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Quantifier-Elimination for the First-Order Theory of Boolean Algebras with Linear Cardinality Constraints [chapter]

Peter Revesz
2004 Lecture Notes in Computer Science  
We present for the first-order theory of atomic Boolean algebras of sets with linear cardinality constraints a quantifier elimination algorithm.  ...  We also explain the connection of this new logical result with the evaluation of relational calculus queries on constraint databases that contain Boolean linear cardinality constraints.  ...  Acknowledgment: I thank the conference organizers, especially András Benczur, for encouraging submission of this paper.  ... 
doi:10.1007/978-3-540-30204-9_1 fatcat:4jaji3a2pjcfbit3suhp3jq3jm

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

Bruno Courcelle
2008 Lecture Notes in Computer Science  
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.  ...  Graph structure is a flexible concept covering many different types of graph properties.  ...  I thank A. Blumensath, M. 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

Patterns of quadratic residues and nonresidues for infinitely many primes

Steve Wright
2007 Journal of Number Theory  
We solve problem (1) and we show that problem (2) is equivalent to a purely combinatorial problem concerning families of subsets of a finite set.  ...  For sets S of (essentially) small cardinality, we solve problem (2). Related results and some associated enumerative combinatorics are also discussed.  ...  I also thank the referee for several comments which lead to significant improvements in the exposition of this paper.  ... 
doi:10.1016/j.jnt.2006.06.003 fatcat:jrcfykf3una2ho2rhcdhwcmmoe

Model structure on differential graded commutative algebras over the ring of differential operators [article]

Gennaro di Brino, Damjan Pistalo, Norbert Poncin
2017 arXiv   pre-print
We construct a cofibrantly generated model structure on the category of differential non-negatively graded quasi-coherent commutative D_X-algebras, where D_X is the sheaf of differential operators of a  ...  This article is the first of a series of works -located at the interface of homotopical algebra, algebraic geometry, and mathematical physics - on a derived D-geometric approach to the BV-formalism.  ...  Introduction The solution functor of a system of linear PDE-s D · m = 0 is a functor Sol : Mod(D) → Set defined on the category of modules over the ring D of (linear) differential operators of a suitable  ... 
arXiv:1505.07720v2 fatcat:ww2be7qzabh6ljbnrxcc23mgem

Categorified Algebra and Quantum Mechanics [article]

Jeffrey Morton
2006 arXiv   pre-print
Examples include the interpretation of N as the Burnside rig of the category of finite sets with product and coproduct, and the interpretation of N[x] as the category of combinatorial species.  ...  out to be closely related.  ...  the operation of taking the free monoid on a set.  ... 
arXiv:math/0601458v1 fatcat:pdl5xduorzdjlcwl7rnh2e7yau

Page 3816 of Mathematical Reviews Vol. , Issue 80J [page]

1980 Mathematical Reviews  
Kato [Perturbation theory for linear operators, Springer, New York, 1966; MR 34 #3324] proved that if A is an m-accretive linear operator in a Hilbert space, then A has a unique m-accretive square root  ...  Let R be the free associative k-algebra on n’ generators a,, and R<x) the free associative k-algebra in one further indeterminate x.  ... 

Monotone normality in products

P.M. Gartside
1999 Topology and its Applications  
It is shown that if the square of a space is monotonically normal, then all finite powers are monotonically normal and hereditarily paracompact.  ...  Nonetheless, a monotonically normal topological group is constructed, all of whose finite powers are monotonically normal, but which is not linearly stratifiable.  ...  Acknowledgements The author would like to warmly thank Robin Knight for his invaluable assistance in finding a tangle free, nonlinear, filter.  ... 
doi:10.1016/s0166-8641(97)00230-7 fatcat:qndykxog25fmxieke3pv57z5di

The incidence comodule bialgebra of the Baez-Dolan construction [article]

Joachim Kock
2019 arXiv   pre-print
Starting from any operad P, one can consider on one hand the free operad on P, and on the other hand the Baez–Dolan construction on P.  ...  If P is any monoid Ω (considered as a one-coloured operad with only unary operations), the resulting comodule bialgebra is the dual of the near-semiring of Ω-moulds under product and composition, as employed  ...  on various parts of this work.  ... 
arXiv:1912.11320v1 fatcat:bto3lanw3vcbvhvfguzdn3ogxe

Introduction to mathematical logic - A problem solving course [article]

