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Quantifier-Elimination for the First-Order Theory of Boolean Algebras with Linear Cardinality Constraints
[chapter]
2004
Lecture Notes in Computer Science
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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]
2008
Lecture Notes in Computer Science
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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
2007
Journal of Number Theory
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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]
2017
arXiv
pre-print
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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]
2006
arXiv
pre-print
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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
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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
1999
Topology and its Applications
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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]
2019
arXiv
pre-print
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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]
1996
arXiv
pre-print
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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]
2015
arXiv
pre-print
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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
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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
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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]
2020
arXiv
pre-print
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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]
1991
Lecture Notes in Computer Science
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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]
2016
arXiv
pre-print
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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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