## The complexity of tree transducer output languages

Venue: | In Foundations of Software Technology and Theoretical Computer Science (FSTTCS), 2008 (Available at http://arbre.is.s.u-tokyo.ac.jp/˜kinaba/fst.pdf |

Citations: | 1 - 1 self |

### BibTeX

@INPROCEEDINGS{Inaba_thecomplexity,

author = {Kazuhiro Inaba and Sebastian Maneth},

title = {The complexity of tree transducer output languages},

booktitle = {In Foundations of Software Technology and Theoretical Computer Science (FSTTCS), 2008 (Available at http://arbre.is.s.u-tokyo.ac.jp/˜kinaba/fst.pdf},

year = {}

}

### OpenURL

### Abstract

Abstract. Two complexity results are shown for the output languages generated by compositions of macro tree transducers. They are in NSPACE(n) and hence are context-sensitive, and the class is NP-complete. 1

### Citations

157 | Typechecking for XML Transformers
- Milo, Suciu, et al.
(Show Context)
Citation Context ...archy”) of tree translations which contains most known classes of tree translations such as those realized by attribute grammars, by MSO-definable tree translations [5], or by pebble tree transducers =-=[20]-=-. Consider the range, or output language, of a tree translation; it is a set of trees. If we apply “yield” to these trees, i.e., concatenate their leaf symbols from left to right, we obtain a string l... |

134 |
Tree languages, in
- Gécseg, Steinby
- 1997
(Show Context)
Citation Context ... pos(t), t|ν denotes the subtree of t rooted at the node ν. We write |t| as a shorthand for |pos(t)|. A subset L ⊆ TΣ is called a tree language. By REGT, we denote the class of regular tree languages =-=[15]-=-. Let Σ and ∆ be ranked alphabets. A relation τ ⊆ TΣ × T∆ is called a tree translation (over Σ and ∆) or simply a translation. For two translations τ1 and τ2, their sequential composition τ1 ; τ2 (“τ1... |

119 |
Mappings and grammars on trees
- Rounds
- 1970
(Show Context)
Citation Context ...motivated by syntax-directed semantics of programming languages and recently have been applied to XML transformations and query languages [18, 21]. Mtts are a combination of top-down tree transducers =-=[22, 24]-=- and macro grammars [13]. They process the input tree top-down while accumulating several output trees using their context parameters. Sequential composition of mtts gives rise to a powerful hierarchy... |

107 |
Macro tree transducers
- Engelfriet, Vogler
- 1985
(Show Context)
Citation Context ...output languages generated by compositions of macro tree transducers. They are in NSPACE(n) and hence are context-sensitive, and the class is NP-complete. 1 Introduction Macro tree transducers (mtts) =-=[12, 14]-=- are a finite-state machine model of tree-to-tree translations. They are motivated by syntax-directed semantics of programming languages and recently have been applied to XML transformations and query... |

70 |
Bottom-up and top-down tree transformations, a comparison
- Engelfriet
- 1975
(Show Context)
Citation Context ...from the following known results: MT = DtMT ; T (Corollary 6.12 of [12]), T ; LT = DtQREL ; T (Lemma 2.11 of [9]), and DtMT ; DtQREL ⊆ DtMT (Lemma 11 of [11]). By Lemma 2.11 of [9] and Theorem 2.9 of =-=[8]-=-, T ; LT ⊆ LT ; T, which implies that T(F ) is also closed under LT. By the decomposition MT = DtT ; LMT (page 138 of [12]), MT(F ) ⊆ LMT(T(F )). By applying Lemma 6 twice, LMT(T(F )) is in K. ⊓⊔ Theo... |

67 |
H.: Syntax-Directed Semantics — Formal Models Based on Tree Transducers
- Fülöp, Vogler
- 1998
(Show Context)
Citation Context ...output languages generated by compositions of macro tree transducers. They are in NSPACE(n) and hence are context-sensitive, and the class is NP-complete. 1 Introduction Macro tree transducers (mtts) =-=[12, 14]-=- are a finite-state machine model of tree-to-tree translations. They are motivated by syntax-directed semantics of programming languages and recently have been applied to XML transformations and query... |

56 |
Generalized2 sequential machine maps
- Thatcher
(Show Context)
Citation Context ...motivated by syntax-directed semantics of programming languages and recently have been applied to XML transformations and query languages [18, 21]. Mtts are a combination of top-down tree transducers =-=[22, 24]-=- and macro grammars [13]. They process the input tree top-down while accumulating several output trees using their context parameters. Sequential composition of mtts gives rise to a powerful hierarchy... |

