Learning Algorithms for Grammars of Variable Arity Trees
13 Dec 2007-pp 98-103
TL;DR: This paper gives algorithms for inference of local, single type and regular grammar and also considers the use of negative samples in the inference of tree grammars from a set of sample input trees.
Abstract: Grammatical Inference is the technique by which a grammar that best describes a given set of input samples is inferred. This paper considers the inference of tree grammars from a set of sample input trees. Inference of grammars for fixed arity trees is well studied, in this paper we extend the method to give algorithms for inference of grammars for variable arity trees. We give algorithms for inference of local, single type and regular grammar and also consider the use of negative samples. The variable arity trees we consider can be used for representation of XML documents and the algorithms we have given can be used for validation as well as for schema inference.
••29 Jan 2012
TL;DR: A systems engineering view towards the requirements specification process and a method for the flowdown process is presented and a case study based on an electric Unmanned Aerial Vehicle scenario demonstrates how top level requirements for performance, cost, and safety flow down to the health management level and specify quantitative requirements for prognostic algorithm performance.
Abstract: Prognostics and Health Management (PHM) principles have considerable promise to change the game of lifecycle cost of engineering systems at high safety levels by providing a reliable estimate of future system states. This estimate is a key for planning and decision making in an operational setting. While technology solutions have made considerable advances, the tie-in into the systems engineering process is lagging behind, which delays fielding of PHM-enabled systems. The derivation of specifications from high level requirements for algorithm performance to ensure quality predictions is not well developed. From an engineering perspective some key parameters driving the requirements for prognostics performance include: (1) maximum allowable Probability of Failure (PoF) of the prognostic system to bound the risk of losing an asset, (2) tolerable limits on proactive maintenance to minimize missed opportunity of asset usage, (3) lead time to specify the amount of advanced warning needed for actionable decisions, and (4) required confidence to specify when prognosis is sufficiently good to be used. This paper takes a systems engineering view towards the requirements specification process and presents a method for the flowdown process. A case study based on an electric Unmanned Aerial Vehicle (e-UAV) scenario demonstrates how top level requirements for performance, cost, and safety flow down to the health management level and specify quantitative requirements for prognostic algorithm performance.
TL;DR: This paper considers bottom-up tree automata and discusses the sequential distributed version of this model, and finds that the ∗- mode does not increase the power, whereas the other modes increase thePower.
Abstract: Tree automata have been defined to accept trees. Different types of acceptance like bottom-up, top-down, tree walking have been considered in the literature. In this paper, we consider bottom-up tree automata and discuss the sequential distributed version of this model. Generally, this type of distribution is called cooperative distributed automata or the blackboard model. We define the traditional five modes of cooperation, viz. ∗-mode, t-mode, = k, ≥ k, ≤ k (k ≥ 1) modes on bottom-up tree automata. We discuss the accepting power of cooperative distributed tree automata under these modes of cooperation. We find that the ∗- mode does not increase the power, whereas the other modes increase the power. We discuss a few results comparing the acceptance power under different modes of cooperation.
TL;DR: An algorithm is presented to modify an inferred grammar so that it does not recognize any tree from a given negative sample, and all the results are applicable to tree languages in which any symbol may appear in a tree with an arbitrary number of descendants.
Abstract: This paper considers the problem of grammatical inference of tree grammars as a general problem. It is shown that the problem does not have a unique solution, and that there is a very large number of solutions. It is also shown that all inference algorithms must have the same logical structure, and that all proposed inference algorithms are, in this way, equivalent and equally correct. The paper reviews the use of negative samples in the process of grammatical inference, and emphasizes the fact that negative samples are needed to narrow down the large number of valid solutions, and to guarantee the convergence of any inference algorithm. To accomplish these purposes, an algorithm is presented to modify an inferred grammar so that it does not recognize any tree from a given negative sample. Furthermore, all the results are applicable to tree languages in which any symbol may appear in a tree with an arbitrary number of descendants.
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