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Isomorphisms and 1-L reductions

1988
*
Journal of computer and system sciences (Print)
*

All sets complete for NP under

doi:10.1016/0022-0000(88)90033-5
fatcat:qxmgzsutozaetfujbhftpwp5ka
*1*-*L**reductions*are complete under length-increasing, invertible,*and*"almost one-one" <;*reductions*. All sets complete for PSPACE under*1*-*L**reductions*are p-*isomorphic*. ... This paper also benefited from the careful scrutiny*and*helpful comments of an anonymous referee. ... ACKNOWLEDGMENTS Stimulating discussions with the following people influenced the direction in which this work developed: my thesis advisor: Kim King, Juris Hartmanis, Deborah Joseph, Steve Mahaney, Osamu Watanabe,*and*...##
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On the p-isomorphism conjecture

1991
*
Theoretical Computer Science
*

We show, for example, the following claim: if EXPSPACE ("Gf DSPACE(2Po'Y)) has a non-pisomorphic pair of complete sets, then it has a complete set that is not p-

doi:10.1016/0304-3975(91)90284-9
fatcat:azhmxws2zvbj5h7aiy7ah7uvyu
*isomorphic*to U*and*that is of the form ... ., on the p-*isomorphism*conjecture (Note), Theoretical Computer Science 83 (1991) 337-343. ... Ko*and*the referee for their comments*and*suggestions that helped him to improve the presentation of this paper. He also thanks Professor P. Young for his encouragement. ...##
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Strong Reductions and Isomorphism of Complete Sets
[chapter]

2007
*
Lecture Notes in Computer Science
*

We study the structure of the polynomial-time complete sets for NP

doi:10.1007/978-3-540-77050-3_14
fatcat:33tddc6u2vdghdzr4w2uft6avy
*and*PSPACE under strong nondeterministic polynomial-time*reductions*(SNP-*reductions*). ... are SNP-*isomorphic*. ... For example, we now know that all*1*-*L*-complete sets for NP*and*PSPACE are p-*isomorphic*[8, 7] . ...##
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On traces of Frobenius endomorphisms

2014
*
Finite Fields and Their Applications
*

Thus, tr (A p ) = tr ((A ′ ) p )

doi:10.1016/j.ffa.2013.10.003
fatcat:nqt7bvsxfbetjcdcmcykvmzgea
*and**L*p = (tr (A p ), p, −*1*, 0) = (tr ((A ′ ) p ), p, −*1*, 0) =*L*′ p . ... To answer this question, let us compare the local zetas for the*L*(E CM , s)*and**L*(A RM , s); it follows from lemma*1*, that for every n ≥*1*it holds |E CM (F p n )| = |K 0 (O εn )|*1*. ...##
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Polynomial-Time Isomorphism of 1-L-Complete Sets

1996
*
Journal of computer and system sciences (Print)
*

Let C be any complexity class closed under log-lin

doi:10.1006/jcss.1996.0057
fatcat:xhzlsnzpgbhivfff7yghp6ipua
*reductions*. We show that all sets complete for C under*1*-*L**reductions*are polynomialtime*isomorphic*to each other. ... As a corollary, we show that all sets complete for C under two-way DFA*reductions*are polynomial-time*isomorphic*to each other. ] ... ACKNOWLEDGMENTS We thank the anonymous referees for many helpful suggestions*and*improvements. ...##
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Reductions to Graph Isomorphism

2008
*
Theory of Computing Systems
*

For the case of Turing reducibilities we show that for any k ≥ 0 an NC k+

doi:10.1007/s00224-008-9159-1
fatcat:qguumsz2tbc6tgxlkxmuesxndq
*1**reduction*to GI can be transformed into an AC k*reduction*to the same problem. ... We show that several reducibility notions coincide when applied to the Graph*Isomorphism*(GI) problem. ... But the type of*isomorphism*can tell us whether G A i,j ∼ = H A i,j*and*whether G B k,*l*∼ = H B k,*l*. ...##
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Reductions to Graph Isomorphism
[chapter]

2007
*
Lecture Notes in Computer Science
*

For the case of Turing reducibilities we show that for any k ≥ 0 an NC k+

doi:10.1007/978-3-540-77050-3_13
fatcat:cgglfesjhjhz5kul76vigsn4j4
*1**reduction*to GI can be transformed into an AC k*reduction*to the same problem. ... We show that several reducibility notions coincide when applied to the Graph*Isomorphism*(GI) problem. ... But the type of*isomorphism*can tell us whether G A i,j ∼ = H A i,j*and*whether G B k,*l*∼ = H B k,*l*. ...##
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The Role Of Exotic Affine Spaces In the Classification Of Homogeneous Affine Varieties
[chapter]

2004
*
Encyclopaedia of Mathematical Sciences
*

If we identify Y with the

doi:10.1007/978-3-662-05652-3_9
fatcat:zbtexsf6mrhynnnaggp5ghbwz4
*L*-invariant subvarietyŝ −*1*(*1*) ⊂ U , we obtain a natural action of*L*on Y*and*the*isomorphism*U ∼ = Y × V is*L*-equivariant. ... The*reductive*group*L*acts by conjugation on both U = R u (G)*and*V = R u (H)*and*these actions are*isomorphic*to a linear representations. ...##
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On p-torsion of p-adic elliptic curves with additive reduction
[article]

