# Tree Automata

@article{Gcseg1984TreeA, title={Tree Automata}, author={Ferenc G{\'e}cseg and Magnus Steinby}, journal={ArXiv}, year={1984}, volume={abs/1509.06233} }

Exercise 14 (yield(Rec) and CF) 1. Give a context-free grammar over the terminal alphabet {(a ,) a , (b ,) b } generating the Dyck language of well-bracketed strings. 3. Give a regular tree grammar G in normal form such that for some e, the language yield e (L(G)) is the language from 1. 4. Using the construction from the lecture, transform the regular tree grammar G from 2. into a context-free grammar G such that L(G) = yield γ (L(G)). Is there a simpler context-free grammar generating the…

## Figures from this paper

## 127 Citations

Multiple Context-Free Tree Grammars: Lexicalization and Characterization

- Computer ScienceTheor. Comput. Sci.
- 2018

Context-Free Grammars with Storage

- Computer ScienceArXiv
- 2014

The context-free S languages can be obtained from the deterministic one-way S automaton languages by way of the delta operations on languages, introduced in this paper.

ALTERNATING REGULAR TREE GRAMMARS IN THE FRAMEWORK OF LATTICE-VALUED LOGIC

- Computer Science
- 2016

Two different ways of introducing alternation for lattice-valued regular tree grammars and top-down tree automata are compared and a characterization of the state alternating regular tree grammar in terms of {LASA}.

Spinal-Formed Context-Free Tree Grammars

- Computer ScienceTheory of Computing Systems
- 2000

It is shown that the class of string languages generated by spine Grammars coincides with that of tree adjoining grammars.

Fuzzy Deterministic Top-down Tree Automata

- Computer ScienceArXiv
- 2019

It is proved that the path closure of any regular L-fuzzy tree language is DT-recognizable, and that it is decidable whether a regular L/subfamily of that language isDT- Recognizable.

The Equivalence, Unambiguity and Sequentiality Problems of Finitely Ambiguous Max-Plus Tree Automata are Decidable

- Computer ScienceMFCS
- 2017

This paper shows that these three problems are decidable for finitely ambiguous max-plus tree automata, which aremax-plus automata that operate on trees instead of words that are strictly more expressive than deterministic max- plus automata.

Regular Description of Context-Free Graph Languages

- Computer ScienceJ. Comput. Syst. Sci.
- 1996

It is shown that in this way exactly the class of C-edNCE graph languages (generated by C-EDNCEgraph grammars) is obtained, one of the largest known classes of context-free graph languages.

The HOM problem is decidable

- Computer ScienceSTOC '10
- 2010

An algorithm that, given a tree homomorphism H and a regular tree language L represented by a tree automaton, determines whether H(L) is regular, settles a question that has been open for a long time and proves the universality problem is decidable for languages represented by tree automata with equality constraints.

Descendants of a recognizable tree language for prefix constrained linear monadic term rewriting with position cutting strategy

- Computer ScienceTheor. Comput. Sci.
- 2018

Sequentiality, second order monadic logic and tree automata

- Computer ScienceProceedings of Tenth Annual IEEE Symposium on Logic in Computer Science
- 1995

The paper describes a direct construction of an automaton recognizing the set of terms that have needed redexes, which yields immediate consequences: strong sequentiality of possibly overlapping linear rewrite systems is decidable in EXPTIME; for strongly sequential rewrite systems, neededRedexes can be read directly on the automaton.

## References

SHOWING 1-10 OF 230 REFERENCES

Tree acceptors and grammar forms

- Mathematics, Computer ScienceComputing
- 2005

AbstractThe following generalization of a well-known result in tree acceptors is established. For each context-free grammarG and tree acceptor
$$\mathfrak{A}$$
there exists a strict interpretationG′…

On the Representation of Finite Automata

- Computer Science, MathematicsDCFS
- 2005

An unique string representation, up to isomorphism, for initially connected deterministic finite automata (ICDFA’s) with n states over an alphabet of k symbols is given and how its enumeration provides an alternative way to obtain the exact number of ICDFA”s is shown.

Context-free grammars on trees

- Computer ScienceSTOC
- 1969

This paper defines the tree analogue of a non deterministic generalized sequential machine and obtain results about the domain and range of such a mapping and relates these results to the theory of generalized finite automata6.

Formal languages and their relation to automata

- Computer ScienceAddison-Wesley series in computer science and information processing
- 1969

The theory of formal languages as a coherent theory is presented and its relationship to automata theory is made explicit, including the Turing machine and certain advanced topics in language theory.

Languages in general algebras

- MathematicsSTOC
- 1969

It is shown (Theorem 2.1.3) that phrase structure (PS) languages are the same as the CF languages in any (finitely generated) generic algebra, and the notion of algebraic transduction generalizes the idea of binary transduction as presented for generic monadic algebras by Elgot and Mezei (EM).

Compositions of n tree transducers

- Computer ScienceSTOC
- 1972

It is shown that transductions need not preserve surface sets and exhibits a hierarchy of tree languages obtained by successive transduction, as well as a list of first-order axioms for plane (ordered) trees.

Tree Acceptors and Some of Their Applications

- Mathematics, Computer ScienceJ. Comput. Syst. Sci.
- 1970