Richard M. Karp and Richard J. Lipton. Some Connections Between Nonuniform and Uniform Complexity Classes. In Proceedings of the 12th Annual ACM Symposium on Theory of Computing, pages 302--309, 1980. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
First 50 documents Next 50
Rice-Style Theorems for Complexity Theory - Hemaspaandra, Thakur (2001) (Correct)
.... under reasonable complexity theoretic assumptions, RE #m hardness does not imply NP # m hardness (though, in fact, under other complexity theoretic assumption we will see that RE # m hardness does imply NP # m hardness) We first state a useful definition and result due to Karp and Lipton [KL80] Definition 4.4 [KL80] and each function f : N N, is defined as follows. #g) #L 1 # C) #x) g(1 x ) f( x ) x ## #x, g(1 x )# L 1 ) and each function class F is defined as follows. #f # F) L # C f ] Theorem 4.5 [KL80] If SAT P O(log n) ....
....assumptions, RE #m hardness does not imply NP # m hardness (though, in fact, under other complexity theoretic assumption we will see that RE # m hardness does imply NP # m hardness) We first state a useful definition and result due to Karp and Lipton [KL80] Definition 4. 4 [KL80] and each function f : N N, is defined as follows. #g) #L 1 # C) #x) g(1 x ) f( x ) x ## #x, g(1 x )# L 1 ) and each function class F is defined as follows. #f # F) L # C f ] Theorem 4.5 [KL80] If SAT P O(log n) then P = NP. We can now ....
[Article contains additional citation context not shown here]
R. Karp and R. Lipton. Some connections between nonuniform and uniform complexity classes. In Proceedings of the 12th ACM Symposium on Theory of Computing, pages 302--309. ACM Press, April 1980. An extended version has also appeared as: Turing machines that take advice, L'Enseignement Mathematique, 2nd series, 28, 1982, pages 191--209.
Random Access to Advice Strings - And Collapsing Results (Correct)
....asymmetry is not present in the relativized proof. In order to rectify this problem we propose a model of computation that is more stringent than the usual relativization computation. This turns out to be equivalent to a generalization of the notion of advice strings proposed by Karp and Lipton [KL80]. Intuitively, any relativized result can be regarded as a comparison between complexity classes under a certain nonuniform setting provided by an (infinite) advice, namely an oracle. Here we generalize the advice string formulation of Karp and Lipton by allowing random access to the advice ....
....status of a collapse of PSPACE to P under random access to advice is particularly interesting in view of a result of Kozen [Ko78] If PSPACE P, then there exists a proof of this fact by diagonalization. 2 Random Access to Advice Strings Recall the definition of C poly by Karp and Lipton [KL80]. We generalize this notion by allowing the underlying machines to have random access to an advice string. Let us fix any length function # from N to N. A function s : n ## 0, is called an advice function of size #(n) Given any advice function s of size #(n) we say a language L is in the ....
R. Karp and R. Lipton, Some connections between nonuniform and uniform complexity classes, in Proc. 12th ACM Symposium on Theory of Computing (STOC'80), ACM, 302--309, 1980. (An extended version appeared as: Turing machines that take advice, in L'Enseignement Mathematique (2nd series) 28, 191--209, 1982.)
SIGACT News Complexity Theory Column 6 - Dept Of Computer (Correct)
....[Wat94] has taken a first step towards a resolution. He shows that one may relax the hypothesis to polynomially valued functions if one adds a certain constraint on the behavior of h. Below, we quickly summarize some of the other main results of Hemaspaandra et al. HNOS94] Definition 2.5 1. KL80] For any class of sets C, C=poly denotes the class of sets L for which there exist a set A 2 C and a polynomially length bounded function h : Sigma Sigma such that for every x, it holds that x 2 L if and only if hx; h(0 jxj )i 2 A. 2. BBS86] Let ExtendedLow 2 denote fL j NP L ....
R. Karp and R. Lipton. Some connections between nonuniform and uniform complexity classes. In Proceedings of the 12th ACM Symposium on Theory of Computing, pages 302--309, April 1980. An extended version has also appeared as: Turing machines that take advice, L'Enseignement Math'ematique, 2nd series 28, 1982, pages 191--209.
Links Between Complexity Theory and Constrained Block Coding - Stockmeyer, Modha (2002) (Correct)
....if the polynomial hierarchy is strict, then each of these statements is false. Parts 1) 2) 3) and 5) of this corollary are immediate from Theorems 2.3, 3.1, 3.2, 3.3, and 3.4, and Propositions 2.5 and 2.6. Part 4) is an implication of part 3) using methods of Adleman [37] and Karp and Lipton [38]. Part 6) is proved from part 4) as follows. The decision version of circuit minimization has instances where is a circuit and , and the question is whether there is a circuit equivalent to with . This problem has a form: there exists a such that and, for all inputs , A standard argument ....
