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27,761
Where the REALLY Hard Problems Are
- IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI-91),VOLUME 1
, 1991
"... It is well known that for many NP-complete problems, such as K-Sat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NP-complete problems can be summarized by at least one "order parameter", and that the hard p ..."
Abstract
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Cited by 683 (1 self)
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It is well known that for many NP-complete problems, such as K-Sat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NP-complete problems can be summarized by at least one "order parameter", and that the hard
The Hard Problem
"... is provided in screen-viewable form for personal use only by members ..."
Abstract
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Cited by 2 (0 self)
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is provided in screen-viewable form for personal use only by members
Proof verification and hardness of approximation problems
- IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
Abstract
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Cited by 797 (39 self)
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in the proof (though this number is a very slowly growing function of the input length). As a consequence we prove that no MAX SNP-hard problem has a polynomial time approximation scheme, unless NP=P. The class MAX SNP was defined by Papadimitriou and Yannakakis [82] and hard problems for this class include
Hard Instances of Hard Problems
"... This paper investigates the instance complexities of problems that are hard or weakly hard for exponential time under polynomial time, many-one reductions. It is shown that almost every instance of almost every problem in exponential time has essentially maximal instance complexity. It follows tha ..."
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This paper investigates the instance complexities of problems that are hard or weakly hard for exponential time under polynomial time, many-one reductions. It is shown that almost every instance of almost every problem in exponential time has essentially maximal instance complexity. It follows
A New Method for Solving Hard Satisfiability Problems
- AAAI
, 1992
"... We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approac ..."
Abstract
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Cited by 730 (21 self)
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We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional
Weakly Hard Problems
, 1994
"... A weak completeness phenomenon is investigated in the complexity class E = DTIME(2 linear ). According to standard terminology, a language H is P m -hard for E if the set Pm (H), consisting of all languages A P m H , contains the entire class E. A language C is P m -complete for E if it ..."
Abstract
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Cited by 17 (7 self)
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is the construction of a language that is weakly P m -complete, but not P m -complete, for E. The existence of such languages implies that previously known strong lower bounds on the complexity of weakly P m -hard problems for E (given by work of Lutz, Mayordomo, and Juedes) are indeed more general than
The Complexity and Distribution of Hard Problems
- SIAM JOURNAL ON COMPUTING
, 1993
"... Measure-theoretic aspects of the P m -reducibility structure of the exponential time complexity classes E=DTIME(2 linear ) and E 2 = DTIME(2 polynomial ) are investigated. Particular attention is given to the complexity (measured by the size of complexity cores) and distribution (abundance in ..."
Abstract
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Cited by 49 (18 self)
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in the sense of measure) of languages that are P m - hard for E and other complexity classes. Tight upper and lower bounds on the size of complexity cores of hard languages are derived. The upper bound says that the P m -hard languages for E are unusually simple, in the sense that they have smaller
Where the Exceptionally Hard Problems Are
, 1995
"... Constraint satisfaction problems exhibit a phase transition as a problem parameter is varied, from a region where most problems are easy and soluble to a region where most problems are easy but insoluble. In the intervening phase transition region, the median problem difficulty is greatest. However, ..."
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Cited by 10 (3 self)
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, in the easy and soluble region, occasional exceptionally hard problems (ehps) can be found, which can be much harder than any problem occurring in the phase transition. In such problems, the first few assignments made by the algorithm create an insoluble subproblem, but the algorithm cannot detect
The Hard Problem of Consciousness Studies
"... The question addressed by the hard problem of philosophy (3), how cognitive representation is acquired from the physical properties of self and the external, is examined from a perspective originating with Boethius(14) that knowledge is dependant on the nature of the perceiver and discussed with res ..."
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The question addressed by the hard problem of philosophy (3), how cognitive representation is acquired from the physical properties of self and the external, is examined from a perspective originating with Boethius(14) that knowledge is dependant on the nature of the perceiver and discussed
Hard-Core Distributions for Somewhat Hard Problems
- In 36th Annual Symposium on Foundations of Computer Science
, 1995
"... Consider a decision problem that cannot be 1 \Gamma ffi approximated by circuits of a given size in the sense that any such circuit fails to give the correct answer on at least a ffi fraction of instances. We show that for any such problem there is a specific "hard-core" set of inputs whic ..."
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Cited by 123 (11 self)
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Consider a decision problem that cannot be 1 \Gamma ffi approximated by circuits of a given size in the sense that any such circuit fails to give the correct answer on at least a ffi fraction of instances. We show that for any such problem there is a specific "hard-core" set of inputs
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27,761
