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Finite Languages for the Representation of Finite Graphs

Andrzej Ehrenfeucht, Joost Engelfriet, Grzegorz Rozenberg
1996 Journal of computer and system sciences (Print)  
The strings of a given (finite, prefix-free) language represent the vertices of the graph; whether or not there is an edge between the vertices represented by two strings is determined by the pair of symbols  ...  We introduce a new way of specifying graphs: through languages, i.e., sets of strings.  ...  ACKNOWLEDGMENT We thank the referees for fruitful suggestions.  ... 
doi:10.1006/jcss.1996.0013 fatcat:4etatc5qeja4jc5k7xas4lk6qi

Automata-based Representations for Infinite Graphs

Salvatore La Torre, Margherita Napoli
2001 RAIRO - Theoretical Informatics and Applications  
This representation, though very interesting for finite graphs, turns out to be quite unsatisfactory for infinite graphs.  ...  The first-difference function is substantially a direct generalization to infinite multi-hypergraphs of the representation introduced by Ehrenfeucht et al. for finite graphs.  ...  by manipulating the regular languages used for the graph representation.  ... 
doi:10.1051/ita:2001122 fatcat:stp3c7oymfgorclg5fjfgur3a4

The monadic theory of finite representations of infinite words

Anuj Dawar, David Janin
2007 Information Processing Letters  
This result can be seen as a translation, onto finite representations of infinite words, of Büchi's automata-theoretic characterization of S1S.  ...  classes of graphs coincide with classes of graphs definable by means of (an extension of) finite state ω-word automata.  ...  From languages of words to classes of unary graphs We first show that for any regular language of infinite words, there is an existential monadic formula that defines, in the finite, the set of all graph  ... 
doi:10.1016/j.ipl.2007.02.014 fatcat:nvdw46e7wzfa3b5qbllnc76vve

Page 2542 of Mathematical Reviews Vol. , Issue 83f [page]

1983 Mathematical Reviews  
“Such a generation of L(G) offers a theoretical framework for developing the algorithms of finite representation by generators and relations of the infinite set of sentential forms which can be obtained  ...  This structuring is done having in view a finite representation of L(G) by a finite set of generators and relations.  ... 

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

Bruno Courcelle
2009 Lecture Notes in Computer Science  
It will review applications to the construction of algorithms, to Graph Theory and to the extension to graphs of Formal Language Theory concepts.  ...  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.  ...  This is due to the chosen representation of a graph by a relational structure.  ... 
doi:10.1007/978-3-642-00982-2_2 fatcat:ryjvoaa7dnefrcruygfnpqso2i

Page 2812 of Mathematical Reviews Vol. , Issue 91E [page]

1991 Mathematical Reviews  
The convergence of the algorithm is established for all cases where the representation to be found is finite-dimensional.  ...  In this paper the author gives an algorithm for the construction 68 COMPUTER SCIENCE 2812 of matrix representations for finitely presented noncommutative algebras.  ... 

Page 2415 of Mathematical Reviews Vol. , Issue 96d [page]

1996 Mathematical Reviews  
Sci. 134 (1994), no. 2, 537-544; MR 95m:68100] that given an arbitrary finite alphabet A, the emptiness problem is undecid- able for the class of languages which are intersections of a DOL language and  ...  On the other hand, we show that the lower bound for the problem is Q(m*) and that the lower bound for the size of a test set for a language defined over an n-letter alphabet is Q(n*).” 96d:68126 68Q45  ... 

Modal model theory [article]

Joel David Hamkins, Wojciech Aleksander Wołoszyn
2020 arXiv   pre-print
The class of all graphs is a particularly insightful case illustrating the remarkable power of the modal vocabulary, for the modal language of graph theory can express connectedness, k-colorability, finiteness  ...  if it is universal for finite graphs.  ...  The arithmetic order relation n ≤ m on these representations is expressible in the language of finite modal graph theory.  ... 
arXiv:2009.09394v1 fatcat:t6sqojahebbapmmdcgxs2b3rsu

Page 4009 of Mathematical Reviews Vol. , Issue 87h [page]

1987 Mathematical Reviews  
It is shown that an arbitrary statement in the monadic language of context- free graphs can be transformed into a tiling condition, describing properties of tilings of graphs by finitely many colors (that  ...  Finitely generated graphs are termed context-free if they are “finitely behaved at infinity” in the following sense: One obtains only finitely many isomorphism types by collecting, for all vertices v,  ... 

