IA Scholar Query: Circle graphs and monadic second-order logic.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgThu, 04 Aug 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Infinite Separation between General and Chromatic Memory
https://scholar.archive.org/work/mnyhycxrkzbjjjj7gpvdyzfoze
In this note, we answer a question from [Alexander Kozachinskiy. State Complexity of Chromatic Memory in Infinite-Duration Games, arXiv:2201.09297]. Namely, we construct a winning condition W over a finite set of colors such that, first, every finite arena has a strategy with 2 states of general memory which is optimal with respect to W, and second, there exists no k such that every finite arena has a strategy with k states of chromatic memory which is optimal with respect to W.Alexander Kozachinskiywork_mnyhycxrkzbjjjj7gpvdyzfozeThu, 04 Aug 2022 00:00:00 GMTTransducers of polynomial growth
https://scholar.archive.org/work/ypscf4k7cvb35b5ohvnwa2mski
The polyregular functions are a class of string-to-string functions that have polynomial size outputs, and which can be defined using finite state models. There are many equivalent definitions of this class, with roots in automata theory, programming languages and logic. This paper surveys recent results on polyregular functions. It presents five of the equivalent definitions, and gives self-contained proofs for most of the equivalences. Decision problems as well as restricted subclasses of the polyregular functions are also discussed.Mikolaj Bojanczykwork_ypscf4k7cvb35b5ohvnwa2mskiTue, 02 Aug 2022 00:00:00 GMTContraction Bidimensionality of Geometric Intersection Graphs
https://scholar.archive.org/work/mpck3cv5gvduvdzbbiyserzg2i
Given a graph G, we define bcg(G) as the minimum k for which G can be contracted to the uniformly triangulated grid Γ_k. A graph class G has the SQGC property if every graph G∈ G has treewidth 𝒪( bcg(G)^c) for some 1≤ c<2. The SQGC property is important for algorithm design as it defines the applicability horizon of a series of meta-algorithmic results, in the framework of bidimensionality theory, related to fast parameterized algorithms, kernelization, and approximation schemes. These results apply to a wide family of problems, namely problems that are contraction-bidimensional. Our main combinatorial result reveals a wide family of graph classes that satisfy the SQGC property. This family includes, in particular, bounded-degree string graphs. This considerably extends the applicability of bidimensionality theory for contraction bidimensional problems.Julien Baste, Dimitrios M. Thilikoswork_mpck3cv5gvduvdzbbiyserzg2iWed, 20 Jul 2022 00:00:00 GMTProduct structure of graph classes with bounded treewidth
https://scholar.archive.org/work/j4bhjoyxnnevtnltqxhsrgt6hq
We show that many graphs with bounded treewidth can be described as subgraphs of the strong product of a graph with smaller treewidth and a bounded-size complete graph. To this end, define the "underlying treewidth" of a graph class 𝒢 to be the minimum non-negative integer c such that, for some function f, for every graph G ∈𝒢 there is a graph H with tw(H) ≤ c such that G is isomorphic to a subgraph of H ⊠ K_f(tw(G)). We introduce disjointed coverings of graphs and show they determine the underlying treewidth of any graph class. Using this result, we prove that the class of planar graphs has underlying treewidth 3; the class of K_s,t-minor-free graphs has underlying treewidth s (for t ≥max{s,3}); and the class of K_t-minor-free graphs has underlying treewidth t-2. In general, we prove that a monotone class has bounded underlying treewidth if and only if it excludes some fixed topological minor. We also study the underlying treewidth of graph classes defined by an excluded subgraph or excluded induced subgraph. We show that the class of graphs with no H subgraph has bounded underlying treewidth if and only if every component of H is a subdivided star, and that the class of graphs with no induced H subgraph has bounded underlying treewidth if and only if every component of H is a star.Rutger Campbell and Katie Clinch and Marc Distel and J. Pascal Gollin and Kevin Hendrey and Robert Hickingbotham and Tony Huynh and Freddie Illingworth and Youri Tamitegama and Jane Tan and David R. Woodwork_j4bhjoyxnnevtnltqxhsrgt6hqMon, 18 Jul 2022 00:00:00 GMTTwin-width VII: groups
https://scholar.archive.org/work/nkozaaxusbcpvan3rxzr452cfe
