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### A First Order Logic Definition of Beyond-Planar Graphs

Franz J. Brandenburg
<span title="">2018</span> <i title="Journal of Graph Algorithms and Applications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4joumle7hffilk276fkubvhxcq" style="color: black;">Journal of Graph Algorithms and Applications</a> </i> &nbsp;
Examples are 1-planar, fan-planar, fan-crossing free, and quasiplanar graphs.  ...  Beyond-planarity is a collective term for classes of graphs that extend the planar graphs and are defined by drawings with restrictions on crossings.  ...  First-Order Logic Formulas In algebra and logic, a graph G is a structure with a set of vertices and a binary relation for the edges such that adj(u, v) if and only if there is an edge e = {u, v}.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7155/jgaa.00455">doi:10.7155/jgaa.00455</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6cnawb4ok5cshfpzrtcat2dsli">fatcat:6cnawb4ok5cshfpzrtcat2dsli</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190224201506/http://pdfs.semanticscholar.org/6816/f5d56efbb19ceec882c43348580cf78694ef.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/68/16/6816f5d56efbb19ceec882c43348580cf78694ef.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7155/jgaa.00455"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

### Distributed Graph Automata

Fabian Reiter
<span title="">2015</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cnybbxuptncftdgxtodn5edz7m" style="color: black;">2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science</a> </i> &nbsp;
Combining ideas from distributed algorithms and alternating automata, we introduce a new class of finite graph automata that recognize precisely the languages of finite graphs definable in monadic second-order  ...  As an application, we suggest how suitable graph automata might be useful in formal verification of distributed algorithms, using Floyd-Hoare logic.  ...  Their combined expertise was especially helpful for the part about verification of distributed algorithms.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/lics.2015.27">doi:10.1109/lics.2015.27</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/lics/Reiter15.html">dblp:conf/lics/Reiter15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bu53ore6lfewtd274d2tpfoxdm">fatcat:bu53ore6lfewtd274d2tpfoxdm</a> </span>
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### Nowhere dense graph classes and algorithmic applications. A tutorial at Highlights of Logic, Games and Automata 2019 [article]

Sebastian Siebertz
<span title="2019-09-15">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
These notes, prepared for a tutorial at Highlights of Logic, Games and Automata 2019, are a brief introduction to the theory of nowhere denseness, driven by algorithmic applications.  ...  The notion of nowhere dense graph classes was introduced by Nešetřil and Ossona de Mendez and provides a robust concept of uniform sparseness of graph classes.  ...  Introduction The notion of excluded minors is celebrated as one of the most successful notions in contemporary graph theory and has an immense influence on algorithmic graph theory.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1909.06752v1">arXiv:1909.06752v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ced723x72bcqnkjldtrs6dkfgu">fatcat:ced723x72bcqnkjldtrs6dkfgu</a> </span>
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### Monadic Second-Order Logic for Graphs: Algorithmic and Language Theoretical Applications [chapter]

Bruno Courcelle
<span title="">2009</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
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.  ...  Many algorithmic properties follow from such logical descriptions.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-00982-2_2">doi:10.1007/978-3-642-00982-2_2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ryjvoaa7dnefrcruygfnpqso2i">fatcat:ryjvoaa7dnefrcruygfnpqso2i</a> </span>
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### Structural and Logical Approaches to the Graph Isomorphism Problem [chapter]

Martin Grohe
<span title="2012-01-17">2012</span> <i title="Society for Industrial and Applied Mathematics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ja7dpjgz2nhjlovlil3ij5m7ei" style="color: black;">Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms</a> </i> &nbsp;
Simple and generic algorithms that do not use the properties of specific graph classes.  ...  Colour Refinement Weisfeiler Lehman Individualisation Refinement Simple and generic algorithms that do not use the properties of specific graph classes.  ...  Level-k Sherali-Adams relaxation (L k ) Variables Otto 2012) k-WL distinguishes G and H iff COMP k−1 ∪ CONT k ∪ NN k has a solution.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/1.9781611973099.16">doi:10.1137/1.9781611973099.16</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/soda/Grohe12.html">dblp:conf/soda/Grohe12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i6ma4uwn6fauvi27ewzp2odbea">fatcat:i6ma4uwn6fauvi27ewzp2odbea</a> </span>
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### Phylogenetic incongruence through the lens of Monadic Second Order logic

