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Regular Tree and Regular Hedge Languages over Unranked Alphabets: Version 1
, 2001
"... We survey the basic results on regular tree languages over unranked alphabets; that is, we use an unranked alphabet for the labels of nodes, we allow unbounded, yet regular, degree nodes and we treat sequences of trees that, following Courcelle, we call hedges. The survey was begun by the first ..."
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Cited by 113 (5 self)
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We survey the basic results on regular tree languages over unranked alphabets; that is, we use an unranked alphabet for the labels of nodes, we allow unbounded, yet regular, degree nodes and we treat sequences of trees that, following Courcelle, we call hedges. The survey was begun by the first and third authors. Subsequently, when they discovered that the second author had already written a summary of this view of tree automata and languages, the three authors decided to join forces and produce a consistent review of the area. The survey is still unfinished because we have been unable to find the time to finish it. We are making it available in this unfinished form as a research report because it has, already, been heavily cited in the literature.
On the MyhillNerode Theorem for Trees
"... The MyhillNerode Theorem as stated in [6] says that for a set R of strings over a finite alphabet, the following statements are equivalent: (i) R is regular (ii) R is a union of classes of a rightinvariant equivalence relation of index finite (iii) the relation R is of finite index, where x R y i ..."
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Cited by 9 (1 self)
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The MyhillNerode Theorem as stated in [6] says that for a set R of strings over a finite alphabet, the following statements are equivalent: (i) R is regular (ii) R is a union of classes of a rightinvariant equivalence relation of index finite (iii) the relation R is of finite index, where x R y i 8z 2 xz 2 R $ yz 2 R. This result generalizes in a straightforward way to automata on finite trees. I rediscovered this generalization in connection with work on finitely presented algebras, and stated it without proof or attribution in [7, 8], being at that time under the impression that it was folklore and completely elementary. Itwas again rediscovered independently by Z. Fülöp and S. Vagvolgyi and reported in a recent contribution to this Bulletin [5]. In that paper they attribute the result to me. In fact, the result goes back at least ten years earlier to the late 1960s. It is difficult to attribute it to any one paper, since it seems to have been in the air at a time when the theory of finite automata on trees was undergoing intense development. In a sense, it is an inevitable consequence Myhill and Nerode's work [9, 10], since "conventional finite automata theory goes through for the generalizationand it goes through quite neatly " [11]. The first explicit
On the Efficient Classification of Data Structures by Neural Networks
, 1997
"... In the last few years it has been shown that recurrent neural networks are adequate for processing general data structures like trees and graphs, which opens the doors to a number of new interesting applications previously unexplored. In this paper, we analyze the efficiency of learning the membersh ..."
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Cited by 5 (2 self)
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In the last few years it has been shown that recurrent neural networks are adequate for processing general data structures like trees and graphs, which opens the doors to a number of new interesting applications previously unexplored. In this paper, we analyze the efficiency of learning the membership of DOAGs (Directed Ordered Acyclic Graphs) in terms of local minima of the error surface by relying on the principle that their absence is a guarantee of efficient learning. We give sufficient conditions under which the error surface is local minima free. Specifically, we define a topological index associated with a collection of DOAGs that makes it possible to design the architecture so as to avoid local minima. 1 Introduction It is wellknown that connectionist models are not only capable of dealing with static patterns, but also with sequential inputs. Real world, however, often proposes structured domains that can hardly be represented by simple sequences. For instance, there are cas...
Partial automata and finitely generated congruences: an extension of Nerode’s theorem
 Proc. Conf. Logical Methods in Math. and Comp. Sci
, 1992
"... For Anil Nerode, on the occasion of his 60 th birthday ..."
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Cited by 3 (0 self)
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For Anil Nerode, on the occasion of his 60 th birthday