Twin-width is a recently introduced graph parameter with applications in algorithmics, combinatorics, and finite model theory. For graphs of bounded degree, finiteness of twin-width is preserved by quasi-isometry. Thus, through Cayley graphs, it defines a group invariant. We prove that groups which are abelian, hyperbolic, ordered, solvable, or with polynomial growth, have finite twin-width. Twin-width can be characterised by excluding patterns in the self-action by product of the group elements. Based on this characterisation, we propose a strengthening called uniform twin-width, which is stable under constructions such as group extensions, direct products, and direct limits. The existence of finitely generated groups with infinite twin-width is not immediate. We construct one using a result of Osajda on embeddings of graphs into groups. This implies the existence of a class of finite graphs with unbounded twin-width but containing 2^O(n)· n! graphs on vertex set {1,...,n}, settling a question asked in a previous work.Édouard Bonnet, Colin Geniet, Romain Tessera, Stéphan Thomasséwork_nkozaaxusbcpvan3rxzr452cfeFri, 15 Jul 2022 00:00:00 GMTFirst Order Logic and Twin-Width in Tournaments and Dense Oriented Graphs
https://scholar.archive.org/work/zxnqz3vcyzeihbpeja6vxapb4u
We characterise the classes of tournaments with tractable first-order model checking. For every hereditary class of tournaments 𝒯, first-order model checking either is fixed parameter tractable, or is AW[*]-hard. This dichotomy coincides with the fact that 𝒯 has either bounded or unbounded twin-width, and that the growth of 𝒯 is either at most exponential or at least factorial. From the model-theoretic point of view, we show that NIP classes of tournaments coincide with bounded twin-width. Twin-width is also characterised by three infinite families of obstructions: 𝒯 has bounded twin-width if and only if it excludes one tournament from each family. This generalises results of Bonnet et al. on ordered graphs. The key for these results is a polynomial time algorithm which takes as input a tournament T and compute a linear order < on V(T) such that the twin-width of the birelation (T,<) is at most some function of the twin-width of T. Since approximating twin-width can be done in polynomial time for an ordered structure (T,<), this provides a polytime approximation of twin-width for tournaments. Our results extend to oriented graphs with stable sets of bounded size, which may also be augmented by arbitrary binary relations.Colin Geniet, Stéphan Thomasséwork_zxnqz3vcyzeihbpeja6vxapb4uFri, 15 Jul 2022 00:00:00 GMTAccelerating Verified-Compiler Development with a Verified Rewriting Engine
https://scholar.archive.org/work/4ttkgtqne5andohxrwxgjmm5vq
Compilers are a prime target for formal verification, since compiler bugs invalidate higher-level correctness guarantees, but compiler changes may become more labor-intensive to implement, if they must come with proof patches. One appealing approach is to present compilers as sets of algebraic rewrite rules, which a generic engine can apply efficiently. Now each rewrite rule can be proved separately, with no need to revisit past proofs for other parts of the compiler. We present the first realization of this idea, in the form of a framework for the Coq proof assistant. Our new Coq command takes normal proved theorems and combines them automatically into fast compilers with proofs. We applied our framework to improve the Fiat Cryptography toolchain for generating cryptographic arithmetic, producing an extracted command-line compiler that is about 1000× faster while actually featuring simpler compiler-specific proofs.Jason Gross and Andres Erbsen and Jade Philipoom and Miraya Poddar-Agrawal and Adam Chlipalawork_4ttkgtqne5andohxrwxgjmm5vqTue, 12 Jul 2022 00:00:00 GMTSimplicial quantum contextuality
https://scholar.archive.org/work/qwctn6ix5bhcxid7is5zl3m3iq
We introduce a new framework for contextuality based on simplicial sets, combinatorial models of topological spaces that play a prominent role in modern homotopy theory. Our approach extends measurement scenarios to consist of spaces (rather than sets) of measurements and outcomes, and thereby generalizes nonsignaling distributions to simplicial distributions, which are distributions on spaces modeled by simplicial sets. Using this formalism we present a topologically inspired new proof of Fine's theorem for characterizing noncontextuality in Bell scenarios. Strong contextuality is generalized suitably for simplicial distributions, allowing us to define cohomological witnesses that extend the earlier topological constructions restricted to algebraic relations among quantum observables to the level of probability distributions. Foundational theorems of quantum theory such as the Gleason's theorem and Kochen-Specker theorem can be expressed naturally within this new language.Cihan Okay, Aziz Kharoof, Selman Ipekwork_qwctn6ix5bhcxid7is5zl3m3iqSat, 09 Jul 2022 00:00:00 GMTTreewidth versus clique number. II. Tree-independence number