"Everything Is Everything" Revisited: Shapeshifting Data Types with Isomorphisms and Hylomorphisms

Paul Tarau, University of North Texas
2009 Complex Systems  
Other applications range from stream iterators on combinatorial objects to succinct data representations and the generation of random instances. † a general framework for bijective encodings between heterogeneous  ...  This paper is an exploration of isomorphisms between elementary data types (e.g., natural numbers, sets, finite functions, graphs, hypergraphs) and their extension to hereditarily finite universes through  ...  7) † a mechanism for lifting encodings to hereditarily finite data types (4) and its application to derive Ackermann's encoding for hereditarily finite sets † a new instance of hereditarily finite representations  ... 
doi:10.25088/complexsystems.18.4.475 fatcat:y6t5qz6vwvfgfdfpsc3qgmfci4

Page 5265 of Mathematical Reviews Vol. , Issue 98H [page]

1998 Mathematical Reviews  
For a class K of string languages, Int(X) is the class of all graph  ...  Some paths of the graph represent PDA computations. Finite automata correspond to a special case of the pushdown graphs.  ... 

Page 2133 of Mathematical Reviews Vol. , Issue 83e [page]

1983 Mathematical Reviews  
This result is the natural analogue for the recursively enumerable languages of the Chomsky-Schiitzenberger representation of the context-free languages.”  ...  languages that would be as essential for the theory of graph languages as the regular languages are for string languages.  ... 

Towards developing generation algorithms for text-to-text applications

Radu Soricut, Daniel Marcu
2005 Proceedings of the 43rd Annual Meeting on Association for Computational Linguistics - ACL '05  
This framework uses IDL-expressions as a representation formalism, and a generation mechanism based on algorithms for intersecting IDL-expressions with probabilistic language models.  ...  We present both theoretical and empirical results concerning the correctness and efficiency of these algorithms.  ...  Because both formalisms are used for representing finite languages, they have equivalent representational power.  ... 
doi:10.3115/1219840.1219849 dblp:conf/acl/SoricutM05 fatcat:kszk6hgubzcjhamrudcspnqu2a

Decidability and Expressiveness of Finitely Representable Recognizable Graph Languages

H. J. Sander Bruggink, Mathias Hülsbusch
2011 Electronic Communications of the EASST  
Recently automaton functors were proposed as acceptors of recognizable graph languages. They promise to be a useful tool for the verification of dynamic systems, for example for invariant checking.  ...  Since automaton functors may contain an infinite number of finite state sets, one must restrict to finitely representable ones for implementation reasons.  ...  For implementation purposes, we need to impose restrictions to automaton functors in order to ensure that they have finite representations.  ... 
doi:10.14279/tuj.eceasst.41.580 dblp:journals/eceasst/BrugginkH11 fatcat:57fyyovxyzfshg4pfahhjtfh6y

Narrowing the narrowing space [chapter]

Sergio Antoy, Zena M. Ariola
1997 Lecture Notes in Computer Science  
We introduce a framework for managing as a whole the space of a narrowing computation. The aim of our framework is to find a finite representation of an infinite narrowing space.  ...  This, in turn, allows us to replace an infinite enumeration of computed answers with an equivalent finite representation. We provide a semidecidable condition for this result.  ...  If the narrowing space of a goal g has a graph representation, then the set S of computed expressions of g has a finite representation. Proof.  ... 
doi:10.1007/bfb0033833 fatcat:nlms3soq3nfa5pjjoolai7u36i
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