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Instance Complexity
, 1994
"... We introduce a measure for the computational complexity of individual instances of a decision problem and study some of its properties. The instance complexity of a string x with respect to a set A and time bound t, ic t (x : A), is defined as the size of the smallest specialcase program for A that ..."
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Cited by 32 (1 self)
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We introduce a measure for the computational complexity of individual instances of a decision problem and study some of its properties. The instance complexity of a string x with respect to a set A and time bound t, ic t (x : A), is defined as the size of the smallest specialcase program for A
On ResourceBounded Instance Complexity
 Theoretical Computer Science A
, 1995
"... The instance complexity of a string x with respect to a set A and time bound t, ic t (x : A), is the length of the shortest program for A that runs in time t, decides x correctly, and makes no mistakes on other strings (where "don't know" answers are permitted). The Instance Complexit ..."
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Cited by 19 (9 self)
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The instance complexity of a string x with respect to a set A and time bound t, ic t (x : A), is the length of the shortest program for A that runs in time t, decides x correctly, and makes no mistakes on other strings (where "don't know" answers are permitted). The Instance
Instance Complexity of NPhard sets
, 1999
"... Instance complexity was introduced by Orponen, Ko, Schöning, and Watanabe [7, 14, 15] as a measure of the complexity of individual instances of a decision problem. Comparing instance complexity to Kolmogorov complexity (i.e. the inherent complexity of a string), they introduced the notion of ph ..."
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Instance complexity was introduced by Orponen, Ko, Schöning, and Watanabe [7, 14, 15] as a measure of the complexity of individual instances of a decision problem. Comparing instance complexity to Kolmogorov complexity (i.e. the inherent complexity of a string), they introduced the notion of p
Nondeterministic communication complexity and instance complexity
"... Abstract. We study the relationship between nondeterministic communication complexity [8, 9, 4] and instance complexity [7]. For that purpose, the witness of the nondeterministic communication protocol executed by Alice and Bob is interpreted by Alice as a program p that, for t sufficiently large, ..."
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Abstract. We study the relationship between nondeterministic communication complexity [8, 9, 4] and instance complexity [7]. For that purpose, the witness of the nondeterministic communication protocol executed by Alice and Bob is interpreted by Alice as a program p that, for t sufficiently large
Nondeterministic Instance Complexity and HardtoProve Tautologies
"... In this note we rst formalize the notion of hard tautologies using a nondeterministic generalization of instance complexity. We then show, under reasonable complexitytheoretic assumptions, that there are innitely many propositional tautologies that are hard to prove in any sound propositional p ..."
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Cited by 3 (2 self)
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In this note we rst formalize the notion of hard tautologies using a nondeterministic generalization of instance complexity. We then show, under reasonable complexitytheoretic assumptions, that there are innitely many propositional tautologies that are hard to prove in any sound propositional
Nondeterministic instance complexity and proof systems with advice
 In Proc. 3rd International Conference on Language and Automata Theory and Applications, volume 5457 of Lecture Notes in Computer Science
"... Abstract. Motivated by strong KarpLipton collapse results in bounded arithmetic, Cook and Krajíček [7] have recently introduced the notion of propositional proof systems with advice. In this paper we investigate the following question: Do there exist polynomially bounded proof systems with advice f ..."
The knowledge complexity of interactive proof systems

, 1989
"... Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/nonHamiltonian. In th ..."
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Cited by 1246 (39 self)
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Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian
Learning in graphical models
 STATISTICAL SCIENCE
, 2004
"... Statistical applications in fields such as bioinformatics, information retrieval, speech processing, image processing and communications often involve largescale models in which thousands or millions of random variables are linked in complex ways. Graphical models provide a general methodology for ..."
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Cited by 806 (10 self)
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Statistical applications in fields such as bioinformatics, information retrieval, speech processing, image processing and communications often involve largescale models in which thousands or millions of random variables are linked in complex ways. Graphical models provide a general methodology
Universally composable security: A new paradigm for cryptographic protocols
, 2013
"... We present a general framework for representing cryptographic protocols and analyzing their security. The framework allows specifying the security requirements of practically any cryptographic task in a unified and systematic way. Furthermore, in this framework the security of protocols is preserved ..."
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Cited by 833 (37 self)
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is preserved under a general protocol composition operation, called universal composition. The proposed framework with its securitypreserving composition operation allows for modular design and analysis of complex cryptographic protocols from relatively simple building blocks. Moreover, within this framework
Depthfirst IterativeDeepening: An Optimal Admissible Tree Search
 Artificial Intelligence
, 1985
"... The complexities of various search algorithms are considered in terms of time, space, and cost of solution path. It is known that breadthfirst search requires too much space and depthfirst search can use too much time and doesn't always find a cheapest path. A depthfirst iteratiwdeepening a ..."
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Cited by 527 (24 self)
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The complexities of various search algorithms are considered in terms of time, space, and cost of solution path. It is known that breadthfirst search requires too much space and depthfirst search can use too much time and doesn't always find a cheapest path. A depthfirst iteratiw
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