Above are papers related to the following paper: [Paper_ID] Paper #12155. 	[Title] Exact Learning of -DNF Formulas with Malicious Membership Queries [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1121537. 	[Title] How Many Queries are Needed to Learn? [Abstract] 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 6= NP. In particular, we show that an honest class is exactly polynomial-query learnable if and only if it is learnable using an oracle for p Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12198. 	[Title] Exact Identification of Read-once Formulas Using Fixed Points of Amplification Functions [Abstract] In this paper we describe a new technique for exactly identifying certain classes of read-once Boolean formulas. The method is based on sampling the input-output behavior of the target formula on a probability distribution that is determined by the fixed point of the formula's amplification function (defined as the probability that a 1 is output by the formula when each input bit is 1 independently with probability p). By performing various statistical tests on easily sampled variants of the fixed-point distribution, we are able to efficiently infer all structural information about any logarithmic-depth formula (with high probability). We apply our results to prove the existence of short universal identification sequences for large classes of formulas. We also describe extensions of our algorithms to handle high rates of noise, and to learn formulas of unbounded depth in Valiant's model with respect to specific distributions. Most of this research was carried out while all three authors were at MIT Laboratory for Computer Science with support provided by ARO Grant DAAL03-86-K-0171, DARPA Contract N00014-89-J-1988, NSF Grant CCR-88914428, and a grant from the Siemens Corporation. R. Schapire received additional support from AFOSR Grant 89-0506 while at Harvard University. S. Goldman is currently supported in part by a G.E. Foundation Junior Faculty Grant and NSF Grant CCR-9110108. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1108167. 	[Title] On Learning Read-k-Satisfy-j DNF [Abstract] We study the learnability of Read-k-Satisfy-j (RkSj) DNF formulas. These are boolean formulas in disjunctive normal form (DNF), in which the maximum number of occurrences of a variable is bounded by k, and the number of terms satisfied by any assignment is at most j. After motivating the investigation of this class of DNF formulas, we present an algorithm that with high probability finds a DNF formula that is logically equivalent to any unknown RkSj DNF formula to be learned. The algorithm uses the well-studied protocol of equivalence and membership queries, and runs in polynomial time for k j = O( log n log log n ), where n is the number of input variables. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12199. 	[Title] Learning k-term DNF Formulas with an Incomplete Membership Oracle [Abstract] We consider the problem of learning k-term DNF formulas using equivalence queries and incomplete membership queries as defined by Angluin and Slonim. We demonstrate that this model can be applied to non-monotone classes. Namely, we describe a polynomial-time algorithm that exactly identifies a k-term DNF formula with a k-term DNF hypothesis using incomplete membership queries and equivalence queries from the class of DNF formulas. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1126350. 	[Title] Malicious Membership Queries and Exceptions [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12247. 	[Title] Warning: missing six few referencesfixed in proceedings. Learning with Queries but Incomplete Information (Extended Abstract) [Abstract] We investigate learning with membership and equivalence queries assuming that the information provided to the learner is incomplete. By incomplete we mean that some of the membership queries may be answered by I don't know. This model is a worst-case version of the incomplete membership query model of Angluin and Slonim. It attempts to model practical learning situations, including an experiment of Lang and Baum that we describe, where the teacher may be unable to answer reliably some queries that are critical for the learning algorithm. We present algorithms to learn monotone k-term DNF with membership queries only, and to learn monotone DNF with membership and equivalence queries. Compared to the complete information case, the query complexity increases by an additive term linear in the number of I don't know answers received. We also observe that the blowup in the number of queries can in general be exponential for both our new model and the incomplete membership model. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12350. 	[Title] Cryptographic Limitations on Learning Boolean Formulae and Finite Automata [Abstract] In this paper we prove the intractability of learning several classes of Boolean functions in the distribution-free model (also called the Probably Approximately Correct or PAC model) of learning from examples. These results are representation independent, in that they hold regardless of the syntactic form in which the learner chooses to represent its hypotheses. Our methods reduce the problems of cracking a number of well-known public-key cryptosys- tems to the learning problems. We prove that a polynomial-time learning algorithm for Boolean formulae, deterministic finite automata or constant-depth threshold circuits would have dramatic consequences for cryptography and number theory: in particular, such an algorithm could be used to break the RSA cryptosystem, factor Blum integers (composite numbers equivalent to 3 modulo 4), and detect quadratic residues. The results hold even if the learning algorithm is only required to obtain a slight advantage in prediction over random guessing. The techniques used demonstrate an interesting duality between learning and cryptography. We also apply our results to obtain strong intractability results for approximating a gener - alization of graph coloring. fl This research was conducted while the author was at Harvard University and supported by an A.T.& T. Bell Laboratories scholarship. y Supported by grants ONR-N00014-85-K-0445, NSF-DCR-8606366 and NSF-CCR-89-02500, DAAL03-86-K-0171, DARPA AFOSR 89-0506, and by SERC. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #20601. 	[Title] Learning Conjunctions of Horn Clauses [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #20602. 	[Title] Learning Read-Once Formulas with Queries [Abstract] A read-once formula is a boolean formula in which each variable occurs at most once. Such formulas are also called -formulas or boolean trees. This paper treats the problem of exactly identifying an unknown read-once formula using specific kinds of queries. The main results are a polynomial time algorithm for exact identification of monotone read-once formulas using only membership queries, and a polynomial time algorithm for exact identification of general read-once formulas using equivalence and membership queries (a protocol based on the notion of a minimally adequate teacher [1]). Our results improve on Valiant's previous results for read-once formulas [26]. We also show that no polynomial time algorithm using only membership queries or only equivalence queries can exactly identify all read-once formulas. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #95225. 	[Title] Learning Boolean Read-Once Formulas over Generalized Bases [Abstract] A read-once formula is one in which each variable appears on at most a single input. Angluin, Hellerstein, and Karpinski give a polynomial time algorithm that uses membership and equivalence queries to identify exactly read-once boolean formulas over the basis fAND; OR; NOTg [AHK93]. The goal of this work is to consider natural generalizations of these gates, in order to develop exact identification algorithms for more powerful classes of formulas. We show that read-once formulas over a basis of arbitrary boolean functions of constant fan-in k or less (i.e. any f : f0; 1g 1ck ! f0; 1g) are exactly identifiable in polynomial time using membership and equivalence queries. We show that read-once formulas over the basis of arbitrary symmetric boolean functions are also exactly identifiable in polynomial time in this model. Given standard cryptographic assumptions, there is no polynomial time identification algorithm for read-twice formulas over either of these bases using membership and equivalence queries. We further show that for any basis class B meeting certain technical conditions, any polynomial time identification algorithm for read-once formulas over B can be extended to a polynomial time identification algorithm for read-once formulas over the union of B and the arbitrary functions of fan-in k or less. As a result, read-once formulas over the union of arbitrary symmetric and arbitrary constant fan-in gates are also exactly identifiable in polynomial time using membership and equivalence queries. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12158. 	[Title] Randomly Fallible Teachers: Learning Monotone DNF with an Incomplete Membership Oracle [Abstract] We introduce a new fault-tolerant model of algorithmic learning using an equivalence oracle and an incomplete membership oracle, in which the answers to a random subset of the learner's membership queries may be missing. We demonstrate that, with high probability, it is still possible to learn monotone DNF formulas in polynomial time, provided that the fraction of missing answers is bounded by some constant less than one. Even when half the membership queries are expected to yield no information, our algorithm will exactly identify m-term, n-variable monotone DNF formulas with an expected O(mn 2 ) queries. The same task has been shown to require exponential time using equivalence queries alone. We extend the algorithm to handle some one-sided errors, and discuss several other possible error models. It is hoped that this work may lead to a better understanding of the power of membership queries and the effects of faulty teachers on query models of concept learning. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #42207. 	[Title] Asking Questions to Minimize Errors [Abstract] A number of efficient learning algorithms achieve exact identification of an unknown function from some class using membership and equivalence queries. Using a standard transformation such algorithms can easily be converted to on-line learning algorithms that use membership queries. Under such a transformation the number of equivalence queries made by the query algorithm directly corresponds to the number of mistakes made by the on-line algorithm. In this paper we consider several of the natural classes known to be learnable in this setting, and investigate the minimum number of equivalence queries with accompanying counterexamples (or equivalently the minimum number of mistakes in the on-line model) that can be made by a learning algorithm that makes a polynomial number of membership queries and uses polynomial computation time. We are able both to reduce the number of equivalence queries used by the previous algorithms and often to prove matching lower bounds. As an example, consider the class of DNF formulas over n variables with at most k = O(log n) terms. Previously, the algorithm of Blum and Rudich [BR92] provided the best known upper bound of 2 O(k) log n for the minimum number of equivalence queries needed for exact identification. We greatly improve on this upper bound showing that exactly k counterexamples are needed if the learner knows k a priori and exactly k +1 counterexamples are needed if the learner does not know k a priori. This exactly matches known lower bounds [BC92]. For many of our results we obtain a complete characterization of the tradeoff between the number of membership and equivalence queries needed for exact identification. The classes we consider here are monotone DNF formulas, Horn sentences, O(log n)-term DNF formulas, read-k sat-j DNF formulas, read-once formulas over various bases, and deterministic finite automata. Please summarise all the given information.

Paper #12155 has the title `Exact Learning of -DNF Formulas with Malicious Membership Queries  
` and the abstract `nan`.
Question: Which category should Paper #12155 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #12155 has the title `Exact Learning of -DNF Formulas with Malicious Membership Queries  
` and the abstract `nan`.
Question: Which category should Paper #12155 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Theory