Results 11  20
of
224
Inductive Inference, DFAs and Computational Complexity
 2nd Int. Workshop on Analogical and Inductive Inference (AII
, 1989
"... This paper surveys recent results concerning the inference of deterministic finite automata (DFAs). The results discussed determine the extent to which DFAs can be feasibly inferred, and highlight a number of interesting approaches in computational learning theory. 1 ..."
Abstract

Cited by 78 (1 self)
 Add to MetaCart
This paper surveys recent results concerning the inference of deterministic finite automata (DFAs). The results discussed determine the extent to which DFAs can be feasibly inferred, and highlight a number of interesting approaches in computational learning theory. 1
Some Connections between Bounded Query Classes and NonUniform Complexity
 In Proceedings of the 5th Structure in Complexity Theory Conference
, 1990
"... This paper is dedicated to the memory of Ronald V. Book, 19371997. ..."
Abstract

Cited by 70 (23 self)
 Add to MetaCart
This paper is dedicated to the memory of Ronald V. Book, 19371997.
A Theory of Network Localization
, 2004
"... In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigid ..."
Abstract

Cited by 67 (6 self)
 Add to MetaCart
In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly.
Counting Classes: Thresholds, Parity, Mods, and Fewness
, 1996
"... Counting classes consist of languages defined in terms of the number of accepting computations of nondeterministic polynomialtime Turing machines. Well known examples of counting classes are NP, coNP, \PhiP, and PP. Every counting class is a subset of P #P[1] , the class of languages computable ..."
Abstract

Cited by 61 (13 self)
 Add to MetaCart
Counting classes consist of languages defined in terms of the number of accepting computations of nondeterministic polynomialtime Turing machines. Well known examples of counting classes are NP, coNP, \PhiP, and PP. Every counting class is a subset of P #P[1] , the class of languages computable in polynomial time using a single call to an oracle capable of determining the number of accepting paths of an NP machine. Using closure properties of #P, we systematically develop a complexity theory for counting classes defined in terms of thresholds and moduli. An unexpected result is that MOD k iP = MOD k P for prime k. Finally, we improve a result of Cai and Hemachandra by showing that recognizing languages in the class Few is as easy as distinguishing uniquely satisfiable formulas from unsatisfiable formulas (or detecting unique solutions, as in [28]). 1. Introduction Valiant [27] defined the class #P of functions whose values equal the number of accepting paths of polynomialtime bo...
NonTransitive Transfer of Confidence: A Perfect ZeroKnowledge Interactive Protocol for SAT and Beyond
, 1986
"... A perfect zeroknowledge interactive proof is a protocol by which Alice can convince Bob of the truth of some theorem in a way that yields no information as to how the proof might proceed (in the sense of Shannon's information theory). We give a general technique for achieving this goal for any ..."
Abstract

Cited by 57 (5 self)
 Add to MetaCart
A perfect zeroknowledge interactive proof is a protocol by which Alice can convince Bob of the truth of some theorem in a way that yields no information as to how the proof might proceed (in the sense of Shannon's information theory). We give a general technique for achieving this goal for any problem in NP (and beyond). The fact that our protocol is perfect zeroknowledge does not depend on unproved cryptographic assumptions. Furthermore, our protocol is powerful enough to allow Alice to convince Bob of theorems for which she does not even have a proof. Whenever Alice can convince herself probabilistically of a theorem, perhaps thanks to her knowledge of some trapdoor information, she can convince Bob as well, without compromising the trapdoor in any way. This results in a nontransitive transfer of confidence from Alice to Bob, because Bob will not be able to convince anyone else afterwards. Our protocol is dual to those of [GrMiWi86a, BrCr86]. 1. INTRODUCTION Assume that Alice h...
On the complexity of space bounded interactive proofs (extended abstract
 In Proceedings of FOCS
, 1989
"... ..."
The Quantum Challenge to Structural Complexity Theory
, 1992
"... This is a nontechnical survey paper of recent quantummechanical discoveries that challenge generally accepted complexitytheoretic versions of the ChurchTuring thesis. In particular, building on pionering work of David Deutsch and Richard Jozsa, we construct an oracle relative to which there exi ..."
Abstract

Cited by 54 (5 self)
 Add to MetaCart
This is a nontechnical survey paper of recent quantummechanical discoveries that challenge generally accepted complexitytheoretic versions of the ChurchTuring thesis. In particular, building on pionering work of David Deutsch and Richard Jozsa, we construct an oracle relative to which there exists a set that can be recognized in Quantum Polynomial Time (QP), yet any Turing machine that recognizes it would require exponential time even if allowed to be probabilistic, provided that errors are not tolerated. In particular, QP 6` ZPP relative to this oracle. Furthermore, there are cryptographic tasks that are demonstrably impossible to implement with unlimited computing power probabilistic interactive Turing machines, yet they can be implemented even in practice by quantum mechanical apparatus. 1 Deutsch's Quantum Computer In a bold paper published in the Proceedings of the Royal Society, David Deutsch put forth in 1985 the quantum computer [7] (see also [8]). Even though this may c...
Two applications of inductive counting for complementation problems
 SIAM Journal of Computing
, 1989
"... nondeterministic spacebounded complexity classes are closed under complementation, two further applications of the inductive counting technique are developed. First, an errorless probabilistic algorithm for the undirected graph st connectivity problem that runs in O(log n) space and polynomial exp ..."
Abstract

Cited by 52 (3 self)
 Add to MetaCart
nondeterministic spacebounded complexity classes are closed under complementation, two further applications of the inductive counting technique are developed. First, an errorless probabilistic algorithm for the undirected graph st connectivity problem that runs in O(log n) space and polynomial expected time is given. Then it is shown that the class LOGCFL is closed under complementation. The latter is a special case of a general result that shows closure under complementation of classes defined by semiunbounded fanin circuits (or, equivalently, nondeterministic auxiliary pushdown automata or treesize bounded alternating Turing machines). As one consequence, it is shown that small numbers of "role switches " in twoperson pebbling can be eliminated.
Complexity Classes Defined By Counting Quantifiers
, 1991
"... We study the polynomial time counting hierarchy, a hierarchy of complexity classes related to the notion of counting. We investigate some of their structural properties, settling many open questions dealing with oracle characterizations, closure under boolean operations, and relations with other com ..."
Abstract

Cited by 52 (0 self)
 Add to MetaCart
We study the polynomial time counting hierarchy, a hierarchy of complexity classes related to the notion of counting. We investigate some of their structural properties, settling many open questions dealing with oracle characterizations, closure under boolean operations, and relations with other complexity classes. We develop a new combinatorial technique to obtain relativized separations for some of the studied classes, which imply absolute separations for some logarithmic time bounded complexity classes.
A complexity theory of feasible closure properties
 Journal of Computer and System Sciences
, 1993
"... ..."