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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 107 (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
 Bulletin of the EATCS
, 1992
"... Science Department, Cornell University, Ithaca, New York 14853, USA mention of the equivalence of the tree analogs of (i) and (ii) seems to be by Brainerd [2, 3] and Eilenberg and Wright [4], although the latter claim that their paper "contains nothing that is essentially new, except perhaps for a ..."
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Cited by 9 (1 self)
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Science Department, Cornell University, Ithaca, New York 14853, USA mention of the equivalence of the tree analogs of (i) and (ii) seems to be by Brainerd [2, 3] and Eilenberg and Wright [4], although the latter claim that their paper "contains nothing that is essentially new, except perhaps for a point of view" [4]. A relation on trees analogous to jR was defined and clause (iii) added explicitly by Arbib and Give'on [1, Definition 2.13], although it is also essentially implicit in work of Brainerd [2, 3]. All the cited papers from the 1960s involve heavy use of universal algebra and/or category theory. In these papers, a tree automaton is a finite \Sigmaalgebra, and the map b ffi (see below) is a \Sigmaalgebra homomorphism. Although exceedingly elegant, this approach renders the result less accessible to the average computer science undergraduate. Fulop and V'agvolgyi take a somewhat different approach, appealing to t
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
, 1992
"... Let T \Sigma be the set of ground terms over a finite ranked alphabet \Sigma. We define partial automata on T \Sigma and prove that the finitely generated congruences on T \Sigma are in onetoone correspondence (up to isomorphism) with the finite partial automata on T \Sigma with no inaccessible an ..."
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Cited by 3 (0 self)
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Let T \Sigma be the set of ground terms over a finite ranked alphabet \Sigma. We define partial automata on T \Sigma and prove that the finitely generated congruences on T \Sigma are in onetoone correspondence (up to isomorphism) with the finite partial automata on T \Sigma with no inaccessible and no inessential states. We give an application in term rewriting: every ground term rewrite system has a canonical equivalent system that can be constructed in polynomial time. in: Logical Methods: in Honor of Anil Nerode's Sixtieth Birthday, ed. J. N. Crossley, J. B. Remmel, R. A. Shore, and M. E. Sweedler, Birkhauser, Boston, 1993, 490511. 1 Introduction The MyhillNerode Theorem is a classic result in the theory of finite automata. It dates to work of Myhill [13] and Nerode [14] in the late 1950s, but is still today considered one of the most important results in the subject. It has numerous applications, especially in showing that certain sets are regular or certain apparently s...
Forestregular Languages and Treeregular Languages
, 1995
"... Introduction Forestregular languages were studied byPair et al#PQ68# and Takahashi #Tak75#. They are extensions of treeregular languages #Tha87#. We borrow some concepts from these papers but adopt de#nitions more similar to those for stringregular languages. 2 Forests and trees De#nition 2.1 ..."
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Introduction Forestregular languages were studied byPair et al#PQ68# and Takahashi #Tak75#. They are extensions of treeregular languages #Tha87#. We borrow some concepts from these papers but adopt de#nitions more similar to those for stringregular languages. 2 Forests and trees De#nition 2.1 #forest#. A forest over # is: #1# # #the null forest#, #2# ahui, where a is a symbol in # and u is a forest, or #3# uv, where u and v are forests. The set of forests over # is denoted by F# . For any forest u; v; w 2 F#;u#vw#= #uv#w and u# = #u = u. We abbreviate ah#i as a. Remark. Since abc ###=<F