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In the theory of belief revision, the computation of all maximal subsets (maximal contractions) of a formula set with respect to a set of facts is one of the key problems. In this paper, we try to solve this problem by studying the algorithm to compute all maximal contractions for Horn clauses. First, we point out and prove the conversion relationship between minimal inconsistent subsets of union of the formula set and the set of facts and maximal contractions of the formula set with respect to the set of facts. Second, we prove a necessary condition of a set of Horn clauses to be minimal inconsistent. Then, based on these two conclusions, we propose an interactive algorithm to enumerate all minimal inconsistent subsets of a given set of Horn clauses and a second algorithm to compute maximal contractions from these minimal inconsistent subsets. Finally, we proposed an interactive algorithm to compute maximal contractions for Horn clauses by composing the above two algorithms.

A algebraic system, Test Algebra (TA), identifies faults in combinatorial testing for SaaS (Software-as-a-Service) applications. SaaS is a software delivery model that involves composition, deployment, and execution of mission application on cloud platforms. Testing SaaS applications is challenging because a large number of configurations needs to be tested. Faulty configurations should be identified and corrected before the delivery of SaaS applications. TA proposes an effective way to reuse existing test results to identify test results of candidate configurations. The TA also defines rules to permit results to be combined, and to identify the faulty interactions. Using the TA, configurations can be tested concurrently on different servers and in any order. This paper proposes one MapReduce design of TA concurrent execution in a cloud environment. The optimization of TA analysis is discussed. The proposed solutions are simulated using Hadoop in a cloud environment.

Modern search engines aggregate results from different verticals : webpages, news, images, video, shopping, knowledge cards, local maps, and so on. Unlike “ten blue links,” these search results are heterogeneous in nature and not even arranged in a list on the page. This revolution directly challenges the conventional “ranked list” formulation in ad hoc search. Therefore, finding proper presentation for a gallery of heterogeneous results is critical for modern search engines. We propose a novel framework that learns the optimal page presentation to render heterogeneous results onto search result page (SERP). Page presentation is broadly defined as the strategy to present a set of items on SERP, much more expressive than a ranked list. It can specify item positions, image sizes, text fonts, and any other styles as long as variations are within business and design constraints. The learned presentation is content aware, i.e., tailored to specific queries and returned results. Simulation experiments show that the framework automatically learns eye-catchy presentations for relevant results. Experiments on real data show that simple instantiations of the framework already outperform leading algorithm in federated search result presentation. It means the framework can learn its own result presentation strategy purely from data, without even knowing the “probability ranking principle.”