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Probabilistically Checkable Debate Systems and Nonapproximability of PSPACEHard Functions
, 1995
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Probabilistically Checkable Debate Systems and Nonapproximability of PSPACEHard Functions
, 1995
"... We initiate an investigation of probabilistically checkable debate systems (PCDS), a natural generalization of probabilistically checkable proof systems (PCPS). A PCDS for a language L consists of a probabilistic polynomialtime verifier V and a debate between player 1, who claims that the input x i ..."
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is in L, and player 0, who claims that the input x is not in L. We show that there is a PCDS for L in which V flips O(log n) random coins and reads O(1) bits of the debate if and only if L is in PSPACE. This characterization of PSPACE is used to show that certain PSPACEhard functions are as hard
NCApproximation Schemes for NP and PSPACEHard Problems for Geometric Graphs
, 1997
"... We present NC approximation schemes for a number of graph problems when restricted to geometric graphs including unit disk graphs and graphs drawn in a civilized manner. Our approximation schemes exhibit the same time versus performance tradeoff as the best known approximation schemes for planar gr ..."
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Cited by 121 (1 self)
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disk graphs, many more graph problems have efficient approximation schemes. Our NC approximation schemes can also be extended to obtain efficient NC approximation schemes for several PSPACEhard problems on unit disk graphs specified using a restricted version of the hierarchical specification
Approximation Algorithms for PSPACEHard Hierarchically and Periodically Specified Problems
 SIAM JOURNAL ON COMPUTING
, 1998
"... We study the efficient approximability of basic graph and logic problems in the literature when instances are specified hierarchically as in [35] or are specified by 1dimensional finite narrow periodic specifications as in [58]. We show that, for most of the problems \Pi considered when specified u ..."
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Cited by 8 (0 self)
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time approximation algorithm with performance guarantee (1 + ffl)ae. (ii) \Pi has a polynomial time approximation scheme when restricted to planar instances. These are the first polynomial time approximation schemes for PSPACEhard hierarchically or periodically specified problems. Since several
Efficient Probabilistically Checkable Debates
"... Probabilistically checkable debate systems (PCDSs) are debates between two competing provers, in which a polynomialtime verifier inspects a constant number of bits of the debate. It was shown by Condon, Feigenbaum, Lund, and Shor that every language in PSPACE has a PCDS in which the debate length ..."
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Probabilistically checkable debate systems (PCDSs) are debates between two competing provers, in which a polynomialtime verifier inspects a constant number of bits of the debate. It was shown by Condon, Feigenbaum, Lund, and Shor that every language in PSPACE has a PCDS in which the debate length
Strong Bounds on the Approximability of Two PSPACEhard Problems in Propositional Planning
"... The computational complexity of planning with Stripsstyle operators has received a considerable amount of interest in the literature. However, the approximability of such problems has only received minute attention. We study two Pspacehard optimization versions of propositional planning and pr ..."
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Cited by 1 (1 self)
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problems. In similarity to NPhard approximation problems, Pspacehard approximation problems display a wide variation in the precision with which they can be approximated efficiently. Results in the literature show that some Pspacehard problems have efficient approximation algorithms while others have
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 498 (68 self)
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We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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. We prove that (1 \Gamma o(1)) ln n is a threshold below which set cover cannot be approximated efficiently, unless NP has slightly superpolynomial time algorithms. This closes the gap (up to low order terms) between the ratio of approximation achievable by the greedy algorithm (which is (1 \Gamma
The empirical case for two systems of reasoning
, 1996
"... Distinctions have been proposed between systems of reasoning for centuries. This article distills properties shared by many of these distinctions and characterizes the resulting systems in light of recent findings and theoretical developments. One system is associative because its computations ref ..."
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Cited by 631 (4 self)
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reflect similarity structure and relations of temporal contiguity. The other is “rule based” because it operates on symbolic structures that have logical content and variables and because its computations have the properties that are normally assigned to rules. The systems serve complementary functions
Results 1  10
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