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On the Accepting Power of 2-Tape Büchi Automata [chapter]

Olivier Finkel
2006 Lecture Notes in Computer Science  
We show that, from a topological point of view, 2-tape Büchi automata have the same accepting power than Turing machines equipped with a Büchi acceptance condition.  ...  This surprising result gives answers to questions of Simonnet [Sim92] and of Lescow and Thomas [Tho90, LT94] .  ...  Thanks to the anonymous referees for useful comments on a preliminary version of this paper.  ... 
doi:10.1007/11672142_24 fatcat:h5bs3qyzv5bv7kw7i7jhvkx2ru

An unsolved problem on the powers of 3/2

K. Mahler
1968 Journal of the Australian Mathematical Society  
[5] An unsolved problem on the powers of | 317 We shall use the notation 2 a \\H to denote that H is divisible by 2°, but not by 2 a+1 . 6 Put (15) a k = m k+1 -rn k -l, H k = -^-.  ...  This formula may be written as By the binomial theorem, it implies that T(t)-\-l is the coefficient of z* in the power series in powers of z for and hence T(t)-\-l is also the coefficient of z* in the  ... 
doi:10.1017/s1446788700005371 fatcat:w6fe2afgvrhhrdv4b5my5q6bnu

On the Accepting Power of 2-Tape Büchi Automata [article]

Olivier Finkel
2007 arXiv   pre-print
We show that, from a topological point of view, 2-tape B\"uchi automata have the same accepting power than Turing machines equipped with a B\"uchi acceptance condition.  ...  Thesis, Universit\'e Paris 7, March 1992], and of H. Lescow and W. Thomas [Logical Specifications of Infinite Computations, In: "A Decade of Concurrency", LNCS 803, Springer, 1994, p. 583-621].  ...  Thanks to the anonymous referees for useful comments on a preliminary version of this paper.  ... 
arXiv:0712.0165v1 fatcat:vokth7s2dvbltpvrlxtqdirf6q

Reflections on the Power of the Pen – Issue 2 Editorial

Anna Lawson, Angharad E. Beckett
2022 International Journal of Disability and Social Justice  
The following people deserve particular thanks for their work on this edition: David Abbott (for guiding authors through the process of preparing plain English/lay summaries of their articles); Simon T.M  ...  We note, in particular, the time and care colleagues have been taking to provide constructive feedback, especially (but not only) when they are alerted that the author(s) are early-career.  ...  Particular attention is given to the relationship between Paralympics on the one hand and accessibility and awareness, particularly of the social model of disability, on the other.  ... 
doi:10.13169/intljofdissocjus.2.1.0004 fatcat:nu4l55imhrhyxmfsy22ytkq76a

On the Power Functions of the $E^2$-Test and the $T^2$-Test

P. L. Hsu
1945 The Annals of Mathematical Statistics  
ON THE POWER FUNCTIONS OF THE E?-TEST AND THE 7°-TEST By P. L. Hsu National University of Peking 1. The general linear hypothesis.  ...  The author has proved [3] that of all the critical regions which satisfy (5) and whose power function is a function of an,, alone, the region w is the uniformly most powerful one.  ... 
doi:10.1214/aoms/1177731091 fatcat:ak5f4mbx3fefplyv7lpdothmme

Remarks on the symmetric powers of cusp forms on GL(2) [article]

Dinakar Ramakrishnan
2009 arXiv   pre-print
Moreover, sym^6(pi) is Eisenteinian iff sym^5(pi) is an abelian twist of the functorial product of pi with the symmetric square of a cusp form pi' on GL(2)/F.  ...  Assume that all the symmetric powers sym^m(pi) are modular, i.e., define automorphic forms on GL(m+1)/F. If sym^6(pi) is cuspidal, then all the symmetric powers are cuspidal, for all m.  ...  Forms on adele groups, and his expository papers, Automorphic forms and Artin's conjecture and Elliptic curves and automorphic representations, as well as his seminal  ... 
arXiv:0710.0676v2 fatcat:kyjolwexqva6hjnvtnqgs66doy

On the $2$-class group of some number fields of $2$-power degree

IDRISS JERRARI, ABDELMALEK AZIZI
2022 Turkish Journal of Mathematics  
In this paper, we compute the rank of the 2 -class group of K * n the n -th layer of the cyclotomic Z2 -extension of K * .  ...  Let K be an imaginary cyclic quartic number field whose 2 -class group is isomorphic to Z/2Z × Z/2Z , and let K * denote the genus field of K .  ...  This section is one of the steps of the proof of Theorem 4.2, in which we shall determine the structure of the 2 -class group of K * 1 = K( √ q, ζ 8 ) of degree 32 over Q.  ... 
doi:10.55730/1300-0098.3287 fatcat:zctmzlegkrfp7naelynpgvczzu

