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: Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the probability of given queries being true provided a set of mutually independent random variables, a model (a logic program) and some evidence. The core of solving this inference task involves translating the logic program to a propositional theory and using a model counter. In this paper, we show that for some problems that involve inductive definitions like reachability in a graph, the translation of logic programs to SAT can be expensive for the purpose of solving inference tasks. For such problems, direct implementation of stable model semantics allows for more efficient solving. We present two implementation techniques, based on unfounded set detection, that extend a propositional model counter to a stable model counter. Our experiments show that for particular problems, our approach can outperform a state-of-the-art probabilistic logic programming solver by several orders of magnitude in terms of running time and space requirements, and can solve instances of significantly larger sizes on which the current solver runs out of time or memory.
Example Output: Stable Model Counting and Its Application in Probabilistic Logic Programming

Example Input: Encoding finite linear CSPs as Boolean formulas and solving them by using modern SAT solvers has proven to be highly effective, as exemplified by the award-winning sugar system. We here develop an alternative approach based on ASP. This allows us to use first-order encodings providing us with a high degree of flexibility for easy experimentation with different implementations. The resulting system aspartame re-uses parts of sugar for parsing and normalizing CSPs. The obtained set of facts is then combined with an ASP encoding that can be grounded and solved by off-the-shelf ASP systems. We establish the competitiveness of our approach by empirically contrasting aspartame and sugar.
Example Output: Aspartame: Solving Constraint Satisfaction Problems with Answer Set Programming

Example Input: Learning useful information across long time lags is a critical and difficult problem for temporal neural models in tasks like language modeling. Existing architectures that address the issue are often complex and costly to train. The Delta Recurrent Neural Network (Delta-RNN) framework is a simple and highperforming design that unifies previously proposed gated neural models. The DeltaRNN models maintain longer-term memory by learning to interpolate between a fast-changing data-driven representation and a slowly changing, implicitly stable state. This requires hardly any more parameters than a classical simple recurrent network. The models outperform popular complex architectures, such as the Long Short Term Memory (LSTM) and the Gated Recurrent Unit (GRU) and achieve state-of-the art performance in language modeling at character and word levels and yield comparable performance at the subword level.
Example Output:
Learning Simpler Language Models with the Delta Recurrent Neural Network Framework