Abstract. We consider the problem of learning a finite automaton M of n states with input alphabet X and output alphabet Y when a teacher has helpfully or randomly labeled the states of M using labels from a set L. The learner has access to label queries; a label query with input string w returns both the output and the label of the state reached by w. Because different automata may have the same output behavior, we consider the case in which the teacher may "unfold" M to an output equivalent machine M and label the states of M for the learner. We give lower and upper bounds on the number of label queries to learn the output behavior of M in these different scenarios. We also briefly consider the case of randomly labeled automata with randomly chosen transition functions.
Contextual hypergraph grammars represent a generalization of contextual grammars by considering hypergraphs instead of strings as underlying data structures. These grammars are important for both computational and modeling capabilities especially for the newly emergent domain of self-assembling DNA structures.In this paper we show how startingfrom a given Boolean function, we construct a contextual hypergraph grammar able to model the self-assembling tile process that performs the corresponding computations 1. INTRODUCTION Contextual hypergraph grammars were introduced in [1] as a generalization of contextual grammars by considering hypergraphs instead of strings as underlying data structures. A contextual hypergraph grammar is given by finite sets of axioms and contexts both being hypergraph. We believe that the notion of context defined as a hypergraph with external nodes is related in a more appropriate way to the generally accepted notion of context, in the sense that our context is a matching and connecting unit with pre-existent knowledge. In the same time the context is added to form a more elaborate information.Contextual hypergraph grammars are an important class of grammars for both computational and modeling capabilities especially for the newly emergent domain of self-assembling DNA structures. We can find notions regarding the self-assembling templates for Boolean Tree-Like Circuits (BTLCs) in [2][3]. Using contextual hypergraph grammars we try to create a visual interpretation for the computational framework used to describe selfassembling structures assimilating hypergraph contexts with DNA interacting tiles.
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