https://scholar.archive.org/work/hu4xgrrj5vaxzbdb3xb4jsyuua
In 2020, we initiated a systematic study of graph classes in which the treewidth can only be large due to the presence of a large clique, which we call (tw,ω)-bounded. While (tw,ω)-bounded graph classes are known to enjoy some good algorithmic properties related to clique and coloring problems, it is an interesting open problem whether (tw,ω)-boundedness also has useful algorithmic implications for problems related to independent sets. We provide a partial answer to this question by means of a new min-max graph invariant related to tree decompositions. We define the independence number of a tree decomposition 𝒯 of a graph as the maximum independence number over all subgraphs of G induced by some bag of 𝒯. The tree-independence number of a graph G is then defined as the minimum independence number over all tree decompositions of G. Generalizing a result on chordal graphs due to Cameron and Hell from 2006, we show that if a graph is given together with a tree decomposition with bounded independence number, then the Maximum Weight Independent Packing problem can be solved in polynomial time. Applications of our general algorithmic result to specific graph classes will be given in the third paper of the series [Dallard, Milanič, and Štorgel, Treewidth versus clique number. III. Tree-independence number of graphs with a forbidden structure].Clément Dallard, Martin Milanič, Kenny Štorgelwork_hu4xgrrj5vaxzbdb3xb4jsyuuaFri, 01 Jul 2022 00:00:00 GMTZMK Zeitschrift für Medien- und Kulturforschung. Schalten und Walten
https://scholar.archive.org/work/hykxofh3ovcs7kzpbykz7exkou
ZMK 11 | 2020 into space. If complex semiconductor circuits can finally take over thought processes such as arithmetic or even speech, then they are still bodies of thought. So Schalten on its turn brings with it Walten like its own shadow, and, of course, media theory is interested in this remaining ontological shadow of digitization and of mediatization in general. But there is even more than the necessary pertinence of Walten even under digital conditions. Walten is not only the unavoidable substrate of Schalten, it can also emerge from it. One striking example can be seen in what Raymond Williams called the flow. The flux of images on TV is, due to the switchability of the screen picture, continuously and constantly interrupted in a most abrupt way by switching over to other images, most heterogenuous image types, TV genres, broadcast formats. They interfere with each other in a way to only leave caleidoscopic meaningless fragments, tiny bits and pieces of what used to be for instance, news, advertising, wheater forecasts, sports, shows, episodes, fictions, live transmissions, announcements, wrap ups, and so forth. There is no coherence of whatsoever quality, especially if it comes to semantics, to meaning or to any form of Gestalt. The term of coherence (or of interruption) loses any significance. Switching operates, as Hartmut Winkler once put it, an operation directed against any kind of context and hence of text. But, Williams observes, a strange kind of rhythm, or of surfing on the surface of the fragmented sequence of distinctions and of switching operations that comes into being. Based on highly frequent interruptions, a flow of plasticity and viscosity arises, a state of experience or even existence, a mode of being, which integrates viewers, images, switchable pictures, sounds, and the world beyond. Flow is a bodily and hence physical, material phenomenon, not just a structure or a sequence of otherwise disembodied distinctions. It hence brings physis back into the game. Flow emerges from switching, Schalten, but it rules in the sense of Walten. What can be found in the switchable picture may also emerge elsewhere. The Maltese Cross in the movie camera (and projector) could also be adressed here, or, even more general, language. In what André Martinet called la double articulation du langage, the articulation or segmentation of what has already been articulated or fragmented, the coherent dominion of sense emerges as both an artifact, and hence on the side of switching, and an unavoidably and unquestionably ruling condition of existence. Signals, discernable and switchable entities, as they emerge from ruling noise may on their turn, if sequenced, generate a kind of second order flow-like noise and as such turn into given conditions of existence. The cloud, or looped CCTV Systems, or the pervasion of the habitat with computers, and hence switches, may be regarded in a comparable way as modes of turning Schalten into Walten. In this sense, with the topic of Schalten und Walten, the last issue of the ZMK endeavors to investigate the entry or implementation of the mathematical, switch-(:Unkn) Unknown, Mediarep.Org, Lorenz Engell, Bernhard Siegertwork_hykxofh3ovcs7kzpbykz7exkouWed, 29 Jun 2022 00:00:00 GMTThe Gaussian conditional independence inference problem
