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159
The Computational Complexity of Probabilistic Planning
 Journal of Artificial Intelligence Research
, 1998
"... We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought; we examine totally ordered plans, acyclic plans, and loopin ..."
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Cited by 77 (5 self)
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We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought; we examine totally ordered plans, acyclic plans, and looping plans, and partially ordered plans under three natural definitions of plan value. We show that problems of interest are complete for a variety of complexity classes: PL, P, NP, coNP, PP, NP PP, coNP PP , and PSPACE. In the process of proving that certain planning problems are complete for NP PP , we introduce a new basic NP PP complete problem, EMajsat, which generalizes the standard Boolean satisfiability problem to computations involving probabilistic quantities; our results suggest that the development of good heuristics for EMajsat could be important for the creation of efficient algorithms for a wide variety of problems.
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. ..."
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Cited by 71 (23 self)
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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 ..."
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Cited by 62 (6 self)
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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 ..."
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Cited by 61 (13 self)
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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 prob ..."
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Cited by 56 (5 self)
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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
 In 30th Annual Symposium on Foundations of Computer Science
, 1989
"... Some of the most exciting developments in complexity theory in recent years concern the complexity of interactive proof systems, defined by Goldwasser, Micali and Rackoff (1985) and independently by Babai (1985). In this paper, we survey results on the complexity of space bounded interactive proof s ..."
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Cited by 54 (5 self)
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Some of the most exciting developments in complexity theory in recent years concern the complexity of interactive proof systems, defined by Goldwasser, Micali and Rackoff (1985) and independently by Babai (1985). In this paper, we survey results on the complexity of space bounded interactive proof systems
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 ..."
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Cited by 53 (5 self)
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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 ..."
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Cited by 53 (4 self)
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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 ..."
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Cited by 52 (0 self)
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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 for Feasible Closure Properties
, 1991
"... The study of the complexity of sets encompasses two complementary aims: (1) establishing  usually via explicit construction of algorithms  that sets are feasible, and (2) studying the relative complexity of sets that plausibly might be feasible but are not currently known to be feasible (such as ..."
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Cited by 47 (3 self)
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The study of the complexity of sets encompasses two complementary aims: (1) establishing  usually via explicit construction of algorithms  that sets are feasible, and (2) studying the relative complexity of sets that plausibly might be feasible but are not currently known to be feasible (such as the NPcomplete sets and the PSPACEcomplete sets). For the study of the complexity of closure properties, a recent urry of results [21, 33, 49, 6, 7, 16] has established an analog of (1); these papers explicitly demonstrate many closure properties possessed by PP and C=P (and the proofs implicitly give closure properties of the function class #P). The present paper presents and develops, for function classes such as #P, SpanP, OptP, and MidP, an analog of (2): a general theory of the complexity of closure properties. In particular, we show that subtraction is hard for the closure properties of each of these classes: each is closed under subtraction if and only if it is closed under every polynom...