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Instance Complexity

by Pekka Orponen, Ker-I Ko, Uwe Schöning, Osamu Watanabe , 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 ..."
Abstract - Cited by 32 (1 self) - Add to MetaCart
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

by Lance Fortnow, Martin Kummer - 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 ..."
Abstract - Cited by 19 (9 self) - Add to MetaCart
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

by Martin Mundhenk , 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

by Armando B. Matos, Andreia C. Teixeira, André C. Souto
"... 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

by V. Arvind, J. Köbler , M. Mundhenk, J. Torán
"... 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 ..."
Abstract - Cited by 3 (2 self) - Add to MetaCart
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

by Olaf Beyersdorff, Johannes Köbler, Sebastian Müller - 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 ..."
Abstract - Cited by 10 (6 self) - Add to MetaCart
has small nondeterministic instance complexity. 1

The knowledge complexity of interactive proof systems

by Shafi Goldwasser, Silvio Micali, Charles Rackoff - , 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 ..."
Abstract - Cited by 1246 (39 self) - Add to MetaCart
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

by Michael I. Jordan - 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 ..."
Abstract - Cited by 806 (10 self) - Add to MetaCart
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

by Ran Canetti , 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 ..."
Abstract - Cited by 833 (37 self) - Add to MetaCart
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

by Richard E. Korf - 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 ..."
Abstract - Cited by 527 (24 self) - Add to MetaCart
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
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