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Automata theory on trees and partial orders
[chapter]
1997
Lecture Notes in Computer Science
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The paper reviews recent results which aim at generalizing nite automata theory from words and trees to labelled partial orders (presented as labelled directed acyclic graphs), with an emphasis on logical ...
Graph acceptors and their specialization for pictures, \tiling systems", are presented, and their equivalence to existential monadic second-order logic is reviewed. ...
Graph Acceptors and Existential Monadic Logic Over words or trees, there is a simple argument to show that monadic secondorder formulas and nite automata are expressively equivalent: Acceptance of a word ...
doi:10.1007/bfb0030586
fatcat:xe7c4rmzbvautdrin2igsfgurq
Uniform and nonuniform recognizability
2003
Theoretical Computer Science
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We show how this approach encompasses known models of nondeterministic automata over ÿnite words, trees, pictures, and graphs, and present some elementary metaresults connecting uniform recognizability ...
, nonuniform recognizability, and monadic second-order logic. ...
Starting from the expressive equivalence between ÿnite automata and monadic second-order logic over words (as shown in [2, 12] ) or over trees [9, 21] , one may compare the expressive power of recognizers ...
doi:10.1016/s0304-3975(01)00229-8
fatcat:4btfarn3pfdchiijplmiesg4wa
Languages recognised by finite semigroups, and their generalisations to objects such as trees and graphs, with an emphasis on definability in monadic second-order logic
[article]
2020
arXiv
pre-print
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However, the algebraic approach can be extended to structures beyond words, e.g.~infinite words, or trees or graphs. ...
These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. ...
Show that for graphs without edges, mso 1 and mso 2 has the same expressive power as first-order logic. Exercise 172. ...
arXiv:2008.11635v1
fatcat:r6jidclh2zdtznsfsfsyfs3eam
Languages, Automata, and Logic
[chapter]
1997
Handbook of Formal Languages
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-words and their determinization, and a self-contained proof of the \Rabin Tree Theorem". ...
Central points are the connection between nite automata and monadic second-order logic, the Ehrenfeucht-Fra ss e technique in the context of formal language theory, nite automata on ! ...
Zielonka on a pre-nal version contributed a lot to improve the text. Finally, I thank the members of the theory group in Kiel for e cient help and support, and G. ...
doi:10.1007/978-3-642-59126-6_7
fatcat:3ak2gtvtvnbbffvgeniim7f3mi
Page 7468 of Mathematical Reviews Vol. , Issue 94m
[page]
1994
Mathematical Reviews
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Monadic second-order logic (an extension of first-order logic with quantified variables denoting sets of elements of the domain) is used to define sets of graphs. ...
{For the entire collection see MR 94c:00024.}
94m:68107 68Q50 03B15 03C85 05C99 68R10 Courcelle, Bruno (F-BORD-LB; Talence) Graph grammars, monadic second-order logic and the theory of graph minors. ...
Page 5089 of Mathematical Reviews Vol. , Issue 2000g
[page]
2000
Mathematical Reviews
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- tifier alternation hierarchy over grids and pictures (441-460); Thomas Schwentick, Padding and the expressive power of existen- tial second-order logics (461—477); Ludwig Staiger, Rich w-words and monadic ...
, Concurrent con- straint programming and non-commutative logic (406-423); Ina Schiering, A hierarchical approach to monadic second-order logic over graphs (424-440); Nicole Schweikardt, The monadic quan ...
Separator logic and star-free expressions for graphs
[article]
2021
arXiv
pre-print
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A corollary is that, given k and a graph language represented by an formula, one can decide if the language can be defined in either of two equivalent formalisms on graphs of pathwidth at most k. ...
This is first-order logic on graphs which is allowed to use the edge relation, and for every n ∈{0,1,...} a relation of arity n+2 which says that "vertex s can be connected to vertex t by a path that avoids ...
By saying that a graph is connected and has no cycles, we can define trees in separator logic. In this paper, we are most interested in the expressive power of separator logic. ...
arXiv:2107.13953v2
fatcat:ulxnbtoj4ve33etnh2mkcj2sxa
Trees, grids, and MSO decidability: From graphs to matroids
2006
Theoretical Computer Science
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Monadic second order (MSO) logic has proved to be a useful tool in many areas of application, reaching from decidability and complexity to picture processing, correctness of programs and parallel processes ...
