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.

Example Input: This papers shows that using separators, which is a pair of two complementary contractors, we can easily and efficiently solve the localization problem of a robot with sonar measurements in an unstructured environment. We introduce separators associated with the Minkowski sum and the Minkowski difference in order to facilitate the resolution. A test-case is given in order to illustrate the principle of the approach.
Example Output: Minkowski Operations of Sets with Application to Robot Localization

Example Input: Practically all programming languages allow the programmer to split a program into several modules which brings along several advantages in software development. In this paper, we are interested in the area of answer-set programming where fully declarative and nonmonotonic languages are applied. In this context, obtaining a modular structure for programs is by no means straightforward since the output of an entire program cannot in general be composed from the output of its components. To better understand the effects of disjunctive information on modularity we restrict the scope of analysis to the case of disjunctive logic programs (DLPs) subject to stable-model semantics. We define the notion of a DLP-function, where a well-defined input/output interface is provided, and establish a novel module theorem which indicates the compositionality of stable-model semantics for DLP-functions. The module theorem extends the well-known splitting-set theorem and enables the decomposition of DLP-functions given their strongly connected components based on positive dependencies induced by rules. In this setting, it is also possible to split shared disjunctive rules among components using a generalized shifting technique. The concept of modular equivalence is introduced for the mutual comparison of DLP-functions using a generalization of a translation-based verification method.
Example Output: Modularity Aspects of Disjunctive Stable Models

Example Input: Exploration in an unknown environment is the core functionality for mobile robots. Learning-based exploration methods, including convolutional neural networks, provide excellent strategies without human-designed logic for the feature extraction [1]. But the conventional supervised learning algorithms cost lots of efforts on the labeling work of datasets inevitably. Scenes not included in the training set are mostly unrecognized either. We propose a deep reinforcement learning method for the exploration of mobile robots in an indoor environment with the depth information from an RGB-D sensor only. Based on the Deep Q-Network framework [2], the raw depth image is taken as the only input to estimate the Q values corresponding to all moving commands. The training of the network weights is end-to-end. In arbitrarily constructed simulation environments, we show that the robot can be quickly adapted to unfamiliar scenes without any man-made labeling. Besides, through analysis of receptive fields of feature representations, deep reinforcement learning motivates the convolutional networks to estimate the traversability of the scenes. The test results are compared with the exploration strategies separately based on deep learning [1] or reinforcement learning [3]. Even trained only in the simulated environment, experimental results in real-world environment demonstrate that the cognitive ability of robot controller is dramatically improved compared with the supervised method. We believe it is the first time that raw sensor information is used to build cognitive exploration strategy for mobile robots through end-to-end deep reinforcement learning.
Example Output:
Towards cognitive exploration through deep reinforcement learning for mobile robots