....the symbol ; denote this set of words containing One Two by For those readers familiar with complexity theory, the argument follows. Using that 6 MBE D, it follows as in [37] that if MBE D2 P 6 P poly. Hemaspaandra et al. 39, Theorem 11] have observed that a result of Karp and Lipton [38] relativizes; in particular, if 6 P poly then 6 =6 for all k 3. As will become clear shortly, the symbol serves as a synchronization symbol ; for example, the DIFs we construct have the property that, in any block codebook of symbol words, the (unique) occurrence of appears at the same ....
[Article contains additional citation context not shown here]
R. M. Karp and R. J. Lipton, "Some connections between nonuniform and uniform complexity classes," in Proc. 12st ACM Symp. Theory of Computing, 1980, pp. 302--309.
Distance-based merging: A general framework and some.. - Konieczny, Lang, Marquis (2001) (1 citation) (Correct)
.... etant donn e IC pouvait toujours etre repr esent e par une formule equivalente dont la taille est polynomiale en jEj jICj alors on aurait NP P poly [5] ce qui est consid er e comme peu vraisemblable puisque cela entrainerait l effondrement de la hi erarchie polynomiale au deuxi eme niveau [9]. Pour en revenir a la complexit e de l interrogation, nous avons obtenu le r esultat tr es g en eral suivant pour les op erateurs a partir de distances : Proposition 1 Soit 4 un op erateur de fusion a partir de distances, soit un ensemble de croyances E et soient deux formules IC et ff ....
R.M. Karp and R.J. Lipton. Some connections between non-uniform and uniform complexity classes. In Proceedings of the Twelfth ACM Symposium on Theory of Computing (STOC'80), pages 302--309, 1980.
Oracles and Queries that are Sufficient for Exact.. - Bshouty, Cleve.. (1996) (51 citations) (Correct)
....every NP set has polynomial size circuits Kushilevitz and Mansour [KM91] have shown that depth O(logn) decision trees are exactly learnable with high probability using membership queries. then the polynomial hierarchy collapses to ZPP . This improves the previous result of Karp and Lipton [KL80] where Sigma 2 appears in place of ZPP . Let us comment on a particular technique used in this paper. For our results concerning learning with equivalence queries and an NP oracle, our approach builds on the investigation of the query complexity of learning by Kannan in [K93] Kannan shows ....
.... 22(1) rules out the possibility for monotone read twice DNF (since the CNF size might be exponentially large) 7 Applications to Structural Complexity Theory Watanabe [W94] has observed that a consequence of Theorem 7(b) in Section 3 is an improvement of the following result of Karp and Lipton [KL80]. Theorem 23 [KL80] If every NP set has polynomial size circuits then the polynomial hierarchy collapses to Sigma 2 . It is clear that ZPP is contained in Sigma 2 but the other direction of containment is not known (and would be surprising) Watanabe has observed the following, and we ....
[Article contains additional citation context not shown here]
Richard M. Karp and Richard J. Lipton. Some Connections Between Nonuniform and Uniform Complexity Classes. In Proceedings of the 12th Annual ACM Symposium on Theory of Computing, pages 302--309, 1980.
Super-Polynomial versus Half-Exponential Circuit Size.. - Miltersen, Variyam.. (1999) (3 citations) (Correct)
....of size O(n ) for some fixed k (page 41) The proof of the lemma proceeds as follows: If SAT (the problem of deciding the satisfiability of boolean formulae) does not have polynomial circuits, then the lemma is true. In the case of SAT having polynomial circuits, by Karp and Lipton s theorem [11], the polynomial hierarchy collapses to 2 . This implies that # 3 can be simulated in # O(1) 2 , and since it was already established that # 3 contains functions of superpolynomial circuit complexity for any superpolynomial f , the lemma follows. After proving the above lemma, ....
R. M. Karp and R. J. Lipton. Some connections between nonuniform and uniform complexity classes. Proceedings of the 12th ACM Symposium on Theory of Computing, (1980), pp. 302--309.
Decoding of Reed Solomon codes beyond the error-correction bound - Sudan (1997) (83 citations) (Correct)
....problem seems to well solved. Bruck and Naor [6] present a code (not well known, but nevertheless easily presented) for which they show that the existence of small size maximum likelihood decoding circuits would imply the collapse of the polynomial hierarchy (using a result of Karp and Lipton s [14]) However the codes presented by Bruck and Naor do not have large distance. It still remains open if the maximum likelihood decoding problem is hard for any constant distance code. The Reed Solomon codes would have formed a good 15 candidate to show hardness of this problem, except that it is ....
R. Karp and R. Lipton. Some connections between nonuniform and uniform complexity classes. Proceedings of the 12th Annual ACM Symposium on Theory of of Computing, pp. 302-309, 1980.
Oracles and Queries that are Sufficient for - Exact Learning Nader (Correct)
No context found.
Richard M. Karp and Richard J. Lipton. Some Connections Between Nonuniform and Uniform Complexity Classes. In Proceedings of the 12th Annual ACM Symposium on Theory of Computing, pages 302--309, 1980.
Research Reports on - Mathematical And Computing (Correct)
No context found.
R. Karp and R. Lipton, Some connections between nonuniform and uniform complexity classes, in Proc. 12th ACM Symposium on Theory of Computing (STOC'80), ACM, 302--309, 1980. (An extended version appeared as: Turing machines that take advice, in L'Enseignement Mathematique (2nd series) 28, 191--209, 1982.)
