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Recursion and iteration in continuous theories: The "M-construction"

1983
*
Journal of computer and system sciences (Print)
*

*The*second aim is to present a construction which takes an algebraic

*theory*T

*and*yields another algebraic

*theory*M(T) whose morphisms correspond to systems of

*recursion*equations over T. ... .,

*the*correspondence between T

*and*M(T) is functorial. ... INTRODUCTION

*The*"

*M*-

*construction*" was first outlined

*in*[ 121, then exploited

*in*[ 131

*and*[ 151. An improved presentation

*in*terms of S-sorted

*theories*is given

*in*[ 14) . See also 14, 5, 7, 161. ...

##
###
A domain theory for statistical probabilistic programming

2019
*
Proceedings of the ACM on Programming Languages (PACMPL)
*

These are expressive languages for building Bayesian models of

doi:10.1145/3290349
fatcat:qvrwc47q3fcnxdxriv5m4ueume
*the*kinds used*in*computational statistics*and*machine learning. ... We give an adequate denotational semantics for languages with*recursive*higher-order types,*continuous*probability distributions,*and*soft constraints. ... It has been helpful to discuss this work with*the*Oxford PL*and*Foundations groups, at*the*Domains 2018*and*HOPE 2018 workshops,*and*with Marcelo Fiore, Chris Heunen, Paul Levy, Carol Mak, Gordon Plotkin ...##
###
A mathematical theory of cooperative communication
[article]

2020
*
arXiv
*
pre-print

Cooperative communication plays a central role

arXiv:1910.02822v2
fatcat:nklofoginjeq3kmaj5xwhpkony
*in**theories*of human cognition, language, development, culture,*and*human-robot interaction. ... Through a connection to*the**theory*of optimal transport, we establishing a mathematical framework for cooperative communication. ... This material is based on research sponsored by*the*Air Force Research Laboratory*and*DARPA under agreement number FA8750-17-2-0146*and**the*Army Research Office*and*DARPA under agreement HR00112020039. ...##
###
Quantum complexity theory

1993
*
Proceedings of the twenty-fifth annual ACM symposium on Theory of computing - STOC '93
*

*In*

*the*case that V is a Hilbert space, V * is called

*the*dual of V

*and*is

*the*set of all

*continuous*linear functionals on V ,

*and*

*the*dual space V * is also a Hilbert space. ... is a major breakthrough

*in*complexity

*theory*. ... This paper has greatly benefited from

*the*careful reading

*and*many useful comments of Richard Jozsa

*and*Bob Solovay. ...

##
###
An Outline of Inner Model Theory
[chapter]

2009
*
Handbook of Set Theory
*

Say x is

doi:10.1007/978-1-4020-5764-9_20
fatcat:mrpuyhgxkvfmnhwdz3rfwabvba
*the*α th real*in**the**M*-*constructibility*order. ...*recursive**in*M ♯ n . ... Fullness guarantees that*in**the*comparison of two mice*in*F , neither side drops along*the*branch leading to*the*final model,*and*thus we have*iteration*maps on both sides. ...##
###
Page 4653 of Mathematical Reviews Vol. , Issue 85j
[page]

1985
*
Mathematical Reviews
*

Bloom, Stephen L. (1-STIT); 85j:68067 Thatcher, James W. (1-IBM); Wagner, Eric G. (1-IBM); Wright, Jesse B. (1-IBM)

*Recursion**and**iteration**in**continuous**theories*:*the*“*M*-*construction*”. J. Comput. ...*The*main results*in**the*paper are*the*characterization of*the*free*iterative*matrix*theories**and**the*free*recursive*matrix*theories*. ...##
###
Quantum Complexity Theory

1997
*
SIAM journal on computing (Print)
*

*In*

*the*case that V is a Hilbert space, V * is called

*the*dual of V

*and*is

*the*set of all

*continuous*linear functionals on V ,

*and*

*the*dual space V * is also a Hilbert space. ... is a major breakthrough

*in*complexity

*theory*. ... This paper has greatly benefited from

*the*careful reading

*and*many useful comments of Richard Jozsa

*and*Bob Solovay. ...

