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On polynomial time isomorphisms of some new complete sets

1978
*
Journal of computer and system sciences (Print)
*

HARTMANIS,

doi:10.1016/0022-0000(78)90027-2
fatcat:q775w4wqyradhphkiyneqi2rtu
*On**polynomial**time**isomorphisms**of**complete**sets*, in "Pro- ceedings*of*Theoretical Computer Science 3rd GI Conference, March 1977," pp. l-15, Lecture Notes in Computer Science ...*ISOMORPHISMS**OF*NP*COMPLETE**SETS*We recall that NP, PTAPE, and EXTAPE denote, respectively, the families*of*languages acceptable in nondeterministic*polynomial**time*, in*polynomial*tape, and exponential ...##
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Page 3613 of Mathematical Reviews Vol. , Issue 2000e
[page]

2000
*
Mathematical Reviews
*

It states that the NP-

*complete**sets*, which are,*of*course, all*polynomial*-*time*reducible to each other, are in fact*polynomial*-*time**isomorphic*. ... The authors consider AC°-reducibility, a restricted form*of**polynomial*-*time*reducibility. The main result*of*the paper is that the AC’-*complete**sets*for NP are AC’-*isomorphic*. ...##
###
Page 7322 of Mathematical Reviews Vol. , Issue 90M
[page]

1990
*
Mathematical Reviews
*

For deterministic exponential-

*time*(E)*complete**sets*, L. Berman proved that any*polynomial*-*time*many-*one**complete**set*is*polynomial*-*time**one*-*one**complete*. ... We show that our results for NE apply to*some*limited classes*of**complete**sets*and prove*polynomial**isomorphism*for these classes.” ...##
###
Page 3129 of Mathematical Reviews Vol. , Issue 82g
[page]

1982
*
Mathematical Reviews
*

From the text: “The purpose

*of*this paper is to collect together*some**new*and old results*on**isomorphism**complete*matrix problems. ... In this investigation, we mention*some**isomorphism**complete*problems*on*matrices, a particularly rich source*of**isomorphism**complete*problems which do not obviously entail the determination*of**isomorphism*...##
###
The Comparison of Tree-Sibling Time Consistent Phylogenetic Networks Is Graph Isomorphism-Complete

2014
*
The Scientific World Journal
*

Several

doi:10.1155/2014/254279
pmid:24982934
pmcid:PMC3996867
fatcat:q3qhblkvirf4begvjcjb5aeyya
*polynomial**time*computable metrics*on*the class*of*semibinary tree-sibling*time*consistent phylogenetic networks are available in the literature; in particular, the problem*of*deciding if two networks ...*polynomial**time*. ... Acknowledgments The authors would like to thank Antoni Lozano for his comments*on*an early version*of*this paper. ...##
###
Page 662 of Mathematical Reviews Vol. , Issue 95b
[page]

1995
*
Mathematical Reviews
*

*Some*probabilistic complexity classes are introduced, including the class BPP (bounded error probabilistic

*polynomial*

*time*) and its subset RP (random

*polynomial*

*time*). ... Deep results

*of*group theory have been ap- plied to develop

*polynomial*-

*time*algorithms for the

*isomorphism*

*of*special classes

*of*graphs. ...

##
###
Reductions among polynomial isomorphism types

1985
*
Theoretical Computer Science
*

Arbitrary

doi:10.1016/0304-3975(85)90139-2
fatcat:rcdlxgrbm5cvlaylucumosgaty
*sets*A and B are*of*the same*polynomial*many-*one*degree if each is*polynomial*many-*one*reducible to the other. ... Berman and Hartmanis have observed that all known NP-*complete**sets*are*polynomially**isomorphic*, and have conjectured that all NP-*complete**sets*(*complete*under Karp-reducibility) are*isomorphic*. ... 3 We use as the universal*set*N, which is the*set*{0, 1, 2,...}*of*natural numbers. By*polynomial*functions or*sets*we mean*polynomial**time*computable. ...##
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Towards an Isomorphism Dichotomy for Hereditary Graph Classes

2017
*
Theory of Computing Systems
*

We show that

doi:10.1007/s00224-017-9775-8
fatcat:7afqdktaubhtll2kklqcdzvbeq
*isomorphism**of*graphs*of*bounded generalized color valence can be solved in*polynomial**time*. ... First, we develop a methodology to show*isomorphism**completeness**of*the*isomorphism*problem*on*graph classes by providing a general framework unifying various reduction techniques. ... size acting faithfully*on*a*set*, we can compute the stabilizer*of*any given subset in*polynomial**time*. ...##
###
Some remarks on witness functions for nonpolynomial and noncomplete sets in NP

1985
*
Theoretical Computer Science
*

Since these

doi:10.1016/0304-3975(85)90140-9
fatcat:v4yaas767bhubcy5i4j5bfunju
*sets*seem not to be all*polynomially**isomorphic*, we counter the conjecture*of*Berman and Hartmanis that all NP-*complete**sets*are*isomorphic*to SAT with our own conjecture that not all k-creative ... an extended survey entitled, "*Some*structural properties*of**polynomial*reducibilities and*sets*in NP". ... Are all NP-*complete**sets**complete*under*one*-*one**polynomial**time*reductions? Under*one*-*one*and honest*polynomial**time*reductions ? Wg(,) = {0, 1, 2,... } iff h(g(i)) ~ Wg(,) iff h(g(i)) ~ A. ...##
###
Page 3786 of Mathematical Reviews Vol. , Issue 84i
[page]

1984
*
Mathematical Reviews
*

It is proved that the first problem is log-

*complete*in the second class (24)*of*the*polynomial*-*time*hierarchy and that the second problem is log-*complete*in NP. ... ., 117, Springer, Berlin-*New*York, 1981. Authors’ summary: “The complexity*of*the problem*of*finding*isomorphism**of*two graphs is*one**of*the most famous problems in complexity theory [R. C. ...##
###
Page 467 of Mathematical Reviews Vol. , Issue 96a
[page]

1996
*
Mathematical Reviews
*

Since an

*isomorphism*may encode rare instances*of**one*problem to fre- quent instances*of*another, an*isomorphism*need not preserve random probability distributions*of*instances; two natural NP-*complete*... The paper provides detailed proof and ex- amples to prove that these average-case NP-*complete*problems are*polynomially**isomorphic*under many-*one*reductions. ...##
###
Testing homotopy equivalence is isomorphism complete

1986
*
Discrete Applied Mathematics
*

It is shown that homotopy equivalence

doi:10.1016/0166-218x(86)90074-0
fatcat:6d6wh7dx4jcwxa3pkizer2bppm
*of*finite topological spaces is*polynomially*equivalent to testing graph*isomorphism*. ... Introduction A problem that is*polynomial**time*equivalent to graph*isomorphism*is known as*isomorphism**complete*([l] , [2] , [3] , [51, [6] ). ... So q~ restricted to X is an*isomorphism**of*X and Y. Thus the transformation X~)( is a*polynomial**time*reduction*of*poser*isomorphism*to*isomorphism**of*cores. ...##
###
Towards an Isomorphism Dichotomy for Hereditary Graph Classes
[article]

2014
*
arXiv
*
pre-print

We show that

arXiv:1411.1977v1
fatcat:4s5nlu54pnfwrdpht47ztm4dri
*isomorphism**of*graphs*of*bounded generalized color valence can be solved in*polynomial**time*. ... First, we develop a methodology to show*isomorphism**completeness**of*the*isomorphism*problem*on*graph classes by providing a general framework unifying various reduction techniques. ...*On*all but finitely many classes*of*the form (H 1 , H 2 )-free the graph*isomorphism*problem is*polynomial**time*solvable or*isomorphism*-*complete*. Contribution. ...##
###
Witness-isomorphic reductions and the local search problem (extended abstract)
[chapter]

1995
*
Lecture Notes in Computer Science
*

We study witness-

doi:10.1007/3-540-60246-1_134
fatcat:jg7lbky2ezashmvwkqhbzhd4sm
*isomorphic*reductions, a type*of*structurepreserving reduction between NP-decision problems. ... Buhrman for suggesting the proof*of*Theorem 11. ... are*polynomial*-*time**isomorphic*. ...##
###
Page 4503 of Mathematical Reviews Vol. , Issue 80K
[page]

1980
*
Mathematical Reviews
*

frac- tions, compositions and quotients

*of**polynomials*in*one*variable with general coefficients.” 80k:68028 Hong Jiawei (Hong, Jia Weil] 80k:68029*On*lower bounds*of**time*complexity*of**some*algorithms ... Hartmanis, J. 80k:68027*On*log-tape*isomorphisms**of**sets*. Theoret. Comput. Sci. 7 (1978), no. 3, 273-286. ...
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