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Complexity in Convex Languages [chapter]

Janusz Brzozowski
2010 Lecture Notes in Computer Science  
Closure properties of convex languages have been studied in this general framework of binary relations.  ...  There are several advantages of studying the class of convex languages and its subclasses together. These classes are all definable by binary relations, in fact, by partial orders.  ...  I am grateful to Galina Jirásková for a very careful reading of the manuscript, and to Jeff Shallit for the reference to Frobenius numbers.  ... 
doi:10.1007/978-3-642-13089-2_1 fatcat:zaikqi3zffas5hnirzepaw2khu

Essentiality and convexity in the ranking of opportunity sets

Matthew Ryan
2016 Social Choice and Welfare  
We restrict attention to binary relations which are re ‡exive and transitive (pre-orders) and which further satisfy a monotonicity and desirability condition.  ...  This paper studies the essential elements (Puppe, 1996) associated with binary relations over opportunity sets.  ...  The convex hull of a set its "closure" with respect to forming convex combinations. Closure spaces provide an algebraic abstraction of the general notion of a closure operation.  ... 
doi:10.1007/s00355-016-0994-8 fatcat:3x4ptxpz7bbpxcxnhkedhb6sha

On the minimality and global consistency of row-convex constraint networks

Peter van Beek, Rina Dechter
1995 Journal of the ACM  
Finally, we generalize the results for binary constraint networks to networks with non-binary constraints. 2  ...  In this paper, we identify a property of binary constraints called row convexity and show its usefulness in deciding when a form of local consistency called path consistency is sucient to guarantee that  ...  Acknowledgements The authors wish to thank the referees for their careful reading of the paper and their helpful comments.  ... 
doi:10.1145/210346.210347 fatcat:5xciy346hfev5bw53pzvwqeu64

Closure operators: Complexity and applications to classification and decision-making [article]

Hamed Hamze Bajgiran, Federico Echenique
2022 arXiv   pre-print
We study the complexity of closure operators, with applications to machine learning and decision theory. In machine learning, closure operators emerge naturally in data classification and clustering.  ...  In decision theory, they can model equivalence of choice menus, and therefore situations with a preference for flexibility.  ...  Some of these applications are related to convex geometries and their representations.  ... 
arXiv:2202.05339v2 fatcat:macwigi47nho5onaniilc63d2m

Similarity and Bisimilarity for Countable Non-Determinism and Higher-Order Functions (Extended Abstract)

Søren B. Lassen, Corin S. Pitcher
1998 Electronical Notes in Theoretical Computer Science  
The di erences between the relations are illustrated by simple examples, and their continuity properties are discussed.  ...  It is also shown that, in some cases, the addition of countable non-determinism to a programming language with nite non-determinism alters the theory of the language.  ...  Acknowledgement We w ould like to thank Ralph Loader, Peter Mosses, Luke Ong, Stan Wainer, and especially Andrew Moran for helpful conversations.  ... 
doi:10.1016/s1571-0661(05)80704-2 fatcat:fxl5sxwd4vgytcuxbzuhucshd4

Decision problems for convex languages

Janusz Brzozowski, Jeffrey Shallit, Zhi Xu
2011 Information and Computation  
Similar results are proved for some subclasses of convex languages: the prefix-, suffix-, factor-, and subword-closed languages, and the prefix-, suffix-, factor-, and subword-free languages.  ...  We examine decision problems for various classes of convex languages, previously studied by Ang and Brzozowski, originally under the name "continuous languages".  ...  We thank the referees for their helpful comments, especially about NL-completeness, and also for their improvements to several proofs.  ... 
doi:10.1016/j.ic.2010.11.009 fatcat:widvjgzcbjeudmj3fn42s5nsvq

Infinitary Howe's Method

Paul Blain Levy
2006 Electronical Notes in Theoretical Computer Science  
That excludes, for example, languages with countable sum types, and has repeatedly caused problems in the literature.  ...  Both extensions possess the key properties of Howe's extension, but it is their intersection that is compatible.  ...  (For a finitary language, these are, respectively, the Howe extension and its dual.) Each of these possesses the same special properties enjoyed by Howe's extension that are used to show simulation.  ... 
doi:10.1016/j.entcs.2006.06.006 fatcat:6ma4k5xg4nhvbckpozmaiiynwq

Quantifier elimination for quasi-real closed fields

Mickaël Matusinski, Simon Müller
2021 Comptes rendus. Mathematique  
We prove quantifier elimination for the theory of quasi-real closed fields with a compatible valuation.  ...  This unifies the same known results for algebraically closed valued fields and real closed valued fields. Résumé.  ...  Acknowledgment The authors wish to thank Salma Kuhlmann for initiating and supporting their collaboration, and also for helpful discussion on the subject.  ... 
doi:10.5802/crmath.169 fatcat:fdju22e2xjexdfdq2ytr4eabj4