https://scholar.archive.org/work/hzmnfg7kmbe77ijyxwv7efiryu
Die vorliegende Dissertation beschäftigt sich mit Strukturen Gaußscher bedingter Unabhängigkeit und ihrem Inferenzproblem. Bedingte Unabhängigkeit (engl. conditional independence, CI) ist ein Begriff aus der Wahrscheinlichkeits- und Informationstheorie und "Gaußsch" bezieht sich auf die bekannte multivariate Normalverteilung. Die CI-Relation einer multivariaten Zufallsvariable , deren Komponenten durch eine endliche Menge N indiziert sind, enthält Informationen darüber, welche Komponenten I die Verteilung anderer Komponenten J beeinflussen, wenn der Wert wieder anderer Komponenten K bekannt ist. Diese Relation wird als [ I ?? J j K] oder kurz (I; JjK) geschrieben. Bedingte Unabhängigkeit ist also eine dreiwertige Relation auf Teilvektoren von , die komplexe Abhängigkeiten zwischen den Variablen in kodiert. CI-Relationen werden formal in einem Zweig der künstlichen Intelligenz über logische Inferenzregeln studiert. Solche Inferenzregeln nehmen die folgende Form an: "wenn bestimmte bedingte Unabhängigkeiten gelten, welche (Disjunktionen von) anderen Unabhängigkeiten müssen ebenfalls gelten?" Kenntnis dieser Regeln erlaubt die automatische Deduktion von Informationen über die Abhängigkeitsstruktur von beobachteten Zufallsvariablen. Die Regeln, welche für CI-Relationen gelten, hängen von der Art der Wahrscheinlichkeitsverteilung ab. Binäre Verteilungen erfüllen beispielsweise andere Inferenzregeln als die kontinuierlichen Gaußschen Verteilungen. Eine multivariat Gauß-verteilte Zufallsvariable ist vollständig durch ihre Parameter, den Mittelwert 2 RN und die Kovarianzmatrix Σ 2 PDN, bestimmt. Unter dieser speziellen Annahme ist die bedingte Unabhängigkeitsaussage [ I ?? J j K] äquivalent zu einer Rangbedingung an die Teilmatrix von Σ mit Zeilen I [ K und Spalten J [ K, nämlich dass diese Matrix Rang jKj hat. Dieses Kriterium erlaubt die Behandlung von Gaußscher CI mit Mitteln der kommutativen Algebra, da die Rangbedingung als das Verschwinden einer Reihe von Polynomen in den Einträgen von Σ formuliert werden kann. Das [...]Tobias Boege, Universitäts- Und Landesbibliothek Sachsen-Anhalt, Martin-Luther Universität, Thomas Kahle, Volker Kaibelwork_hzmnfg7kmbe77ijyxwv7efiryuMon, 27 Jun 2022 00:00:00 GMTOn Random Graph Properties
https://scholar.archive.org/work/besi6kkwsfbo7fzgsi6ol6edii
We consider 15 properties of labeled random graphs that are of interest in the graph-theoretical and the graph mining literature, such as clustering coefficients, centrality measures, spectral radius, degree assortativity, treedepth, treewidth, etc. We analyze relationships and correlations between these properties. Whereas for graphs on a small number of vertices we can exactly compute the average values and range for each property of interest, this becomes infeasible for larger graphs. We show that graphs generated by the graph generator with p = 1/2 model well the underlying space of all labeled graphs with a fixed number of vertices. The later observation allows us to analyze properties and correlations between these properties for larger graphs. We then use linear and non-linear models to predict a given property based on the others and for each property, we find the most predictive subset. We experimentally show that pairs and triples of properties have high predictive power, making it possible to estimate computationally expensive to compute properties with ones for which there are efficient algorithms.Hang Chen, Vahan Huroyan, Stephen Kobourov, Myroslav Kryvenwork_besi6kkwsfbo7fzgsi6ol6ediiThu, 23 Jun 2022 00:00:00 GMTTopos and Stacks of Deep Neural Networks
https://scholar.archive.org/work/xw4jwxtjbbfetawfm7jayjlwgi
