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Circle graphs and monadic second-order logic

Bruno Courcelle
2008 Journal of Applied Logic  
By using the (canonical) split decomposition of a circle graph, we define in monadic second-order logic with auxiliary linear orders all its chord diagrams.  ...  This article is part of a project consisting in expressing, whenever possible, graph properties and graph transformations in monadic second-order logic or in its extensions using modulo p cardinality set  ...  Makowsky for his numerous helpful comments and suggestions of references.  ... 
doi:10.1016/j.jal.2007.05.001 fatcat:brlwmphywfcldlg3smd54jjpsa

A hierarchical approach to monadic second-order logic over graphs [chapter]

Ina Schiering
1998 Lecture Notes in Computer Science  
The expressiveness of existential monadic second-order logic is investigated over several classes of nite graphs among them the graphs of bounded tree-width.  ...  Among other results we show that existential monadic second-order logic on graphs of bounded tree-width is not closed under complement.  ...  second-order properties, and closure of existential monadic second-order logic under complement.  ... 
doi:10.1007/bfb0028029 fatcat:5trrqacoengfda7andndm6mk7u

Bounds on the propagation of selection into logic programs

C. Beeri, P. Kanellakis, F. Bancilhon, R. Ramakrishnan
1987 Proceedings of the sixth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '87  
We demonstrate the connection of these two cases, respectively, with the weak monadic second-order theory of one successor and with monadic generalized spectra.  ...  In particular, we study the class of chain programs and formalize selection propagation on such a logic program as: the task of finding an equivalent program containing only monadic derived predicates.  ...  ACKNOWLEDGMENTS We thank Stavros Cosmadakis, Ron Fagin, Phokion Kolaitis, and Moshe Vardi for their many helpful comments.  ... 
doi:10.1145/28659.28683 dblp:conf/pods/BeeriKBR87 fatcat:ln5lk6ot4zafvdklmjb5s7ooyi

Bounds on the propagation of selection into logic programs

Catriel Beeri, Paris Kanellakis, Francois Bancilhon, Raghu Ramakrishnan
1990 Journal of computer and system sciences (Print)  
We demonstrate the connection of these two cases, respectively, with the weak monadic second-order theory of one successor and with monadic generalized spectra.  ...  In particular, we study the class of chain programs and formalize selection propagation on such a logic program as: the task of finding an equivalent program containing only monadic derived predicates.  ...  ACKNOWLEDGMENTS We thank Stavros Cosmadakis, Ron Fagin, Phokion Kolaitis, and Moshe Vardi for their many helpful comments.  ... 
doi:10.1016/0022-0000(90)90035-j fatcat:5mkro4bjhncxleun6zk5vtmrrm

A Gentle Introduction to Applications of Algorithmic Metatheorems for Space and Circuit Classes

Till Tantau
2016 Algorithms  
It is not difficult to show that, just like the 99 vertex cover problem and just like about any other interesting problem, the even cycle problem can 100 be described in monadic second-order logic and,  ...  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  ...  To sum up, the logic we have been looking for is monadic second-order logic over graphs.  ... 
doi:10.3390/a9030044 fatcat:4njcekeavbeufbltvu5y4rxkxa

Automata theory on trees and partial orders [chapter]

Wolfgang Thomas
1997 Lecture Notes in Computer Science  
Graph acceptors and their specialization for pictures, \tiling systems", are presented, and their equivalence to existential monadic second-order logic is reviewed.  ...  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  ...  It starts with a characterization of rst-order logic and treats monadic second-order quanti cation separately.  ... 
doi:10.1007/bfb0030586 fatcat:xe7c4rmzbvautdrin2igsfgurq

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

Bruno Courcelle
2008 Lecture Notes in Computer Science  
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  ...  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.  ...  Fellows and I. 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

Charles Peirce on the Classification of Dyadic Relations and the Implications for Mathematical Logic [article]

