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

Stephen L. Bloom, James W. Thatcher, Eric G. Wagner, Jesse B. Wright
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.  ... 
doi:10.1016/0022-0000(83)90037-5 fatcat:t6ilio5qofazffx7amjhel4rpe

A domain theory for statistical probabilistic programming

Matthijs Vákár, Ohad Kammar, Sam Staton
2019 Proceedings of the ACM on Programming Languages (PACMPL)  
These are expressive languages for building Bayesian models of 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  ... 
doi:10.1145/3290349 fatcat:qvrwc47q3fcnxdxriv5m4ueume

A mathematical theory of cooperative communication [article]

Pei Wang, Junqi Wang, Pushpi Paranamana, Patrick Shafto
2020 arXiv   pre-print
Cooperative communication plays a central role 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.  ... 
arXiv:1910.02822v2 fatcat:nklofoginjeq3kmaj5xwhpkony

Quantum complexity theory

Ethan Bernstein, Umesh Vazirani
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.  ... 
doi:10.1145/167088.167097 dblp:conf/stoc/BernsteinV93 fatcat:k5zp4zqxbrappefvy5repc6hxe

An Outline of Inner Model Theory [chapter]

John R. Steel
2009 Handbook of Set Theory  
Say x is 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.  ... 
doi:10.1007/978-1-4020-5764-9_20 fatcat:mrpuyhgxkvfmnhwdz3rfwabvba

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: theM-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

Ethan Bernstein, Umesh Vazirani
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.  ... 
doi:10.1137/s0097539796300921 fatcat:gt2bmvrhf5f4pecisljp65kumi

The diamond lemma for ring theory

George M Bergman
1978 Advances in Mathematics  
, 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  ... 
doi:10.1016/0001-8708(78)90010-5 fatcat:p2hmdqvysjabfncxxbxwqn3jky

Descriptive set theory and forcing; How to prove theorems about Borel sets the hard way [article]

Arnold Miller
1994 arXiv   pre-print
Section 14 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] ).  ... 
arXiv:math/9401202v1 fatcat:g74gmuoqtfh3vl2ttuvhrfeuse

Confinement for all values of the coupling in four-dimensional SU(2) gauge theory [article]

E. T. Tomboulis
2007 arXiv   pre-print
A derivation is given from first principles of 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,  ... 
arXiv:0707.2179v1 fatcat:bjm4itjktvdr7houizhfpuxtpi

A DSEL for Computational Category Theory

Aleksandar M. Bakic
2010 Zenodo  
Computational category 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.  ... 
doi:10.5281/zenodo.3247827 fatcat:7inuxowowjeqlitkp34tr5zngm

A DSEL for Computational Category Theory

Aleksandar M. Bakic
2010 Zenodo  
Computational category 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.  ... 
doi:10.5281/zenodo.3247828 fatcat:pl3vq7wl65cnfoywkzsg6l2uvu

Independence and port oracles for matroids, with an application to computational learning theory

Collette R. Coullard, Lisa Hellerstein
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.  ... 
doi:10.1007/bf01844845 fatcat:cjitvomrzrbqfapzq5u5hd37ti

Complexity theory for spaces of integrable functions [article]

Florian Steinberg
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.  ... 
arXiv:1612.06419v2 fatcat:afmg7rhuozdt5cf6cpif4ntfze

Axiomatic stable homotopy theory

Mark Hovey, John H. Palmieri, Neil P. Strickland
1997 Memoirs of the American Mathematical Society  
We define 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 .  ... 
doi:10.1090/memo/0610 fatcat:3snf7wg2cfcv5ggvepumnc4i2a
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