Every known artificial deep neural network (DNN) corresponds to an object in a canonical Grothendieck's topos; its learning dynamic corresponds to a flow of morphisms in this topos. Invariance structures in the layers (like CNNs or LSTMs) correspond to Giraud's stacks. This invariance is supposed to be responsible of the generalization property, that is extrapolation from learning data under constraints. The fibers represent pre-semantic categories (Culioli, Thom), over which artificial languages are defined, with internal logics, intuitionist, classical or linear (Girard). Semantic functioning of a network is its ability to express theories in such a language for answering questions in output about input data. Quantities and spaces of semantic information are defined by analogy with the homological interpretation of Shannon's entropy of P.Baudot and D.Bennequin in 2015). They generalize the measures found by Carnap and Bar-Hillel (1952). Amazingly, the above semantical structures are classified by geometric fibrant objects in a closed model category of Quillen, then they give rise to homotopical invariants of DNNs and of their semantic functioning. Intentional type theories (Martin-Loef) organize these objects and fibrations between them. Information contents and exchanges are analyzed by Grothendieck's derivators.Jean-Claude Belfiore, Daniel Bennequinwork_xw4jwxtjbbfetawfm7jayjlwgiThu, 16 Jun 2022 00:00:00 GMTMorphometric Analysis on Vanniyar Basin in Dharmapuri, Southern India, Using Geo-Spatial Techniques
https://scholar.archive.org/work/433hvctwazcojess54rgnxw6fq
The Vanniyar basin is located in Dharmapuri district, South India, and is severely affected by climate change. Due to changing climatic conditions and resulting poor precipitation characteristics, this district has received less rainfall over the last three decades (Dharmapuri District Statistical Hand book 2020). The objective of this investigative study is to utilize morphometric techniques and analyze their properties using GIS and image processing techniques. The linear, aerial, and relief morphometric aspects of the Vanniyar basin are analyzed. From the preliminary investigation, the study area occupies the Archean group of rocks. The drainage pattern of the Vanniyar basin is sub-dendritic to dendritic and classified into fifth-order drainage basins. The mean drainage density of the Vanniyar basin is 1.95 km/km2, which indicates that the basin has very permeable soil with intermediate drainage and low to moderate relief. The circularity ratio value reveals that the basin is circular with high to moderate relief and a structurally controlled drainage system. The elongation ratio value reveals that the basin is characterized by high susceptibility to erosion and sediment load. The stream length ratio between the streams of different orders of the Vanniyar basin shows a change in each sub-basin, indicating late youth stage of geomorphic development. From these research studies, farmers in the Vanniyar basin, river Cauvery may now comprehend their drainage basin's geohydrological characteristics.S. Suresh, P. Krishnanwork_433hvctwazcojess54rgnxw6fqThu, 02 Jun 2022 00:00:00 GMTGeneralized point-free spaces, pointwise
https://scholar.archive.org/work/c27qgqtv3bdd7l5rvgkssg2mfm
We survey foundational principles of Grothendieck's generalized spaces, including a critical glossary of the various, and often conflicting, terminological usages. Known results using generalized points support a fully pointwise notation for these essentially point-free structures. This includes some from dependent type theory to deal with bundles as continuous space-valued maps, mapping base point to fibre.Steven Vickerswork_c27qgqtv3bdd7l5rvgkssg2mfmThu, 02 Jun 2022 00:00:00 GMTETH-Tight Algorithms for Finding Surfaces in Simplicial Complexes of Bounded Treewidth
https://scholar.archive.org/work/m7yapsngizeyxbnreiij55tv3u
Given a simplicial complex with n simplices, we consider the Connected Subsurface Recognition (c-SR) problem of finding a subcomplex that is homeomorphic to a given connected surface with a fixed boundary. We also study the related Sum-of-Genus Subsurface Recognition (SoG) problem, where we instead search for a surface whose boundary, number of connected components, and total genus are given. For both of these problems, we give parameterized algorithms with respect to the treewidth k of the Hasse diagram that run in 2^{O(k log k)}n^{O(1)} time. For the SoG problem, we also prove that our algorithm is optimal assuming the exponential-time hypothesis. In fact, we prove the stronger result that our algorithm is ETH-tight even without restriction on the total genus.Mitchell Black, Nello Blaser, Amir Nayyeri, Erlend Raa Vågset, Xavier Goaoc, Michael Kerberwork_m7yapsngizeyxbnreiij55tv3uWed, 01 Jun 2022 00:00:00 GMTTFLEX: Temporal Feature-Logic Embedding Framework for Complex Reasoning over Temporal Knowledge Graph
