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

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 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

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

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

has small nondeterministic instance complexity. 1

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

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

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

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