In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

We first consider the problem of learning k-parities in the on-line mistake-bound model: given a hidden vector x ∈ {0, 1} with |x| = k and a sequence of “questions” a1, a2, · · · ∈ {0, 1} , where the algorithm must reply to each question with 〈ai, x〉 (mod 2), what is the best tradeoff between the number of mistakes made by the algorithm and its time complexity? We improve the previous best result of Buhrman et. al. [BGM10] by an exp(k) factor in the time complexity. Second, we consider the problem of learning k-parities in the presence of classification noise of rate η ∈ (0, 1/2). A polynomial time algorithm for this problem (when η > 0 and k = ω(1)) is a longstanding challenge in learning theory. Grigorescu et al. [GRV11] showed an algorithm running in time ( n k/2 )1+4η+o(1) . Note that this algorithm inherently requires time ( n k/2 ) even when the noise rate η is polynomially small. We observe that for sufficiently small noise rate, it is possible to break the ( n k/2 ) barrier. In particular, if for some function f(n) = ω(1) and α ∈ [1/2, 1), k = n/f(n) and η = o(f(n)/ log n), then there is an algorithm for the problem with running time poly(n) · ( n k )1−α · e.
On learning k-parities with and without noise

So-called combined approaches answer a conjunctive query over a description logic ontology in three steps: first, they materialise certain consequences of the ontology and the data; second, they evaluate the query over the data; and third, they filter the result of the second phase to eliminate unsound answers. Such approaches were developed for various members of the DL-Lite and the EL families of languages, but none of them can handle ontologies containing nominals. In our work, we bridge this gap and present a combined query answering approach for ELHO ⊥—a logic that contains all features of the OWL 2 EL standard apart from transitive roles and complex role inclusions. This extension is nontrivial because nominals require equality reasoning, which introduces complexity into the first and the third step. Our empirical evaluation suggests that our technique is suitable for practical application, and so it provides a practical basis for conjunctive query answering in a large fragment of OWL 2 EL.
Introducing Nominals to the Combined Query Answering Approaches for EL

Path planning for multiple robots is well studied in the AI and robotics communities. For a given discretized environment, robots need to find collision-free paths to a set of specified goal locations. Robots can be fully anonymous, non-anonymous, or organized in groups. Although powerful solvers for this abstract problem exist, they make simplifying assumptions by ignoring kinematic constraints, making it difficult to use the resulting plans on actual robots. In this paper, we present a solution which takes kinematic constraints, such as maximum velocities, into account, while guaranteeing a user-specified minimum safety distance between robots. We demonstrate our approach in simulation and on real robots in 2D and 3D environments.

Path Planning With Kinematic Constraints For Robot Groups