Steven Kelk, Leo van Iersel, Celine Scornavacca, Mathias Weller
<span title="">2016</span> <i title="Journal of Graph Algorithms and Applications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4joumle7hffilk276fkubvhxcq" style="color: black;">Journal of Graph Algorithms and Applications</a> </i> &nbsp;
The notion of treewidth, which is most famously associated with the celebrated Graph Minors project of Robertson and Seymour [24], has had a profound impact upon algorithm design.  ...  The FPT proof by Bryant and Lagergren [10] proves that the display graph (the graph obtained by identifying all taxa with the same label) has bounded treewidth (in the number of input trees), and then  ...  Again, we will formulate a logical query on the display graph to answer the question "Is k ≤ k ′ ?" for increasing values of k ′ , until k ′ = k is reached and the answer to the query is "yes".  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7155/jgaa.00390">doi:10.7155/jgaa.00390</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ne7rpnylt5hhhlrz6acfk4c3sy">fatcat:ne7rpnylt5hhhlrz6acfk4c3sy</a> </span>
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### Signal-flow graph analysis and implementation of novel power tracking algorithm using fuzzy logic controller

S. Venkatesan, M. Saravanan, S. Venkatanarayanan
<span title="">2021</span> <i title="Inderscience Publishers"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7or2zekhifhghpk7rd5kk27dfu" style="color: black;">International Journal of Business Intelligence and Data Mining</a> </i> &nbsp;
This paper discussed merits of novel modified perturb and observe (P&O) maximum power point tracker (MPPT) algorithm for stand-alone solar PV system using interleaved LUO converter with fuzzy logic controller  ...  The proposed interleaved LUO converter based PV system with fuzzy controller reduces considerable amount of ripple content and also proposed MPPT algorithm creates less hunting around maximum power point  ...  Signal flow graphs GON, GOFF are obtained and combined to form a single signal flow graph as shown in Figure 7(a).  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1504/ijbidm.2021.111742">doi:10.1504/ijbidm.2021.111742</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/alrpkojb4ncozepfiffa7bzbda">fatcat:alrpkojb4ncozepfiffa7bzbda</a> </span>
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### A run-time graph-based Polynomial Placement and routing algorithm for virtual FPGAS

R. Ferreira, L. Rocha, A. Santos, J. Nacif, Stephan Wong, Luigi Carro
<span title="">2013</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/plojvu5mhreuxnue5ey7fivkbi" style="color: black;">2013 23rd International Conference on Field programmable Logic and Applications</a> </i> &nbsp;
The placement and routing (P&R) of the hardware modules is a computationally intensive task, and the state-of-art algorithms are not suitable to place and route modules at run-time.  ...  . (2) Implicit Graph Model: the FPGA is modelled as an implicit graph with a direct correspondence to the physical FPGA, and the P&R is performed as a graph mapping problem by exploring the node locality  ...  Fig. 3 (b) depicts 4 track nodes: Logic Block and Track Nodes Switch Box The switch box (SW) is the key component in the FPGA design.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/fpl.2013.6645514">doi:10.1109/fpl.2013.6645514</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/fpl/FerreiraRSNWC13.html">dblp:conf/fpl/FerreiraRSNWC13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uijocslafvdeblewr3rq7ynk64">fatcat:uijocslafvdeblewr3rq7ynk64</a> </span>
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### A Swarm Intelligence Graph-Based Pathfinding Algorithm Based on Fuzzy Logic (SIGPAF): A Case Study on Unmanned Surface Vehicle Multi-Objective Path Planning

Charis Ntakolia, Dimitrios V. Lyridis
<span title="2021-11-09">2021</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/zxbcd6icyvawjnotp3d7oyl6sm" style="color: black;">Journal of Marine Science and Engineering</a> </i> &nbsp;
This study aims to enhance the performance of SIGPA algorithm by integrating fuzzy logic in order to cope with the multiple objectives and generate quality solutions.  ...  To this end, a swarm intelligence graph-based pathfinding algorithm (SIGPA) has been proposed in the recent literature.  ...  OPTINET has been co-financed by the European Regional Development Fund of the European Union and Greek national funds through the Operational Program Competitiveness, Entrepreneurship and Innovation, under  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/jmse9111243">doi:10.3390/jmse9111243</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i2cia4q3jjhurnxwaao6vgavaq">fatcat:i2cia4q3jjhurnxwaao6vgavaq</a> </span>
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### AN ALGORITHM TO COMPUTE THE LOGICAL ENTROPY OF A DIRECTED GRAPH

