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. Storing and using specific instances improves the performance of several supervised learning algorithms. These include algorithms that learn decision trees, classification rules, and distributed networks. However, no investigation has analyzed algorithms that use only specific instances

This article presents a theory in which automatization is construed as the acquisition of a domain-specific knowledge base, formed of separate representations, instances, of each exposure to the task. Processing is considered automatic if it relies on retrieval of stored instances, which will occur

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

the rapidly developing systematic connections between FPT and useful heuristic algorithms | a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs

We give a general complexity classification scheme for monotone computation, including monotone space-bounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a