Observations on Measure and Lowness for Δ_2^p - Lutz (Correct)
No context found.
R. Karp and R. Lipton. Some connections between nonuniform and uniform complexity classes. In Proc. 12th ACM Symp. Theory of Computer Science, pages 302--309, 1980.
Almost Everywhere High Nonuniform Complexity - Lutz (1992) (99 citations) (Correct)
No context found.
R.M. Karp and R.J. Lipton, Some connections between nonuniform and uniform complexity classes, Proceedings of the 12th ACM Symposium on the Theory of Computing, 1980, pp. 302--309.
Uniform hardness vs. randomness tradeoffs for Arthur-Merlin .. - Gutfreund, Shaltiel, al. (Correct)
No context found.
R. M. Karp and R. J. Lipton. Some connections between nonuniform and uniform complexity classes. In Twelfth Annual ACM Symposium on Theory of Computing (STOC '80), pages 302--309, New York, Apr. 1979. ACM.
Derandomization That is Rarely Wrong From Short Advice.. - Goldreich, Wigderson (2002) (Correct)
No context found.
R.M. Karp and R.J. Lipton. Some connections between nonuniform and uniform complexity classes. In 12th STOC, pages 302-309, 1980.
Unknown - Tr Electronic Colloquium (1997) (Correct)
No context found.
R. Karp and R. Lipton. Some connections between nonuniform and uniform complexity classes. In Proceedings of the 12th ACM Symposium on Theory of Computing, pp. 302--309, 1980.
Knowledge compilation = Query rewriting + View synthesis - Cadoli, Mancini (Correct)
No context found.
R. M. Karp and R. J. Lipton. Some connections between non-uniform and uniform complexity classes. In Proceedings of the Twelfth ACM Symposium on Theory of Computing (STOC'80), pages 302--309, 1980.
Lecture Notes on Computational Complexity - Trevisan (2004) (Correct)
No context found.
R.M. Karp and R.J. Lipton. Some connections between nonuniform and uniform complexity classes. In Proceedings of the 12th ACM Symposium on Theory of Computing, pages 302--309, 1980.
Complete Sets and Structure in Subrecursive Classes - Buhrman, Torenvliet (1998) (7 citations) (Correct)
No context found.
R. Karp and R. Lipton. Some connections between nonuniform and uniform complexity classes. In Proc. 12th ACM Symposium on Theory of Computing, pages 302--309, 1980.
Algebraic Properties for Deterministic Selectivity - Hemaspaandra, Hempel (2001) (Correct)
No context found.
R. Karp and R. Lipton. Some connections between nonuniform and uniform complexity classes. In Proceedings of the 12th ACM Symposium on Theory of Computing, pages 302-309. ACM Press, April 1980. An extended version has also appeared as: Turing machines that take advice, L'Enseignement Mathematique, 2nd series, 28, 1982, pages 191-209.
The Boolean Hierarchy of NP-Partitions - Kosub, Wagner (2000) (3 citations) (Correct)
No context found.
R. M. Karp and R. J. Lipton. Some connections between nonuniform and uniform complexity classes. In Proceedings 12th ACM Symposium on Theory of Computing, pages 302-309, 1980.
Lower Bounds and the Hardness of Counting Properties - Hemaspaandra, Thakur (2002) (Correct)
No context found.
R. Karp and R. Lipton. Some connections between nonuniform and uniform complexity classes. In Proceedings of the 12th ACM Symposium on Theory of Computing, pages 302--309. ACM Press, April 1980. An extended version has also appeared as: Turing machines that take advice, L'Enseignement Mathematique, 2nd series, 28, 1982, pages 191--209.
Complicated Complementations - Harry Buhrman Cwi (Correct)
No context found.
R. Karp and R. Lipton. Some connections between nonuniform and uniform complexity classes. In Proc. 12th ACM Symposium on Theory of Computing, pages 302--309, 1980.
Optimal Advice - Lane Hemaspaandra Department (1994) (1 citation) (Correct)
No context found.
R. Karp and R. Lipton. Some connections between nonuniform and uniform complexity classes. In Proceedings of the 12th ACM Symposium on Theory of Computing, pages 302--309, April 1980. An extended version has also appeared as: Turing machines that take advice, L'Enseignement Math'ematique, 2nd series 28, 1982, pages 191--209.
On Pseudorandomness and Resource-Bounded Measure - Arvind Institute Of (1997) (9 citations) (Correct)
No context found.
R. M. Karp and R. J. Lipton. Some connections between nonuniform and uniform complexity classes. In Proc. 12th ACM Symposium on Theory of Computing, 302-309. ACM Press, 1980.
New Lowness Results for ZPP^NP and other Complexity Classes - Arvind, Köbler (Correct)
No context found.
R. M. Karp and R. J. Lipton, Some connections between nonuniform and uniform complexity classes, Proceedings of the 12th ACM Symposium on Theory of Computing, ACM Press, (1980), 302-309.
First 50 documents Next 50
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC