Results 1  10
of
83
The quantitative structure of exponential time
 Complexity Theory Retrospective II
, 1997
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Data mining, hypergraph transversals, and machine learning
, 1997
"... Several data mining problems can be formulated as problems of finding maximally specific sentences that are interesting in a database. We first show that this problem has a close relationship with the hypergraph transversal problem. We then analyze two algorithms that have been previously used in da ..."
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Cited by 78 (5 self)
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Several data mining problems can be formulated as problems of finding maximally specific sentences that are interesting in a database. We first show that this problem has a close relationship with the hypergraph transversal problem. We then analyze two algorithms that have been previously used in data mining, proving upper bounds on their complexity. The first algorithm is useful when the maximally specific interesting sentences are &quot;small&quot;. We show that this algorithm can also be used to efficiently solve a special case of the hypergraph transversal problem, improving on previous results. The second algorithm utilizes a subroutine for hypergraph transversals, and is applicable in more general situations, with complexity close to a lower bound for the problem. We also relate these problems to the model of exact learning in computational learning theory, and use the correspondence to derive some corollaries. 1
Discovering All Most Specific Sentences
 ACM Transactions on Database Systems
, 2003
"... this article, we show how the problems of finding frequent sets in relations and of finding minimal keys in databases can be reduced to this formulation. Using this theory extraction formulation [Mannila 1995, 1996; Mannila and Toivonen 1997], one can formulate general results about the complexity o ..."
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Cited by 70 (4 self)
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this article, we show how the problems of finding frequent sets in relations and of finding minimal keys in databases can be reduced to this formulation. Using this theory extraction formulation [Mannila 1995, 1996; Mannila and Toivonen 1997], one can formulate general results about the complexity of algorithms for these data mining tasks
How Many Queries are Needed to Learn?
, 1996
"... We investigate the query complexity of exact learning in the membership and (proper) equivalence query model. We give a complete characterization of concept classes that are learnable with a polynomial number of polynomial sized queries in this model. We give applications of this characterization, i ..."
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Cited by 68 (9 self)
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We investigate the query complexity of exact learning in the membership and (proper) equivalence query model. We give a complete characterization of concept classes that are learnable with a polynomial number of polynomial sized queries in this model. We give applications of this characterization, including results on learning a natural subclass of DNF formulas, and on learning with membership queries alone. Query complexity has previously been used to prove lower bounds on the time complexity of exact learning. We show a new relationship between query complexity and time complexity in exact learning: If any "honest" class is exactly and properly learnable with polynomial query complexity, but not learnable in polynomial time, then P<F NaN> 6= NP. In particular, we show that an honest class is exactly polynomialquery learnable if and only if it is learnable using an oracle for \Sigma p 4 . 1 Introduction Today concept learning is studied under two rigorous frameworks which model t...
New Collapse Consequences Of NP Having Small Circuits
, 1995
"... . We show that if a selfreducible set has polynomialsize circuits, then it is low for the probabilistic class ZPP(NP). As a consequence we get a deeper collapse of the polynomialtime hierarchy PH to ZPP(NP) under the assumption that NP has polynomialsize circuits. This improves on the wellknown ..."
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Cited by 56 (7 self)
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. We show that if a selfreducible set has polynomialsize circuits, then it is low for the probabilistic class ZPP(NP). As a consequence we get a deeper collapse of the polynomialtime hierarchy PH to ZPP(NP) under the assumption that NP has polynomialsize circuits. This improves on the wellknown result of Karp, Lipton, and Sipser (1980) stating a collapse of PH to its second level \Sigma P 2 under the same assumption. As a further consequence, we derive new collapse consequences under the assumption that complexity classes like UP, FewP, and C=P have polynomialsize circuits. Finally, we investigate the circuitsize complexity of several language classes. In particular, we show that for every fixed polynomial s, there is a set in ZPP(NP) which does not have O(s(n))size circuits. Key words. polynomialsize circuits, advice classes, lowness, randomized computation AMS subject classifications. 03D10, 03D15, 68Q10, 68Q15 1. Introduction. The question of whether intractable sets ca...
