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Register a new userDecompositions of Grammar Constraints
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Added by
Toby Walsh
Publication date
2009
fields
Informatics Engineering
and research's language is
English
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A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive constraints. We can then, for instance, use state of the art SAT solvers and profit from their advanced features like fast unit propagation, clause learning, and conflict-based search heuristics. This approach holds promise for solving combinatorial problems in scheduling, rostering, and configuration, as well as problems in more diverse areas like bioinformatics, software testing and natural language processing. In addition, decomposition may be an effective method to propagate other global constraints.
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An attractive mechanism to specify global constraints in rostering and other domains is via formal languages. For instance, the Regular and Grammar constraints specify constraints in terms of the languages accepted by an automaton and a context-free grammar respectively. Taking advantage of the fixed length of the constraint, we give an algorithm to transform a context-free grammar into an automaton. We then study the use of minimization techniques to reduce the size of such automata and speed up propagation. We show that minimizing such automata after they have been unfolded and domains initially reduced can give automata that are more compact than minimizing before unfolding and reducing. Experimental results show that such transformations can improve the size of rostering problems that we can model and run.
State-of-the-art process discovery methods construct free-choice process models from event logs. Consequently, the constructed models do not take into account indirect dependencies between events. Whenever the input behaviour is not free-choice, these methods fail to provide a precise model. In this paper, we propose a novel approach for enhancing free-choice process models by adding non-free-choice constructs discovered a-posteriori via region-based techniques. This allows us to benefit from the performance of existing process discovery methods and the accuracy of the employed fundamental synthesis techniques. We prove that the proposed approach preserves fitness with respect to the event log while improving the precision when indirect dependencies exist. The approach has been implemented and tested on both synthetic and real-life datasets. The results show its effectiveness in repairing models discovered from event logs.
Semantic networks qualify the meaning of an edge relating any two vertices. Determining which vertices are most central in a semantic network is difficult because one relationship type may be deemed subjectively more important than another. For this reason, research into semantic network metrics has focused primarily on context-based rankings (i.e. user prescribed contexts). Moreover, many of the current semantic network metrics rank semantic associations (i.e. directed paths between two vertices) and not the vertices themselves. This article presents a framework for calculating semantically meaningful primary eigenvector-based metrics such as eigenvector centrality and PageRank in semantic networks using a modified version of the random walker model of Markov chain analysis. Random walkers, in the context of this article, are constrained by a grammar, where the grammar is a user defined data structure that determines the meaning of the final vertex ranking. The ideas in this article are presented within the context of the Resource Description Framework (RDF) of the Semantic Web initiative.
Combinatory categorial grammar (CCG) is a grammar formalism used for natural language parsing. CCG assigns structured lexical categories to words and uses a small set of combinatory rules to combine these categories to parse a sentence. In this work we propose and implement a new approach to CCG parsing that relies on a prominent knowledge representation formalism, answer set programming (ASP) - a declarative programming paradigm. We formulate the task of CCG parsing as a planning problem and use an ASP computational tool to compute solutions that correspond to valid parses. Compared to other approaches, there is no need to implement a specific parsing algorithm using such a declarative method. Our approach aims at producing all semantically distinct parse trees for a given sentence. From this goal, normalization and efficiency issues arise, and we deal with them by combining and extending existing strategies. We have implemented a CCG parsing tool kit - AspCcgTk - that uses ASP as its main computational means. The C&C supertagger can be used as a preprocessor within AspCcgTk, which allows us to achieve wide-coverage natural language parsing.
We describe the design and implementation of a reasoning engine that facilitates the gamification of loop-invariant discovery. Our reasoning engine enables students, computational agents and regular software engineers with no formal methods expertise to collaboratively prove interesting theorems about simple programs using browser-based, online games. Within an hour, players are able to specify and verify properties of programs that are beyond the capabilities of fully-automated tools. The hour limit includes the time for setting up the system, completing a short tutorial explaining game play and reasoning about simple imperative programs. Players are never required to understand formal proofs; they only provide insights by proposing invariants. The reasoning engine is responsible for managing and evaluating the proposed invariants, as well as generating actionable feedback.
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