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Inseparability and Strong Hypotheses for Disjoint NP Pairs
[article]

2010
*
arXiv
*
pre-print

This paper investigates the existence of

arXiv:0902.2674v4
fatcat:uy3lpzjgt5e43lsrllhw5bacii
*inseparable**disjoint**pairs*of*NP*languages*and*related*strong**hypotheses*in computational complexity. ... We also relate these conditions to*strong**hypotheses*concerning randomness*and*genericity of*disjoint**pairs*. ... We also investigate the relationships between the two*strong**hypotheses*in our main theorem (i.e., its hypothesis*and*its conclusion)*and**strong**hypotheses*involving the existence of*disjoint**NP**pairs*...##
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Inseparability and Strong Hypotheses for Disjoint NP Pairs

2011
*
Theory of Computing Systems
*

This paper investigates the existence of

doi:10.1007/s00224-011-9326-7
fatcat:kxid7skxpnf7fcplf46dager4a
*inseparable**disjoint**pairs*of*NP*languages*and*related*strong**hypotheses*in computational complexity. ... We also relate these conditions to*strong**hypotheses*concerning randomness*and*genericity of*disjoint**pairs*. ... We also investigate the relationships between the two*strong**hypotheses*in our main theorem (i.e., its hypothesis*and*its conclusion)*and**strong**hypotheses*involving the existence of*disjoint**NP**pairs*...##
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Unions of Disjoint NP-Complete Sets

2014
*
ACM Transactions on Computation Theory
*

*For*example, there is a P-

*inseparable*

*disjoint*

*NP*

*pair*if

*and*only there is a P-

*inseparable*

*pair*whose both components are

*NP*-complete [GS88] . ... Grollmann

*and*Selman [GS88] showed that if P = UP, then there exist P-

*inseparable*

*disjoint*

*NP*

*pairs*. ... Acknowledgments We thank the anonymous referees

*for*numerous helpful suggestions

*and*comments. We thank Eric Allender

*for*pointing out a gap in the proof of one of the claims. ...

##
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Unions of Disjoint NP-Complete Sets
[chapter]

2011
*
Lecture Notes in Computer Science
*

*For*example, there is a P-

*inseparable*

*disjoint*

*NP*

*pair*if

*and*only there is a P-

*inseparable*

*pair*whose both components are

*NP*-complete [GS88] . ... Grollmann

*and*Selman [GS88] showed that if P = UP, then there exist P-

*inseparable*

*disjoint*

*NP*

*pairs*. ... Acknowledgments We thank the anonymous referees

*for*numerous helpful suggestions

*and*comments. We thank Eric Allender

*for*pointing out a gap in the proof of one of the claims. ...

##
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Properties of NP‐Complete Sets

2006
*
SIAM journal on computing (Print)
*

We study several properties of sets that are complete

doi:10.1137/s009753970444421x
fatcat:cnbqn7elwfbmven6r45ybhmi4e
*for*¤ ¦ ¥ . We prove that if § is an ... Buhrman*for*informing them of his work on quasipolynomial density,*and*thank M. Ogihara*for*informing them of his results on polynomial closeness. Also, we received helpful suggestions from L. ... Two*disjoint*sets*and*are P-separable if there is a set . Otherwise, they are P-*inseparable*. Let us say that is a*disjoint**NP*-*pair*such that . ...##
###
Incompleteness in the finite domain
[article]

2017
*
arXiv
*
pre-print

Another reason

arXiv:1601.01487v2
fatcat:k7u6y6rrjndzjobf6tnxvlgvra
*for*putting forward these conjectures is that some results in proof complexity seem to be special cases of such general statements*and*we want to formalize*and*fully understand these statements ... Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond*NP*≠ co*NP*. ... I am also indebted to an anonymous referee*for*pointing out many small errors*and*suggesting improvements of presentation. ...##
###
Generality's price: Inescapable deficiencies in machine-learned programs

2006
*
Annals of Pure and Applied Logic
*

This paper investigates some delicate tradeoffs between the generality of an algorithmic learning device

doi:10.1016/j.apal.2005.06.013
fatcat:ttbhrddmqjdobf3kedhbp3radu
*and*the quality of the programs it learns successfully. ... There are also results in which the complexity of successfully learned programs is asymptotically optimal*and*the learning device is general, but, still thanks to the generality, some of those optimal, ... Klaus Ambos-Spies*for*some very helpful suggestions*and*observations. Grant support was received by J. Case from NSF grant CCR-0208616, by S. Jain from NUS grant R252-000-127-112,*and*by J. ...##
###
On Amitsur's complex

1960
*
Transactions of the American Mathematical Society
*

This program can be extended to the case of certain rings C

doi:10.1090/s0002-9947-1960-0121391-4
fatcat:yip73brkyzcbvaqq3g2gnghgnm
*and*£ but with comparatively*strong**hypotheses*(see the epimorphism proof in Theorem 3). ... If pDp' then 717®Cp' = (717®c,,) ®cvCp' so that*np*= ny. Thus we can divide the set of prime ideals of C into*disjoint*subsets Uk= {p\nt = k} such that if pDp', then pEUk if*and*only if p'E Uk. ... Thus, by Lemma 4.1, -q + (qi + q2) = / ® 1*for*some / in £. Hence p(iD+L(qi-f® 1), 2D+L(q2))=2D+L(q)*and*p(£) = &(ht2). ...##
###
On Amitsur's Complex

