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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
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
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
“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. ...
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
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. ...
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 ...
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
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, ...
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
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. ...
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. ...
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
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
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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