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Finite Languages for the Representation of Finite Graphs

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. ...

##
###
Automata-based Representations for Infinite Graphs

2001
*
RAIRO - Theoretical Informatics and Applications
*

This

doi:10.1051/ita:2001122
fatcat:stp3c7oymfgorclg5fjfgur3a4
*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*. ...##
###
The monadic theory of finite representations of infinite words

2007
*
Information Processing Letters
*

This result can be seen as a translation, onto

doi:10.1016/j.ipl.2007.02.014
fatcat:nvdw46e7wzfa3b5qbllnc76vve
*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*...##
###
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]

2009
*
Lecture Notes in Computer Science
*

It will review applications to

doi:10.1007/978-3-642-00982-2_2
fatcat:ryjvoaa7dnefrcruygfnpqso2i
*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. ...##
###
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]

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. ...

##
###
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

2009
*
Complex Systems
*

Other applications range from stream iterators on combinatorial objects to succinct data

doi:10.25088/complexsystems.18.4.475
fatcat:y6t5qz6vwvfgfdfpsc3qgmfci4
*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*...##
###
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

2005
*
Proceedings of the 43rd Annual Meeting on Association for Computational Linguistics - ACL '05
*

This framework uses IDL-expressions as a

doi:10.3115/1219840.1219849
dblp:conf/acl/SoricutM05
fatcat:kszk6hgubzcjhamrudcspnqu2a
*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. ...##
###
Decidability and Expressiveness of Finitely Representable Recognizable Graph Languages

2011
*
Electronic Communications of the EASST
*

Recently automaton functors were proposed as acceptors

doi:10.14279/tuj.eceasst.41.580
dblp:journals/eceasst/BrugginkH11
fatcat:57fyyovxyzfshg4pfahhjtfh6y
*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*. ...##
###
Narrowing the narrowing space
[chapter]

1997
*
Lecture Notes in Computer Science
*

We introduce a framework

doi:10.1007/bfb0033833
fatcat:nlms3soq3nfa5pjjoolai7u36i
*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. ...
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