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Inseparability and Strong Hypotheses for Disjoint NP Pairs [article]

Lance Fortnow, Jack H. Lutz, Elvira Mayordomo
2010 arXiv   pre-print
This paper investigates the existence of 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  ... 
arXiv:0902.2674v4 fatcat:uy3lpzjgt5e43lsrllhw5bacii

Inseparability and Strong Hypotheses for Disjoint NP Pairs

Lance Fortnow, Jack H. Lutz, Elvira Mayordomo
2011 Theory of Computing Systems  
This paper investigates the existence of 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  ... 
doi:10.1007/s00224-011-9326-7 fatcat:kxid7skxpnf7fcplf46dager4a

Unions of Disjoint NP-Complete Sets

Christian Glaßer, John M. Hitchcock, A. Pavan, Stephan Travers
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.  ... 
doi:10.1145/2591508 fatcat:xgduydj5xrfqdes6uypewitd74

Unions of Disjoint NP-Complete Sets [chapter]

Christian Glaßer, John M. Hitchcock, A. Pavan, Stephen Travers
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.  ... 
doi:10.1007/978-3-642-22685-4_22 fatcat:mwcc4za5hjdgdb5oag3xig23ae

Properties of NP‐Complete Sets

Christian Glaßer, A. Pavan, Alan L. Selman, Samik Sengupta
2006 SIAM journal on computing (Print)  
We study several properties of sets that are complete 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 .  ... 
doi:10.1137/s009753970444421x fatcat:cnbqn7elwfbmven6r45ybhmi4e

Incompleteness in the finite domain [article]

Pavel Pudlak
2017 arXiv   pre-print
Another reason 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.  ... 
arXiv:1601.01487v2 fatcat:k7u6y6rrjndzjobf6tnxvlgvra

Generality's price: Inescapable deficiencies in machine-learned programs

John Case, Keh-Jiann Chen, Sanjay Jain, Wolfgang Merkle, James S. Royer
2006 Annals of Pure and Applied Logic  
This paper investigates some delicate tradeoffs between the generality of an algorithmic learning device 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.  ... 
doi:10.1016/j.apal.2005.06.013 fatcat:ttbhrddmqjdobf3kedhbp3radu

On Amitsur's complex

Alex Rosenberg, Daniel Zelinsky
1960 Transactions of the American Mathematical Society  
This program can be extended to the case of certain rings C 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).  ... 
doi:10.1090/s0002-9947-1960-0121391-4 fatcat:yip73brkyzcbvaqq3g2gnghgnm

On Amitsur's Complex

Alex Rosenberg, Daniel Zelinsky
1960 Transactions of the American Mathematical Society  
This program can be extended to the case of certain rings C 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).  ... 
doi:10.2307/1993305 fatcat:nw36l5wm7rad5iizam6wdyhwmq

A Lexical-Functional Analysis of Predicate Topicalization in German

Gert Webelhuth, Farrell Ackerman
1999 American Journal of Germanic Linguistics and Literatures  
To this end we motivate a revision of Functional Uncertainty as proposed in Kaplan 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) .  ... 
doi:10.1017/s1040820700002456 fatcat:2tupy6jdgjacxfwkdeaimtaduq

Friends and Colleagues: Plurality, Coordination, and the Structure of DP

Caroline Heycock, Roberto Zamparelli
2005 Natural Language Semantics  
Under this hypothesis, the determiner heads the whole noun phrase, 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.  ... 
doi:10.1007/s11050-004-2442-z fatcat:wsxvyew46ra3jmmm76z2bcklua

Logical analysis of data—An overview: From combinatorial optimization to medical applications

Peter L. Hammer, Tibérius O. Bonates
2006 Annals of Operations Research  
These studies include the development of diagnostic 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).  ... 
doi:10.1007/s10479-006-0075-y fatcat:zlrfxygzznadffbrkqcrno6g74

Disjoint NP-pairs

C. Glasser, A.L. Selman, S. Sengupta, Liyu Zhang
18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings.  
We show under reasonable 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] .  ... 
doi:10.1109/ccc.2003.1214430 dblp:conf/coco/GlasserSSZ03 fatcat:s44wpmw46zeznpfxsgvv7glyqm

$F$-regularity, test elements, and smooth base change

Melvin Hochster, Craig Huneke
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.  ... 
doi:10.1090/s0002-9947-1994-1273534-x fatcat:hz4nj7nbhnfntp3mdojolvgjfm

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

Lucien Szpiro, Lloyd West
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 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  ... 
arXiv:1705.05489v1 fatcat:w2koakuro5eohiexjfpjyb3wdi
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