##
###
The diamond lemma for ring theory

1978
*
Advances in Mathematics
*

,

doi:10.1016/0001-8708(78)90010-5
fatcat:p2hmdqvysjabfncxxbxwqn3jky
*and*s'*the*reduction system on Z(*M*)*constructed*above ( (21) Note that*in*a reduction system S constructed as above, there will be four kinds of ambiguities. ... Those results say that*the*classes of relations satisfied*in*certain finitely presented objects are not*recursive*; but trivially, they are*recursively*enumerable,*and**the*process described above is just ...##
###
Descriptive set theory and forcing; How to prove theorems about Borel sets the hard way
[article]

1994
*
arXiv
*
pre-print

Section 14

arXiv:math/9401202v1
fatcat:g74gmuoqtfh3vl2ttuvhrfeuse
*and*15 contain new results concerning*the*lengths of Borel hierarchies*in**the*Cohen*and*random real model. Part 2 contains standard results on*the**theory*of Analytic sets. ... Part 3 has*the*usual separation theorems. Part 4 gives some applications of Gandy forcing. We reverse*the*usual trend*and*use forcing arguments instead of Baire category. ... Perfect Set Forcing*In**the**iterated*Sack's real model*the*continuum is ω 2*and*every set X ⊆ 2 ω of cardinality ω 2 can be mapped*continuously*onto 2 ω (Miller [74] ). ...##
###
Confinement for all values of the coupling in four-dimensional SU(2) gauge theory
[article]

2007
*
arXiv
*
pre-print

A derivation is given from first principles of

arXiv:0707.2179v1
fatcat:bjm4itjktvdr7houizhfpuxtpi
*the*fact that*the*SU(2) gauge*theory*is*in*a confining phase for all values of*the*coupling 0 < g < ∞ defined at lattice spacing (UV regulator) a,*and*space-time ... Under successive decimations*the*flow of*the*effective action*in*these representations is constrained by that*in**the*upper*and*lower bounds which are easily explicitly computable. ...*The*interpolating partition function on Λ (*m*)*constructed*fromc j andF 0 is now defined byZ Λ (m) (β, h, α, t, r) =F 0 (m, h, α, t) |Λ (m) | Z Λ (m) ({c j (m, α, r)}) (3.19) where Z Λ (m) ({c j (m, α, ...##
###
A DSEL for Computational Category Theory

2010
*
Zenodo
*

Computational category

doi:10.5281/zenodo.3247827
fatcat:7inuxowowjeqlitkp34tr5zngm
*theory*is a branch of computer science devoted to*the*study of algorithms which can be stated*in*terms of category*theory*concepts. ... Code snippets*and*examples are presented to help bring this abstract topic closer to practice. ...*The*author is grateful to*the*anonymous reviewers for their help*in*improving this work. ...##
###
A DSEL for Computational Category Theory

2010
*
Zenodo
*

Computational category

doi:10.5281/zenodo.3247828
fatcat:pl3vq7wl65cnfoywkzsg6l2uvu
*theory*is a branch of computer science devoted to*the*study of algorithms which can be stated*in*terms of category*theory*concepts. ... Code snippets*and*examples are presented to help bring this abstract topic closer to practice. ...*The*author is grateful to*the*anonymous reviewers for their help*in*improving this work. ...##
###
Independence and port oracles for matroids, with an application to computational learning theory

1996
*
Combinatorica
*

*In*this context,

*the*algorithm generalizes results of Angluin, Hellerstein,

*and*Karpinski 1],

*and*Raghavan

*and*Schach 17], who showed that certain subclasses of

*the*BMP functions are learnable

*in*polynomial ... Thus, this algorithm solves a problem

*in*computational learning

*theory*; it learns

*the*class of binary matroid port (BMP) functions with membership queries

*in*polynomial time. ... Acknowledgments We thank David Hartvigsen for suggesting

*the*use of ear decompositions

*in*this work,

*and*Nader Bshouty

*and*Andras Frank for useful discussions. ...

##
###
Complexity theory for spaces of integrable functions
[article]

2017
*
arXiv
*
pre-print

*In*contrast to

*the*representation of

*continuous*functions, however, this representation turns out to be discontinuous with respect to both

*the*norm

*and*

*the*weak topology. ...

*The*second part modifies

*the*representation to be

*continuous*

*and*generalizes it to Lp-spaces. ...

*Recursively*for any k <

*m*

*construct*a family of points (x k i ) i∈{1,...,2 m−k−1 } of pairwise distance at least 2 −m such that f (k) (x k i ) ≤ 2 k(m+1) C. ...

##
###
Axiomatic stable homotopy theory

1997
*
Memoirs of the American Mathematical Society
*

We define

doi:10.1090/memo/0610
fatcat:3snf7wg2cfcv5ggvepumnc4i2a
*the*class of Noetherian stable homotopy categories,*and*investigate their special properties. ... We define*and*investigate a class of categories with formal properties similar to those of*the*homotopy category of spectra. ... This is essentially surjective: for any module M , we can choose a presentation i R − → j R − →*M*,*construct*a corresponding cofiber sequence i S − → j S − → X,*and*then X[0] ∈ A*and*π 0 X[0] = M . ...
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