Logic 53 (1991) ] that decidability of monadic theories of countable structures implies that the theory can be reduced via interpretability to a theory of trees. ...
Courcelle, the organizer of the workshop on "Logic and Graph Transformations" at the ICGT 2004 conference, for inviting us to present our research results there. ...
doi:10.1016/j.tcs.2005.10.006
fatcat:dtsh4w7hs5dbtkz6nyqjef3cp4
Two monads for graphs
[article]
2018
arXiv
pre-print
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An introduction to algebras for graphs, based on Courcelle's algebras of hyperedge replacement and vertex replacement. The paper uses monad notation. ...
the expressive power of mso without counting. ...
Monadic second-order logic A classical theme in language theory is to use logic to describe properties of objects such as words, trees, graphs, etc. ...
arXiv:1804.09408v1
fatcat:jq7izicm3rbltg4rtkzcv7qoqy
A Gentle Introduction to Applications of Algorithmic Metatheorems for Space and Circuit Classes
2016
Algorithms
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As an example, by Courcelle's Theorem, all monadic second-order ("in a certain logic") properties of graphs of bounded tree width ("structured in a certain way") can be solved in linear time ("with a certain ...
The underlying algorithmic approach is quite 93 ingenious: On input of a graph, if the graph is tree-like, we apply an algorithmic metatheorem; and if 94 the graph is not tree-like, it must be "highly ...
This takes the first step out of the picture and we get an algorithmic metatheorem where the algorithmic complexity hinges (only) on the complexity of evaluating a tree automaton on an input tree, and ...
doi:10.3390/a9030044
fatcat:4njcekeavbeufbltvu5y4rxkxa
On Monadic Theories of Monadic Predicates
[chapter]
2010
Lecture Notes in Computer Science
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Pioneers of logic, among them J.R. Büchi, M.O. Rabin, S. Shelah, and Y. Gurevich, have shown that monadic second-order logic offers a rich landscape of interesting decidable theories. ...
Prominent examples are the monadic theory of the successor structure S1 = (N, +1) of the natural numbers and the monadic theory of the binary tree, i.e., of the two-successor structure S2 = ({0, 1} * , ...
Acknowledgment Many thanks are due to Nachum Dershowitz for his patience and help and to Christof Löding and Alex Rabinovich for their comments. ...
doi:10.1007/978-3-642-15025-8_30
fatcat:giwx47rl6zaarn7u4rv5fj72pm
On Decidability of MSO Theories of Representable Matroids
[chapter]
2004
Lecture Notes in Computer Science
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We show that, for every finite field , the class of allrepresentable matroids of branch-width at most a constant t has a decidable MSO theory. ...
In the other direction, we prove that every class of -representable matroids with a decidable MSO theory must have uniformly bounded branch-width. ...
Acknowledgement It is a pleasure for us to express our thanks to M. Fellows, M. Hallett, R. Niedermeier and N. ...
doi:10.1007/978-3-540-28639-4_9
fatcat:36run6tgjrhtdpcu7ir6hdnxze
Subject index volumes 1–200
1999
Theoretical Computer Science
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3593
logic, 2574, 3580
first-order linear-time temporal logic, 3049
first-order logic, 823, 1057,2155,2156,2222,2407,
2479,2785,2791,3054,3242,3270
completeness-and
-, 2187
expressive power of ...
theory, 1483
weak logical reductions, 2269
weak model, 252 1
weak monadic
formulas, 1570
logic, 1732, 1802
weak monadic theory of
the tree. 1802
trees, 1802
weak
monotonicity in laguage learning ...
doi:10.1016/s0304-3975(98)00319-3
fatcat:s22ud3iiqjht7lfbtc3zctk7zm
Second-Order Logic over Strings: Regular and Non-regular Fragments
[chapter]
2002
Lecture Notes in Computer Science
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We also give a brief survey of recent results on the complexity of evaluating existential second-order logic over graphs, and a list of interesting open problems. ...
By a well-known result due to Büchi and Trakhtenbrot, all monadic second-order sentences over words describe regular languages. ...
of graphs of bounded tree-width. ...
doi:10.1007/3-540-46011-x_4
fatcat:wnrmwktrprhhnm4cuxl4zwwc2i
Algebraic recognizability of languages
[article]
2006
arXiv
pre-print
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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
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