Two queries
 In CCC
, 1999
"... We consider the question whether two queries to SAT are as powerful as one query. We show that if P NP�℄� P NP�℄then Locally either NP�coNP or NP has polynomialsize circuits. ..."
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Cited by 31 (7 self)
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We consider the question whether two queries to SAT are as powerful as one query. We show that if P NP�℄� P NP�℄then Locally either NP�coNP or NP has polynomialsize circuits.
A Subexponential Exact Learning Algorithm for DNF Using Equivalence Queries
 Information Processing Letters
, 1996
"... We present a 2 time exact learning algorithm for polynomial size DNF using equivalence queries only. In particular, DNF is PAClearnable in subexponential time under any distribution. This is the first subexponential time PAClearning algorithm for DNF under any distribution. ..."
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Cited by 28 (0 self)
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We present a 2 time exact learning algorithm for polynomial size DNF using equivalence queries only. In particular, DNF is PAClearnable in subexponential time under any distribution. This is the first subexponential time PAClearning algorithm for DNF under any distribution.
Pseudorandomness for approximate counting and sampling
 In Proceedings of the 20th IEEE Conference on Computational Complexity
, 2005
"... We study computational procedures that use both randomness and nondeterminism. Examples are ArthurMerlin games and approximate counting and sampling of NPwitnesses. The goal of this paper is to derandomize such procedures under the weakest possible assumptions. Our main technical contribution allow ..."
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Cited by 24 (5 self)
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We study computational procedures that use both randomness and nondeterminism. Examples are ArthurMerlin games and approximate counting and sampling of NPwitnesses. The goal of this paper is to derandomize such procedures under the weakest possible assumptions. Our main technical contribution allows one to “boost” a given hardness assumption. One special case is a proof that EXP � ⊆ NP/poly ⇒ EXP � ⊆ P NP   /poly. In words, if there is a problem in EXP that cannot be computed by polysize nondeterministic circuits then there is one which cannot be computed by polysize circuits that make nonadaptive NP oracle queries. This in particular shows that the various assumptions used over the last few years by several authors to derandomize ArthurMerlin games (i.e., show AM = NP) are in fact all equivalent. In addition to simplifying the framework of AM derandomization, we show that this “unified assumption ” suffices to derandomize several other probabilistic procedures. For these results we define two new primitives that we regard as the natural pseudorandom objects associated with approximate counting and sampling of NPwitnesses. We use the “boosting ” theorem and hashing techniques to construct these primitives using an assumption that is no stronger than that used to derandomize AM. As a consequence, under this assumption, there are deterministic polynomial time algorithms that use nonadaptive NPqueries and perform the following tasks: • approximate counting of NPwitnesses: given a Boolean circuit A, output r such that (1 − ɛ)A −1 (1)  ≤r ≤A −1 (1).
The Boolean Isomorphism Problem
 SIAM JOURNAL ON COMPUTING
, 1996
"... We investigate the computational complexity of the Boolean Isomorphism problem (BI): on input of two Boolean formulas F and G decide whether there exists a permutation of the variables of G such that F and G become equivalent. Our main result is a oneround interactive proof for BI, where the verifi ..."
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Cited by 22 (2 self)
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We investigate the computational complexity of the Boolean Isomorphism problem (BI): on input of two Boolean formulas F and G decide whether there exists a permutation of the variables of G such that F and G become equivalent. Our main result is a oneround interactive proof for BI, where the verifier has access to an NP oracle. To obtain this, we use a recent result from learning theory by Bshouty et.al. that Boolean formulas can be learned probabilistically with equivalence queries and access to an NP oracle. As a consequence, BI cannot be \Sigma p 2 complete unless the Polynomial Hierarchy collapses. This solves an open problem posed in [BRS95]. Further properties of BI are shown: BI has And and Orfunctions, the counting version, #BI, can be computed in polynomial time relative to BI, and BI is selfreducible.