Preface In this course we survey some recent work on the strongly bounded Turing re-ducibilities on the computably enumerable sets. Bounded Turing reducibilities are obtained from classical Turing reducibility by imposing upper bounds on the use functions (i.e., on the size of the oracle queries) of the reductions. The most popular bounded Turing reducibility which has been intensively studied ...

LogicWeb has traditionally lacked devices for dealing with intractable queries. We address this limitation by adopting length-bounded inference, a form of approximate reasoning. A length-bounded inference is of the form pv(P, G, n) which is a success if a query G can be proved from the web page P within n proof steps. It thus makes LogicWeb decidable and more tractable. During the process, we p...

We study learning in Bayesian games (or games with differential information) with an arbitrary number of bounded rational players, i.e., players who choose approximate best response strategies [approximate Bayesian Nash Equilibrium (BNE) strategies] and who also are allowed to be completely irrational in some states of the world. We show that bounded rational players by repetition can reach a l...

Bounded Max-Sum is a message-passing algorithm for solving Distributed Constraint Optimization Problems able to compute solutions with a guaranteed approximation ratio. Although its approximate solutions were empirically proved to be within a small percentage of the optimal solution on low and moderately dense problems, in this paper we show that its theoretical approximation ratio is overestim...

The theory of nite trees is the full rst-order theory of equality in the Herbrand universum (the set of ground terms) over a functional signature containing non-unary function symbols and constants. Albeit decidable, this theory turns out to be of the non-elementary complexity in the sense of Kalmar, i.e., it cannot be decided within time or space bounded by any nite xed tower of exponentials 2...

for 0 ≤ r ≤ k − 1. In particular, dist (f, S π) = O(|π| ) for f ∈ C(I), or, more generally, for f ∈ C(I), such, that f (k−1) satisfies a Lipschitz condition, a result proved earlier by different means [2]. These results are shown to be true even if I is permitted to become infinite and some of the knots are permitted to coalesce. The argument is based on a “local” interpolation scheme Pπ by spl...

In this paper we establish a discrete Calderón’s identity which converges in both Lq(Rn+m) (1 < q <∞) and Hardy space H(R ×Rm) (0 <p ≤ 1). Based on this identity, we derive a new atomic decomposition into (p, q)-atoms (1 < q <∞) on H(R × R) for 0 < p ≤ 1. As an application, we prove that an operator T , which is bounded on Lq(Rn+m) for some 1 < q <∞, is bounded from Hp(Rn×Rm) to Lp(Rn+m) if and...