2013
*
arXiv
*
pre-print

Let E be an elliptic curve with additive

arXiv:1211.5833v2
fatcat:nrogl7hsqvezffdxvzmbq7xdwm
*reduction*over the p-adic numbers,*and*let G be the group of p-adic points on E that have good*reduction*. ... This paper gives necessary*and*sufficient conditions for G to contain non-trivial p-torsion. ... Now assume 6e(K/Q p ) < p −*1*, so that v*L*(p) = 6v K (p) = 6e(K/Q p ) < p −*1*. Now [2, IV.6.4(b)] implies that E*1*(K) is topologically*isomorphic*to m K ,*and*D*1*(*L*) to m*L*. ...##
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Selmer companion curves

2014
*
Transactions of the American Mathematical Society
*

We say that two elliptic curves E

doi:10.1090/s0002-9947-2014-06114-x
fatcat:44guwzyhe5dntacqbkkrkswpy4
*1*, E 2 over a number field K are n-Selmer companions for a positive integer n if for every quadratic character χ of K, there is an*isomorphism*Seln(E χ*1*/K) ∼ = Seln ... We give sufficient conditions for two elliptic curves to be n-Selmer companions,*and*give a number of examples of non-isogenous pairs of companions. ... v above p, either • E*1**and*E 2 have potentially multiplicative*reduction*at v, or • p > 2, E*1**and*E 2 have good*reduction*at v,*and*the*isomorphism*of (i) extends to an*isomorphism*E*1*[p k ] ∼ = E ...##
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Graph Isomorphism and Circuit Size
[article]

2018
*
arXiv
*
pre-print

In this brief note, we observe that the

arXiv:1511.08189v2
fatcat:tnvwhk5bajb3pnpijuljozwgqq
*reduction*of Graph Automorphism to the Rigid Graph Ismorphism problem can be accomplished even using Grollman*and*Selman's notion of a "smart*reduction*". ... It is well-known [KST93] that the complexity of the Graph Automorphism problem is characterized by a special case of Graph*Isomorphism*, where the input graphs satisfy the "promise" of being rigid (that ... Arvind for helpful comments about the graph automorphism problem*and*rigid graphs. ...##
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Reductive pairs arising from representations
[article]

2014
*
arXiv
*
pre-print

Let G be a

arXiv:1412.8603v1
fatcat:6rnbxzjzofgn5lzene6bcdculu
*reductive*algebraic group*and*V a G-module. We consider the question of when (GL(V), rho(G)) is a*reductive*pair of algebraic groups, where rho is the representation afforded by V. ... We first make some observations about general G*and*V, then specialise to the group SL2(K) with K algebraically closed of positive characteristic p. ... Note that ∇(λ) has socle*isomorphic*to*L*(λ),*and*∆(λ) has head*isomorphic*to*L*(λ). Thus Hom SL 2 (*L*(λ),*L*(µ) ⊗*L*(ν)) embeds in Hom SL 2 (∆(λ),*L*(µ) ⊗*L*(ν)). ...##
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Principal bundles over a smooth real projective curve of genus zero

2008
*
Advances in Geometry
*

The tautological line bundle over the real projective line P

doi:10.1515/advgeom.2008.029
fatcat:5qyfep42wfbudpail325zdvg2a
*1*R ,*and*the principal Z/2Zbundle P*1*C −→ P*1*R , together give a principal G m × (Z/2Z)-bundle F on P*1*R . ... Given any principal G-bundle E G over P*1*R , where G is any connected*reductive*linear algebraic group defined over R, we prove that there is a homomorphism ρ : G m × (Z/2Z) −→ G such that E G is*isomorphic*... It is easy to see directly that the two pairs (O X C ,*1*)*and*(O X C , −*1*) are not*isomorphic*. ...##
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One-way functions and the nonisomorphism of NP-complete sets

1991
*
Theoretical Computer Science
*

Hartmanis, J.

doi:10.1016/0304-3975(91)90323-t
fatcat:j2mh2qa4d5cb5e3l34mtvmlnbu
*and*L.A. Hemachandra, One-way functions*and*the nsnisomorphism of NPcomplete sets (Note), Theoretical Computer Science 81 ( 1991) 155-163. ... to*l*-to-*l*length-increasing polynomial-time*reductions*, but that are not p-*isomorphic*[ 151. ... We must now show (Claim*1*) that UA*and*uniuA are not pA-*isomorphic**and*(Claim 2) that &+ is NPA-complete with respect to s kA*reductions*. ...##
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Selmer companion curves
[article]

2012
*
arXiv
*
pre-print

groups Sel_n(E_1^\chi/K)

arXiv:1203.0620v2
fatcat:zlzzst72infotoyjaajmgtc2ly
*and*Sel_n(E_2^\chi/K) of the quadratic twists E_1^\chi, E_2^\chi. ... We say that two elliptic curves E_1, E_2 over a number field K are n-Selmer companions for a positive integer n if for every quadratic character \chi of K, there is an*isomorphism*between the n-Selmer ... v above p, either • E*1**and*E 2 have potentially multiplicative*reduction*at v, or • p > 2, E*1**and*E 2 have good*reduction*at v,*and*the*isomorphism*of (i) extends to an*isomorphism*E*1*[p k ] ∼ = E ...
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