<span title="">2016</span> <i > GESJ: Computer Science and Telecommunications </i> &nbsp; <span class="release-stage">unpublished</span>
After decomposition such algorithms explore separately each one and then combine local solutions into global solution according to the structure of a graph.  ...  By the concept of logical entropy of a directed graph we mean the logical entropy of graph partition into strongly connected components.  ...  AN ALGORITHM TO COMPUTE THE LOGICAL ENTROPY OF THE STRONGLY CONNECTED COMPONENTS We assume that the vertices of a directed graph are .  ...
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### Algorithms for Effective Argumentation in Classical Propositional Logic: A Connection Graph Approach [chapter]

Vasiliki Efstathiou, Anthony Hunter
<i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tnsna54wy5aczcrnakcwhkjwxi" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Different logics provide different definitions for consistency and entailment and hence give us different options for argumentation.  ...  We provide a theoretical framework and algorithms for this proposal, together with some theoretical results and some preliminary experimental results to indicate the potential of the approach.  ...  Proof procedures and algorithms have been developed for finding preferred arguments from a knowledgebase using defeasible logic and following for example Dung's preferred semantics (see for example [7  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-77684-0_19">doi:10.1007/978-3-540-77684-0_19</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/foiks/EfstathiouH08.html">dblp:conf/foiks/EfstathiouH08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tib6gwweyzbydmmjkldlmtcxzi">fatcat:tib6gwweyzbydmmjkldlmtcxzi</a> </span>
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### Computable Categoricity of Graphs with Finite Components [chapter]

Barbara F. Csima, Bakhadyr Khoussainov, Jiamou Liu
<i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/we7cpwkqdbdwxa6px54yglounm" style="color: black;">Logic and Theory of Algorithms</a> </i> &nbsp;
We present a necessary and sufficient condition for certain classes of strongly locally finite graphs to be computably categorical.  ...  A computable graph is computably categorical if any two computable presentations of the graph are computably isomorphic. In this paper we investigate the class of computably categorical graphs.  ...  All our graphs are undirected and infinite. If G is a computable graph isomorphic to a graph G then G is called a computable presentation of G and G is called computably presentable.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-69407-6_15">doi:10.1007/978-3-540-69407-6_15</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/cie/CsimaKL08.html">dblp:conf/cie/CsimaKL08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/antd7lmldnf2xmwtey3b4s4yhe">fatcat:antd7lmldnf2xmwtey3b4s4yhe</a> </span>
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### CG2A: Conceptual Graphs Generation Algorithm

Adam Faci, Marie-Jeanne Lesot, Claire Laudy
<span title="">2021</span> <i title="Atlantis Press"> Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP) </i> &nbsp; <span class="release-stage">unpublished</span>
Conceptual Graphs (CGs) are a formalism to represent knowledge. The production of CG benchmarks is currently a crucial need in the community to validate algorithms.  ...  This paper proposes CG2A, an algorithm to build synthetic CGs exploiting most of their expressivity.  ...  This is immediate considering that CGs are graph-based representations of first-order logic formulas and that relations correspond to atomic formulas, which are 2decomposable [12] .  ...
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### Improving solutions by embedding larger subproblems in a D-Wave quantum annealer

Shuntaro Okada, Masayuki Ohzeki, Masayoshi Terabe, Shinichiro Taguchi
<span title="2019-02-14">2019</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tnqhc2x2aneavcd3gx5h7mswhm" style="color: black;">Scientific Reports</a> </i> &nbsp;
Quantum annealing is a heuristic algorithm that solves combinatorial optimization problems, and D-Wave Systems Inc. has developed hardware implementation of this algorithm.  ...  even for sparse problem graphs.  ...  One of the authors M.O. is grateful to the financial support from JSPS KAKENHI 15H03699 and 16H04382, the JST-START, JST-CREST(No. JPMJCR1402), and the ImPACT program.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1038/s41598-018-38388-4">doi:10.1038/s41598-018-38388-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/apreolfiajcm5fxbih5tyrt5k4">fatcat:apreolfiajcm5fxbih5tyrt5k4</a> </span>
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### Algorithmic Meta Theorems for Sparse Graph Classes [chapter]

Martin Grohe
<span title="">2014</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
The classes of problems are typically defined in terms of logic and structural graph theory.  ...  A well-known example of an algorithmic meta theorem is Courcelle's Theorem, stating that all properties of graphs of bounded tree width that are definable in monadic second-order logic are decidable in  ...  Frick and Grohe [21] gave linear-time algorithms for deciding FO-definable properties of planar graphs and all apex-minor-free graph classes and O(n 1+ ) algorithms for graph classes of bounded local  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-06686-8_2">doi:10.1007/978-3-319-06686-8_2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cr656t7vjbgxjkdjkcldpksgwm">fatcat:cr656t7vjbgxjkdjkcldpksgwm</a> </span>
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