Making Use of Similarity in Referential Semantics [chapter]

Helmar Gust, Carla Umbach
2015 Lecture Notes in Computer Science  
Similarity is then spelled out as indistinguishability with respect to a given set of attributes.  ...  Therefore, expressions of similarity in natural language are of special interest: How to account for their meaning including the results on similarity in Cognitive Science and Artificial Intelligence without  ...  The representational layer facilitates comparing entities in the world with respect to their attributes and, in particular, determine whether they are similar with respect to certain attributes.  ... 
doi:10.1007/978-3-319-25591-0_31 fatcat:3xujur7xqbg43i3iyhbyxzfoka

A ModalWalk Through Space

Marco Aiello, Johan van Benthem
2002 Journal of Applied Non-Classical Logics  
Throughout the modal walk through space, expressive power is analyzed in terms of language design, bisimulations, and correspondence phenomena.  ...  This allows us to see new finestructure in spatial patterns which suggests analogies across these mathematical theories in terms of modal, temporal, and conditional logics.  ...  of modal operator depth up to n in their respective models X, X .  ... 
doi:10.3166/jancl.12.319-363 fatcat:q3ck5fvegzcy5nakui5pru6cgq

Extracting semantics from data cubes using cube transversals and closures

Alain Casali, Rosine Cicchetti, Lotfi Lakhal
2003 Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '03  
With this intention, we introduce two novel concepts: the cube transversals and the cube closures over the cube lattice of a categorical database relation.  ...  Using cube transversals and closures, we define a new characterization of boundary sets which provide a condensed representation of version spaces used to enhance supervised classification.  ...  Acknowledgments We would like to thank Laks V. S. Lakshmanan and Jian Pei for their fruitful and quick answers about the Quotient Cube .  ... 
doi:10.1145/956750.956762 dblp:conf/kdd/CasaliCL03 fatcat:jyx5esbxrrb7pj5dqcejqqafde

Extracting semantics from data cubes using cube transversals and closures

Alain Casali, Rosine Cicchetti, Lotfi Lakhal
2003 Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '03  
With this intention, we introduce two novel concepts: the cube transversals and the cube closures over the cube lattice of a categorical database relation.  ...  Using cube transversals and closures, we define a new characterization of boundary sets which provide a condensed representation of version spaces used to enhance supervised classification.  ...  Acknowledgments We would like to thank Laks V. S. Lakshmanan and Jian Pei for their fruitful and quick answers about the Quotient Cube .  ... 
doi:10.1145/956755.956762 fatcat:4apxirmavnbwzacfpmx4pqkdwq

Quantifier elimination for quasi-real closed fields [article]

Mickaël Matusinski, Simon Müller
2020 arXiv   pre-print
We prove quantifier elimination for the theory of quasi-real closed fields with a compatible valuation.  ...  This unifies the same known results for algebraically closed valued fields and real closed valued fields.  ...  Acknowledgment The authors wish to thank Salma Kuhlmann for initiating and supporting their collaboration, and also for helpful discussion on the subject.  ... 
arXiv:2005.12681v2 fatcat:aa2npr7rvjaxtgv7cg6gad2q3q

Ramsey expansions of Λ-ultrametric spaces [article]

Samuel Braunfeld
2017 arXiv   pre-print
For a finite lattice Λ, Λ-ultrametric spaces are a convenient language for describing structures equipped with a family of equivalence relations.  ...  A point of technical interest is that our proof involves classes with non-unary algebraic closure operations.  ...  The passage from Λ to the language of linear orders ensured that every equivalence relation corresponding to a meet-irreducible in Λ was made convex with respect to at least one of the linear orders added  ... 
arXiv:1710.01193v1 fatcat:noj3aujjzrccnohpmadqi2izjm

Modal logics of some geometrical structures

I. B. Shapirovsky
2007 Problems of Information Transmission  
We study modal logics of regions in a real space ordered by the inclusion and compact inclusion relations.  ...  For various systems of regions, we propose complete finite modal axiomatizations; the described logics are finitely approximable and PSPACE-complete.  ...  As examples of relations between regions, one may consider ⊆ (inclusion), (compact inclusion: A B ⇔ CA ⊆ IB, where I and C are the interior and the closure operators, respectively), their converse ⊇ and  ... 
doi:10.1134/s0032946007030076 fatcat:hk4fx7f4n5dixjqy2rtwq2rlcm
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