On pushdown tree automata

Guessarian, Irène

doi:10.1007/3-540-10828-9_64

Cited by 16 publications

(32 citation statements)

References 3 publications

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“…Kuich [43] generalized these results of Guessarian [32] to formal tree series. He defined pushdown tree automata whose behaviors are formal tree series and showed that the class of behaviors of these pushdown tree automata coincides with the class of algebraic tree series.…”

Section: Theorem 48 the Following Statements On A Tree Languagementioning

confidence: 86%

“…Moreover, we prove a Kleene Theorem due to Bozapalidis [11]. Guessarian [32] introduced the notion of a (top-down) pushdown tree automaton and showed that these pushdown tree automata recognize exactly the class of context-free tree languages. Here a tree language is called context-free iff it is generated by a context-free tree grammar.…”

Section: Theorem 48 the Following Statements On A Tree Languagementioning

confidence: 95%

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Formal Tree Series

Ésik¹,

Kuich²

2002

BRICS

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In this survey we generalize some results on formal tree languages, tree grammars and tree automata by an algebraic treatment using semirings, fixed point theory, formal tree series and matrices. The use of these mathematical constructs makes definitions, constructions, and proofs more satisfactory from an mathematical point of view than the customary ones. The contents of this survey paper is indicated by the titles of the sections:

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Section: Theorem 48 the Following Statements On A Tree Languagementioning

confidence: 86%

Section: Theorem 48 the Following Statements On A Tree Languagementioning

confidence: 95%

Formal Tree Series

Ésik¹,

Kuich²

2002

BRICS

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show abstract

“…In this section, we review Guessarian's [7] method (in slightly adapted form) of converting a context-free tree grammar G to an indexed grammar Ind(G) that generates the same string language.…”

Section: From Context-free Tree Grammars To Indexed Grammarsmentioning

confidence: 99%

“…7 For an indexed grammar, a derivation tree fragment is defined like a derivation tree except that labels of the form A[χ] are allowed on leaf nodes. For a context-free tree grammar G = (N, Σ, P, S), we extend the rewriting relation ⇒ * G to T N ∪Σ (X n ) in an obvious way.…”

Section: Corollary 3 For Every Context-free Tree Grammarmentioning

confidence: 99%

“…Suppose we apply the method of Guessarian [7] reviewed in Section 2.3 to a monadic simple context-free tree grammar G. The resulting indexed grammar Ind(G) is very close to a linear indexed grammar. (For example, the grammar consisting of the first five productions of the grammar in Example 1 is a monadic simple context-free tree grammar, and the productions of the corresponding indexed grammar are the first 11 lines of the grammar in Example 4, with i = 6.)…”

Section: Monadic Indexed Grammarsmentioning

confidence: 99%

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A Generalization of Linear Indexed Grammars Equivalent to Simple Context-Free Tree Grammars

Kanazawa

2014

Formal Grammar

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The Equivalence of Bottom-Up and Top-Down Tree-to-Graph Transducers

Engelfriet

Vogler

1998

Journal of Computer and System Sciences

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We introduce the bottom-up tree-to-graph transducer, which is very similar to the usual (total deterministic) bottom-up tree transducer except that it translates trees into hypergraphs rather than trees, using hypergraph substitution instead of tree substitution. If every output hypergraph of the transducer is a jungle, i.e., a hypergraph that can be unfolded into a tree, then the tree-to-graph transducer is said to be tree-generating and naturally defines a tree-to-tree translation. We prove that bottom-up tree-to-graph transducers define the same treeto-tree translations as the previously introduced top-down tree-to-graph transducers. This is in contrast with the well-known incomparability of the usual bottom-up and top-down tree transducers.] 1998Academic Press

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On pushdown tree automata

Cited by 16 publications

References 3 publications

Formal Tree Series

Formal Tree Series

A Generalization of Linear Indexed Grammars Equivalent to Simple Context-Free Tree Grammars

The Equivalence of Bottom-Up and Top-Down Tree-to-Graph Transducers

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