1960
*
Transactions of the American Mathematical Society
*

This program can be extended to the case of certain rings C

doi:10.2307/1993305
fatcat:nw36l5wm7rad5iizam6wdyhwmq
*and*£ but with comparatively*strong**hypotheses*(see the epimorphism proof in Theorem 3). ... If pDp' then 717®Cp' = (717®c,,) ®cvCp' so that*np*= ny. Thus we can divide the set of prime ideals of C into*disjoint*subsets Uk= {p\nt = k} such that if pDp', then pEUk if*and*only if p'E Uk. ... Thus, by Lemma 4.1, -q + (qi + q2) = / ® 1*for*some / in £. Hence p(iD+L(qi-f® 1), 2D+L(q2))=2D+L(q)*and*p(£) = &(ht2). ...##
###
A Lexical-Functional Analysis of Predicate Topicalization in German

1999
*
American Journal of Germanic Linguistics and Literatures
*

To this end we motivate a revision of Functional Uncertainty as proposed in Kaplan

doi:10.1017/s1040820700002456
fatcat:2tupy6jdgjacxfwkdeaimtaduq
*and*Zaenen (1989) to account*for*filler/gap relations in long distance dependencies. ...*For*this purpose we employ the proposals of T. Mohanan (1990 Mohanan ( /1994 which argue*for*the independence of the construct PREDICATE from its categorial realization. ... principles as the*Strong*Lexicalist Hypothesis*and*Direct Syntactic 18*For*further discussion of this issue see Bresnan*and*Mchombo (1995)*and*Ackerman*and*Lesourd (1997) . ...##
###
Friends and Colleagues: Plurality, Coordination, and the Structure of DP

2005
*
Natural Language Semantics
*

Under this hypothesis, the determiner heads the whole noun phrase,

doi:10.1007/s11050-004-2442-z
fatcat:wsxvyew46ra3jmmm76z2bcklua
*and*the noun heads its own internal projection,*NP*. 1 The semantic distinc- ... different words*for*the intersective*and*in (1)*and*the plurality-forming*and*in (2) . ... ] are*inseparable*. ...##
###
Logical analysis of data—An overview: From combinatorial optimization to medical applications

2006
*
Annals of Operations Research
*

These studies include the development of diagnostic

doi:10.1007/s10479-006-0075-y
fatcat:zlrfxygzznadffbrkqcrno6g74
*and*prognostic systems*for*ovarian cancer, breast cancer*and*lymphoma, the differentiation of various types of idiopathic pneumonia, risk assessment ... The medical applications described include the development of diagnostic*and*prognostic systems in cancer research*and*pulmonology, risk assessment among cardiac patients,*and*the design of biomaterials ...*and*NIH-002748-001). ...
We show under reasonable

doi:10.1109/ccc.2003.1214430
dblp:conf/coco/GlasserSSZ03
fatcat:s44wpmw46zeznpfxsgvv7glyqm
*hypotheses*that nonsymmetric*disjoint**NP*-*pairs*exist, which provides additional evidence*for*the existence of P-*inseparable**disjoint**NP*-*pairs*. ... Concrete candidates*for*P-*inseparable**disjoint**NP*-*pairs*come from problems in UP or in*NP*∩coNP. ... The authors thank Avi Wigderson*for*informing them of the paper by Ben-David*and*Gringauze [BDG98] . ...##
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$F$-regularity, test elements, and smooth base change

1994
*
Transactions of the American Mathematical Society
*

*For*example, it is shown in §6 that

*for*a reduced ring R essentially of finite type over an excellent local ring of characteristic p , if c is not in any minimal prime of R

*and*Rc is regular, then c has ...

*for*tight closure is developed in §6

*and*is then applied in §7 to prove that both tight closure

*and*F-regularity commute with smooth base change under many circumstances (where "smooth" is used to mean ... Y, L'

*and*3"r are linearly

*disjoint*over L. ...

##
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A dynamical Shafarevich theorem for rational maps over number fields and function fields
[article]

2017
*
arXiv
*
pre-print

We also prove auxiliary results on finiteness of reduced effective divisors in P^1_K with good reduction outside of S

arXiv:1705.05489v1
fatcat:w2koakuro5eohiexjfpjyb3wdi
*and*on the existence of global models*for*rational maps. ... More precisely, fix an integer d at least 2*and*let K be either a number field or the function field of a curve X over a field k, where k is of characteristic zero or p>2d-2 that is either algebraically ... More generally one could define a "modular*inseparability*index" as in [S8, §0] ,*and*prove our results*for*maps of bounded modular*inseparability*index, but*for*simplicity we shall state the results ...
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