https://scholar.archive.org/work/2junvojltvebpmw5lwvnuptnwq
Multi-hop logical reasoning over knowledge graph (KG) plays a fundamental role in many artificial intelligence tasks. Recent complex query embedding (CQE) methods for reasoning focus on static KGs, while temporal knowledge graphs (TKGs) have not been fully explored. Reasoning over TKGs has two challenges: 1. The query should answer entities or timestamps; 2. The operators should consider both set logic on entity set and temporal logic on timestamp set. To bridge this gap, we define the multi-hop logical reasoning problem on TKGs. With generated three datasets, we propose the first temporal CQE named Temporal Feature-Logic Embedding framework (TFLEX) to answer the temporal complex queries. We utilize vector logic to compute the logic part of Temporal Feature-Logic embeddings, thus naturally modeling all First-Order Logic (FOL) operations on entity set. In addition, our framework extends vector logic on timestamp set to cope with three extra temporal operators (After, Before and Between). Experiments on numerous query patterns demonstrate the effectiveness of our method.Xueyuan Lin, Chengjin Xu, Haihong E, Fenglong Su, Gengxian Zhou, Tianyi Hu, Ningyuan Li, Mingzhi Sun, Haoran Luowork_2junvojltvebpmw5lwvnuptnwqSat, 28 May 2022 00:00:00 GMTProceedings of the 2022 Joint Workshop of the German Research Training Groups in Computer Science
https://scholar.archive.org/work/lvykkw5kcfhlvolc6paa2sxczu
Having spent two successive years running online to prevent the spread of the Corona virus, the traditional annual meeting of the German Research Training Groups (RTGs) funded by the Deutsche Forschungsgemeinschaft (DFG) in the field of computer science returns to Schloss Dagstuhl --– Leibniz Center for Informatics, one of the world's premier venues for computer science-related seminars. Returning to Dagstuhl and hosting this meeting as an in-person-only event was a deliberate decision to revive interaction modes that many of the funded researchers had yet to experience: fostering personal interchange of ideas and experiences in order to strengthen the connection within the German computer science community. This volume documents the abstracts of the research topics of funded researchers in the participating RTGs. The event was jointly organized by RTG 2475 (Cybercrime and Forensic Computing) and RTG 2428 (ConVeY --- Continuous Verification of Cyber-Physical Systems). It took place between Sunday, June 12 and Wednesday, June 15, 2022, as in-person only Dagstuhl Event 22243. The meeting featured the usual sequence of research presentations by funded researchers, networking meetings for PIs and RTG coordinators, as well as two invited talks, one by Professor Martina Seidl (JKU Linz, Austria) on "Competitions as Scientific Method" and another by Professor Jennifer Byrne (School of Medical Sciences, The University of Sydney, Australia) titled "An introduction to research paper mills". Because last year's event marked the 25th anniversary of the workshop series, it featured a live interview with Professor Otto Spaniol who had initiated the workshop series in 1996. We document the interview in this volume.Felix Freiling, Helmut Seidl, 2022 2022 Joint Workshop Of The German Research Training Groups In Computer Science June 12–June 15work_lvykkw5kcfhlvolc6paa2sxczuTue, 17 May 2022 00:00:00 GMTTopological duality for distributive lattices, and applications
https://scholar.archive.org/work/xnnm6lpovzeg7euoh4xupsxexm
This book is a course in Stone-Priestley duality theory, with applications to logic and theoretical computer science. Our target audience are graduate students and researchers in mathematics and computer science. Our aim is to get in a fairly full palette of duality tools as directly and quickly as possible, then to illustrate and further elaborate these tools within the setting of three emblematic applications: semantics of propositional logics, domain theory in logical form, and the theory of profinite monoids for the study of regular languages and automata. This preprint version contains the first part of the book, a graduate level 'crash course' in duality theory as it is practiced now, and a chapter on applications to domain theory.Mai Gehrke, Sam van Goolwork_xnnm6lpovzeg7euoh4xupsxexmSun, 15 May 2022 00:00:00 GMTEssentials of heterodox and post-Keynesianeconomics
https://scholar.archive.org/work/xl5lkrve4ng2rpegjzpitbnh6i
work_xl5lkrve4ng2rpegjzpitbnh6iFri, 13 May 2022 00:00:00 GMT