Filters








133,749 Hits in 4.4 sec

Isomorphisms and 1-L reductions

Eric W. Allender
1988 Journal of computer and system sciences (Print)  
All sets complete for NP under 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  ... 
doi:10.1016/0022-0000(88)90033-5 fatcat:qxmgzsutozaetfujbhftpwp5ka

On the p-isomorphism conjecture

Osamu Watanabe
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-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.  ... 
doi:10.1016/0304-3975(91)90284-9 fatcat:azhmxws2zvbj5h7aiy7ah7uvyu

Strong Reductions and Isomorphism of Complete Sets [chapter]

Ryan C. Harkins, John M. Hitchcock, A. Pavan
2007 Lecture Notes in Computer Science  
We study the structure of the polynomial-time complete sets for NP 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] .  ... 
doi:10.1007/978-3-540-77050-3_14 fatcat:33tddc6u2vdghdzr4w2uft6avy

On traces of Frobenius endomorphisms

Igor Nikolaev
2014 Finite Fields and Their Applications  
Thus, tr (A p ) = tr ((A ′ ) p ) 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 .  ... 
doi:10.1016/j.ffa.2013.10.003 fatcat:nqt7bvsxfbetjcdcmcykvmzgea

Polynomial-Time Isomorphism of 1-L-Complete Sets

Manindra Agrawal, Somenath Biswas
1996 Journal of computer and system sciences (Print)  
Let C be any complexity class closed under log-lin 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.  ... 
doi:10.1006/jcss.1996.0057 fatcat:xhzlsnzpgbhivfff7yghp6ipua

Reductions to Graph Isomorphism

Jacobo Torán
2008 Theory of Computing Systems  
For the case of Turing reducibilities we show that for any k ≥ 0 an NC k+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 .  ... 
doi:10.1007/s00224-008-9159-1 fatcat:qguumsz2tbc6tgxlkxmuesxndq

Reductions to Graph Isomorphism [chapter]

Jacobo Torán
2007 Lecture Notes in Computer Science  
For the case of Turing reducibilities we show that for any k ≥ 0 an NC k+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 .  ... 
doi:10.1007/978-3-540-77050-3_13 fatcat:cgglfesjhjhz5kul76vigsn4j4

The Role Of Exotic Affine Spaces In the Classification Of Homogeneous Affine Varieties [chapter]

Dennis Snow
2004 Encyclopaedia of Mathematical Sciences  
If we identify Y with the 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.  ... 
doi:10.1007/978-3-662-05652-3_9 fatcat:zbtexsf6mrhynnnaggp5ghbwz4

On p-torsion of p-adic elliptic curves with additive reduction [article]

René Pannekoek
2013 arXiv   pre-print
Let E be an elliptic curve with additive 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 .  ... 
arXiv:1211.5833v2 fatcat:nrogl7hsqvezffdxvzmbq7xdwm

Selmer companion curves

Barry Mazur, Karl Rubin
2014 Transactions of the American Mathematical Society  
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 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  ... 
doi:10.1090/s0002-9947-2014-06114-x fatcat:44guwzyhe5dntacqbkkrkswpy4

Graph Isomorphism and Circuit Size [article]

Eric Allender and Joshua A. Grochow and Dieter van Melkebeek and Cristopher Moore and Andrew Morgan
2018 arXiv   pre-print
In this brief note, we observe that the 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.  ... 
arXiv:1511.08189v2 fatcat:tnvwhk5bajb3pnpijuljozwgqq

Reductive pairs arising from representations [article]

Oliver Goodbourn
2014 arXiv   pre-print
Let G be a 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)).  ... 
arXiv:1412.8603v1 fatcat:6rnbxzjzofgn5lzene6bcdculu

Principal bundles over a smooth real projective curve of genus zero

Indranil Biswas, Johannes Huisman
2008 Advances in Geometry  
The tautological line bundle over the real projective line P 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.  ... 
doi:10.1515/advgeom.2008.029 fatcat:5qyfep42wfbudpail325zdvg2a

One-way functions and the nonisomorphism of NP-complete sets

Juris Hartmanis, Lane A. Hemachandra
1991 Theoretical Computer Science  
Hartmanis, J. 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.  ... 
doi:10.1016/0304-3975(91)90323-t fatcat:j2mh2qa4d5cb5e3l34mtvmlnbu

Selmer companion curves [article]

Barry Mazur, Karl Rubin
2012 arXiv   pre-print
groups Sel_n(E_1^\chi/K) 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  ... 
arXiv:1203.0620v2 fatcat:zlzzst72infotoyjaajmgtc2ly
« Previous Showing results 1 — 15 out of 133,749 results