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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 special-case 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 special-case program for A
On Resource-Bounded 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 NP-hard 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 p-h ..."
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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
Non-deterministic communication complexity and instance complexity
"... Abstract. We study the relationship between non-deterministic communication complexity [8, 9, 4] and instance complexity [7]. For that purpose, the witness of the non-deterministic 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 non-deterministic communication complexity [8, 9, 4] and instance complexity [7]. For that purpose, the witness of the non-deterministic communication protocol executed by Alice and Bob is interpreted by Alice as a program p that, for t sufficiently large
Nondeterministic Instance Complexity and Hard-to-Prove Tautologies
"... In this note we rst formalize the notion of hard tautologies using a nondeterministic generalization of instance complexity. We then show, under reasonable complexity-theoretic 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 complexity-theoretic 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 Karp-Lipton 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
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, 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/non-Hamiltonian. 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 large-scale 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 large-scale 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 security-preserving composition operation allows for modular design and analysis of complex cryptographic protocols from relatively simple building blocks. Moreover, within this framework
Depth-first Iterative-Deepening: 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 breadth-first search requires too much space and depth-first search can use too much time and doesn't always find a cheapest path. A depth-first iteratiw-deepening 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 breadth-first search requires too much space and depth-first search can use too much time and doesn't always find a cheapest path. A depth-first iteratiw
Results 1 - 10
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