Arnold W. Miller
1996 arXiv   pre-print
This is a set of 288 questions written for a Moore-style course in Mathematical Logic. I have used these (or some variation) four times in a beginning graduate course.  ...  Topics covered are: propositional logic axioms of ZFC wellorderings and equivalents of AC ordinal and cardinal arithmetic first order logic, and the compactness theorem Lowenheim-Skolem theorems Turing  ...  one-to-one correspondence with an element of ω A set is countable iff it is either finite or of the same cardinality as ω.  ... 
arXiv:math/9601203v1 fatcat:aw7ratpzxncljorpdbe4kwnnrq

Decomposition Spaces, Incidence Algebras and Möbius Inversion [article]

Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks
2015 arXiv   pre-print
We work on the objective level of homotopy linear algebra with coefficients in infinity-groupoids, developed along the way.  ...  Imposing certain homotopy finiteness conditions yields the notion of M\"obius decomposition space, an extension of the notion of M\"obius category of Leroux.  ...  Then one can take homotopy cardinality, and recover linear algebra over Q. The finiteness conditions are needed to be able to take homotopy cardinality.  ... 
arXiv:1404.3202v5 fatcat:andjk5vfi5ag7nk4dl6zraqahi

Page 1781 of Mathematical Reviews Vol. 51, Issue 6 [page]

1976 Mathematical Reviews  
A continuous map / of a closed cone Cc R™ into R* is said to be piecewise homogeneous linear if there is a finite set fis» Sn Of homogeneous linear functions R"—> R* such that, for each x € C, f(x)=f,(  ...  Also the authors give a set of conditions on an /-ring A under each of which L(A) coincides with the set N of all nilpotents of A. S. P.  ... 

Page 1720 of Mathematical Reviews Vol. 50, Issue 6 [page]

1975 Mathematical Reviews  
Table of Contents: A. V. Buhvalov, The integral representation of linear operators (pp. 5-14); S. A. Vinogradov and V. P. Havin, Free interpolation in H® and in certain other classes of functions.  ...  Erdés, A. Hajnal, L. Pésa, Strong embeddings of graphs into colored graphs (pp. 585-595); P. Erdés and S. H. Hechler, On maximal almost-disjoint families over singular cardinals (pp. 597-604). Vol.  ... 

Plethysms and operads [article]

Alex Cebrian
2020 arXiv   pre-print
We introduce the 𝒯-construction, an endofunctor on the category of generalized operads as a general mechanism by which various notions of plethystic substitution arise from more ordinary notions of substitution  ...  In the special case of one-object unary operads, i.e. monoids, we recover the T-construction of Giraudo.  ...  Lemma 6 .1. 2 . 62 Consider the category of finite ordinals and set maps. (i) The class of monotone pullback squares is closed under composition of squares.  ... 
arXiv:2008.09798v2 fatcat:nfixhhk3wze2jk2m365mzkdiym

Algorithms for determining the smallest number of nonterminals (states) sufficient for generating (accepting) a regular language [chapter]

Kosaburo Hashiguchi
1991 Lecture Notes in Computer Science  
Important note: this is not a "due homework", but rather a "pool of problems" meant to calibrate the scope and depth of the knowledge & skills in CS theory that you (eventually) need to have for exams,  ...  Recall that most (and perhaps even all) of the midterm and final exam questions in this course will come from these problem sets, so your best strategy of studying for the exams in this course is to solve  ...  What is the cardinality of the set of all finite-sized matrices with rational entries? 5. What is the cardinality of the set of all infinite matrices with Boolean entries? 6.  ... 
doi:10.1007/3-540-54233-7_170 fatcat:phnjlcnxdbbsnkq73acbvvezqa

Quadratic Modules, C*-Algebras, and Free Convexity [article]

Vadim Alekseev, Tim Netzer, Andreas Thom
2016 arXiv   pre-print
We show that the usual notion of a free convex hull is not able to detect residual finite-dimensionality. We thus propose a new notion of free convexity, which is coordinate-free.  ...  We characterize semialgebraicity of free convex hulls of semialgebraic sets, and show that they are not always semialgebraic, even at scalar level.  ...  semialgebraic set (finite intersections of such sets are also called basic closed).  ... 
arXiv:1602.01618v1 fatcat:hnwbgqx2ujggbhy5pfdugbtg2y
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