page 4053 of Mathematical Reviews Vol. , Issue 97G [page]

1997 Mathematical Reviews  
|Study of an infinitely small point and applications} Le labyrinthe du continu (Cerisy-la-Salle, 1990), 402-413, Springer, Paris, 1992.  ...  Clearly, if L is recognizable by a finite automaton in the first sense, then it is an ultimately periodic set of integers, and thus recognizable by a finite automaton in the second sense for any base k  ... 

Page 2062 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
The authors study how the alternation of (first- and monadic second-order) quantifications, on the one hand, re- lates to the dot-depth measure of two-dimensional (i.e. picture) languages, on the other  ...  Thirdly, they investigate how an additional prefix of first-order (i.e. element) quantifiers influences the expressive power of MSO formulas.  ... 
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