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.

Ex Input:
We describe a technique to minimize weighted tree automata (WTA), a powerful formalisms that subsumes probabilistic context-free grammars (PCFGs) and latent-variable PCFGs. Our method relies on a singular value decomposition of the underlying Hankel matrix defined by the WTA. Our main theoretical result is an efficient algorithm for computing the SVD of an infinite Hankel matrix implicitly represented as a WTA. We provide an analysis of the approximation error induced by the minimization, and we evaluate our method on real-world data originating in newswire treebank. We show that the model achieves lower perplexity than previous methods for PCFG minimization, and also is much more stable due to the absence of local optima.

Ex Output:
Weighted Tree Automata Approximation by Singular Value Truncation

Ex Input:
The paper analyzes the interaction between humans and computers in terms of response time in solving the image-based CAPTCHA. In particular, the analysis focuses on the attitude of the different Internet users in easily solving four different types of image-based CAPTCHAs which include facial expressions like: animated character, old woman, surprised face, worried face. To pursue this goal, an experiment is realized involving 100 Internet users in solving the four types of CAPTCHAs, differentiated by age, Internet experience, and education level. The response times are collected for each user. Then, association rules are extracted from user data, for evaluating the dependence of the response time in solving the CAPTCHA from age, education level and experience in internet usage by statistical analysis. The results implicitly capture the users' psychological states showing in what states the users are more sensible. It reveals to be a novelty and a meaningful analysis in the state-of-the-art.

Ex Output:
Analysis of the Human-Computer Interaction on the Example of Image-based CAPTCHA by Association Rule Mining

Ex Input:
Domain-independent planning is one of the foundational areas in the field of Artificial Intelligence. A description of a planning task consists of an initial world state, a goal, and a set of actions for modifying the world state. The objective is to find a sequence of actions, that is, a plan, that transforms the initial world state into a goal state. In optimal planning, we are interested in finding not just a plan, but one of the cheapest plans. A prominent approach to optimal planning these days is heuristic state-space search, guided by admissible heuristic functions. Numerous admissible heuristics have been developed, each with its own strengths and weaknesses, and it is well known that there is no single "best" heuristic for optimal planning in general. Thus, which heuristic to choose for a given planning task is a difficult question. This difficulty can be avoided by combining several heuristics, but that requires computing numerous heuristic estimates at each state, and the tradeoff between the time spent doing so and the time saved by the combined advantages of the different heuristics might be high. We present a novel method that reduces the cost of combining admissible heuristics for optimal planning, while maintaining its benefits. Using an idealized search space model, we formulate a decision rule for choosing the best heuristic to compute at each state. We then present an active online learning approach for learning a classifier with that decision rule as the target concept, and employ the learned classifier to decide which heuristic to compute at each state. We evaluate this technique empirically, and show that it substantially outperforms the standard method for combining several heuristics via their pointwise maximum.

Ex Output:
Online Speedup Learning for Optimal Planning