On the power of unique 2-prover 1-round games

Subhash Khot
2002 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing - STOC '02  
We make the following conjecture regarding the power of unique 2-prover games, which we call the Unique Games Conjecture :  ...  A 2-prover game is called unique if the answer of one prover uniquely determines the answer of the second prover and vice versa (we implicitly assume games to be one round games).  ...  Proceedings of the 17th IEEE Annual Conference on Computational Complexity (CCC'02) 1093-0159/02 $17.00 © 2002 IEEE  ... 
doi:10.1145/510014.510017 fatcat:v6b6shr4hbcb5cga27p2osbtxu

On Lie powers of the augmentation ideal in characteristic 2

A.I. Papistas
2011 Journal of Algebra  
In this article we concentrate on Lie powers L n ( ) of , and describe the module decomposition of L 16 ( ), a module of dimension 2690010. In particular, I(L 16 ( )) = {D, V 1 , V 2 , V 3 , * }.  ...  Write L(V ) for the free Lie algebra on V . The action of G on V extends naturally to L(V ), so it becomes a K Gmodule which is direct sum of finite-dimensional submodules.  ...  Bryant for his invaluable advice, suggestions and comments, and the referee for the suggestion on the proof of Lemma 3.1.  ... 
doi:10.1016/j.jalgebra.2011.06.015 fatcat:pq7ge7ai6rachfw5wlvsjrsig4

On the power of unique 2-prover 1-round games

Subhash Khot
2002 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing - STOC '02  
We make the following conjecture regarding the power of unique 2-prover games, which we call the Unique Games Conjecture :  ...  A 2-prover game is called unique if the answer of one prover uniquely determines the answer of the second prover and vice versa (we implicitly assume games to be one round games).  ...  Proceedings of the 17th IEEE Annual Conference on Computational Complexity (CCC'02) 1093-0159/02 $17.00 © 2002 IEEE  ... 
doi:10.1145/509907.510017 dblp:conf/stoc/Khot02a fatcat:72sdsghnnba57byrvfqrtamjye

On the Expressive Power of 2-Stack Visibly Pushdown Automata

Benedikt Bollig, Rajeev Alur
2008 Logical Methods in Computer Science  
Finally, we discuss the expressive power of Büchi 2-stack visibly pushdown automata running on infinite (nested) words.  ...  even express properties beyond the class of context-free languages.  ...  Acknowledgment We thank the anonymous referees for their careful reading and many useful remarks.  ... 
doi:10.2168/lmcs-4(4:16)2008 fatcat:3qd2cy6o2vh7valxxjqe3jsghq

On the fields of $2$-power torsion of certain elliptic curves

C. Rasmussen
2004 Mathematical Research Letters  
Let µ 2 ∞ denote the group of 2-power roots of unity.  ...  The outer pro-2 Galois representation on the projective line minus three points has a kernel whose fixed field, Ω 2 , is a pro-2 extension of Q (µ 2 ∞), unramified away from 2.  ...  This research was supported by the University of Arizona's NSF VIGRE Grant #9977116.  ... 
doi:10.4310/mrl.2004.v11.n4.a10 fatcat:qub5qyg4iza7jph6rowl5ufgze

On the symmetric powers of cusp forms on GL (2) of icosahedral type [article]

Song Wang
2003 arXiv   pre-print
In this note we study the symmetric powers of strongly modular icosahedral representations ρ of Gal (F̅/F), F a number field, and their twisted L--functions.  ...  paper, which may be of independent interest, for the Kim--Shahidi automorphic tensor product π sym^2 (π'), where π and π' are cuspidal automorphic representations of GL (2) / F.  ...  In the Theorem below, sym m (ρ) denotes the symmetric m-th power of ρ, i.e., the composition of ρ with the symmetric m-th power representation of GL 2 (C) into GL m+1 (C).  ... 
arXiv:math/0301074v3 fatcat:64tbea5535h6xf5ho6anabzxxq

On the Differential Properties of the Power Mapping x^p^m+2 [article]

Yuying Man, Yongbo Xia, Chunlei Li, Tor Helleseth
2022 arXiv   pre-print
In this paper, we investigate the differential properties of the power mapping x^p^m+2 over 𝔽_p^n, where n=2m or n=2m-1.  ...  For the case n=2m, by transforming the derivative equation of x^p^m+2 and studying some related equations, we completely determine the differential spectrum of this power mapping.  ...  Moreover, by Lemma 2, one can easily compute the differential spectrum of the power mapping x p t +1 over F p n for any odd prime p. 3.2 The differential spectrum of x p m +2 for p = 3 In this subsection  ... 
arXiv:2204.08118v1 fatcat:blj626h3x5ghjcuurzcnm2huru

Impact of the economic recession on the European power sector's CO 2 emissions

Bruno Declercq, Erik Delarue, William D'haeseleer
2011 Energy Policy  
This paper investigates the impact of the economic recession on CO 2 emissions in the European power sector, during the years 2008 and 2009.  ...  Three main determinants of the power sector's emissions are identified: the demand for electricity, the CO 2 price, and fuel prices (especially gas and coal prices).  ...  However, in the summer of 2008, the economy was hit by a severe recession. The focus of this paper is on CO 2 emission in the power sector, in the years 2008 and 2009.  ... 
doi:10.1016/j.enpol.2010.12.043 fatcat:qss2lvtbirc6njqclnzd5jezqm
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