Jeffrey Downard
2017 arXiv   pre-print
Charles Peirce develops a scheme for classifying different kinds of monadic, dyadic and triadic relations.  ...  His account of these different classes of relations figures prominently in the development of his algebraic and diagrammatic systems of mathematical logic.  ...  and the logical accounts of the categories in order to develop and refine his answers.  ... 
arXiv:1709.05722v1 fatcat:mewvwqloqbcxdjcs6sor66j5m4

Verification of Pointers

Nils Klarlund, Michael I. Schwartzbach
1994 DAIMI Report Series  
Such properties seemed to have called for a full Hoare logic beyond the reach of type checking and decidability.</p><p> </p><p>Our work is based on monadic second-order logic.  ...  </p><p> </p><p>In our approach, we view data types as invariants and devise a logical and decidable framework for expressing global properties of a store consisting of records and pointers.  ...  for which decidability follows from that of second-order monadic tree logic.  ... 
doi:10.7146/dpb.v23i470.6943 fatcat:i34abcwqwvhltn3fuvkck5cizm

Uniform and nonuniform recognizability

Wolfgang Thomas
2003 Theoretical Computer Science  
, nonuniform recognizability, and monadic second-order logic.  ...  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  ...  monadic second-order logic.  ... 
doi:10.1016/s0304-3975(01)00229-8 fatcat:4btfarn3pfdchiijplmiesg4wa

Page 4354 of Mathematical Reviews Vol. , Issue 96g [page]

1996 Mathematical Reviews  
Summary: “We show how membership in classes of graphs de- finable in monadic second-order logic and of bounded treewidth can be decided by finite sets of terminating reduction rules.  ...  The method is constructive in the sense that we describe an algorithm that will produce, from a formula in monadic second-order logic and an integer k such that the class defined by the formula is of treewidth  ... 

Complete Graph Drawings Up to Triangle Mutations [chapter]

Emeric Gioan
2005 Lecture Notes in Computer Science  
For a complete graph drawing, the subsketch is determined, through first order logic formulas, by the size, a corner of the drawing and the crossings of the edges.  ...  The logical structure we introduce here to describe a (topological) graph drawing, called subsketch, is intermediate between the map (determining the drawing when it is planar), and the sketch introduced  ...  From an axiomatic point of view, a general setting is introduced by Courcelle in [2], allowing both logical and geometrical points of view on graph drawings, and leading to applications of monadic second  ... 
doi:10.1007/11604686_13 fatcat:7q5weqpb5nf43avydshl2pi3he

Page 2420 of Mathematical Reviews Vol. 58, Issue 4 [page]

1979 Mathematical Reviews  
By a different 58 + 16247 Logic and Foundations 2420 method of proof (applying a result of Shelah and Stup which uses notions of automata theory) it is known that the strong monadic second-order theory  ...  Siefkes [Biichi’s monadic second order successor arithmetic.  ... 

Functions and Organizational Forms of Graphic-image Modelling of Knowledge

Andrey A. Volkov, Vitaliy Chulkov, Ruben Kazaryan
2014 Procedia Engineering  
It is a set of measures, works and solutions implemented to improve operating characteristics of a construction facility.  ...  The main goal of CR objects is to bring them to the condition meeting the needs of users or requirements of regulatory documentation using the methods of architectural, planning and functional transformation  ...  »; Non homogenous of the second level (triads): a «man -technology -environment» (MTE) triad formed from the above mentioned three monads and three dyads.  ... 
doi:10.1016/j.proeng.2014.12.076 fatcat:erljzjlsqndu5jk67kjfxklg4i

HR* Graph Conditions Between Counting Monadic Second-Order and Second-Order Graph Formulas

Hendrik Radke
2013 Electronic Communications of the EASST  
by a second-order graph formula.  ...  We show, by induction over the structure of formulas and conditions, that (1) any node-counting monadic second-order formula can be expressed by an HR∗ condition and (2) any HR* condition can be expressed  ...  Counting monadic second-order graph formulas are a subclass of second-order graph formulas and an extension of monadic second-order graph formulas [Cou96] .  ... 
doi:10.14279/tuj.eceasst.61.831 dblp:journals/eceasst/Radke12 fatcat:mcbumlzeunduvhs47bvcit5uoi
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