50 | XML type checking with macro tree transducers - Maneth, Berlea, et al. - 2005 |

46 |
Monadic second-order definable graph transductions: A survey, Theor
- Courcelle
- 1994
(Show Context)
Citation Context ...a powerful hierarchy (the “mtt-hierarchy”) of tree translations which contains most known classes of tree translations such as those realized by attribute grammars, by MSO-definable tree translations =-=[5]-=-, or by pebble tree transducers [20]. Consider the range, or output language, of a tree translation; it is a set of trees. If we apply “yield” to these trees, i.e., concatenate their leaf symbols from... |

43 |
Grammars with Macro-like Productions
- Fischer
- 1968
(Show Context)
Citation Context ...ins the IO- and OI- hierarchies [6]. Note that the IO-hierarchy is in DtMT ∗ (REGT) and hence in DSPACE(n) by Corollary 17 of [17]. Since the first level of the OI-hierarchy are the indexed languages =-=[13]-=- which are NP-complete [23], we obtain the following. Corollary 10. The OI-hierarchy is in NSPACE(n) ∩ NP-complete. Acknowledgment This work was partly supported by the Japan Society for the Promotion... |

40 |
The IO- and OI-hierarchies
- Damm
- 1982
(Show Context)
Citation Context ...r leaf symbols from left to right, we obtain a string language. The string languages obtained in this way from the mtt-hierarchy form a large class (containing for instance the IO- and OI-hierarchies =-=[6]-=-) with good properties, such as being a full AFL and having decidable membership, emptiness, and finiteness [7]. In this paper we study the complexity of the output (string or tree) languages of the m... |

33 |
Indexed grammars-an extension of context-free grammars
- Aho
- 1968
(Show Context)
Citation Context ...tribute grammars. Both of these classes are LOG(CFL)-complete by [2] and [10], respectively. Another subclass of our class is that of OI-macro languages, which are equivalent to the indexed languages =-=[1]-=-, by [13]. This class is known to be NP-complete [23]. Hence, our class is NP-hard too (even already at level 2). Our first main result is that output languages of the mtt-hierarchy are NP-complete; t... |

32 |
Macro forest transducers
- Perst, Seidl
(Show Context)
Citation Context ...te-state machine model of tree-to-tree translations. They are motivated by syntax-directed semantics of programming languages and recently have been applied to XML transformations and query languages =-=[18, 21]-=-. Mtts are a combination of top-down tree transducers [22, 24] and macro grammars [13]. They process the input tree top-down while accumulating several output trees using their context parameters. Seq... |

29 | Efficient memory representation of XML document trees
- BUSATTO, LOHREY, et al.
- 2008
(Show Context)
Citation Context ...ying expand as long as possible to e0 = (r0, ϵ) where r0 denotes the right-hand side of the unique ⟨q0, label(s, ϵ)⟩-rule. Note that a similar list representation is used in the proof of Theorem 3 in =-=[4]-=-. MATCH (e, v) 1: while label(e) = + do 2: e ← c-child(e, k) where k = 1 or 2, nondeterministically chosen 3: if c-label(e) ̸= label(v) then 4: return false 5: else if rank(label(v)) = 0 then 6: retur... |

17 | Decidability of the finiteness of ranges of tree transductions
- Drewes, Engelfriet
- 1998
(Show Context)
Citation Context ...the mtt-hierarchy form a large class (containing for instance the IO- and OI-hierarchies [6]) with good properties, such as being a full AFL and having decidable membership, emptiness, and finiteness =-=[7]-=-. In this paper we study the complexity of the output (string or tree) languages of the mtt-hierarchy. Note that we do not explicitly distinguish between string or tree output languages here, because ... |

11 | The complexity of compositions of deterministic tree transducers
- Maneth
- 2002
(Show Context)
Citation Context ...rchy. In terms of space complexity, languages generated by compositions of top-down tree transducers (mtts without context parameters) are known to be in DSPACE(n) [3]. This result was generalized in =-=[17]-=- to compositions of total deterministic mtts. Our second main result is that output languages of the mtt-hierarchy (generated by compositions of nondeterministic mtts) with regular tree languages as i... |

11 |
Tree transducers and tree compressions
- Maneth, Busatto
- 2004
(Show Context)
Citation Context ... on a nondeterministic Turing Machine (|s| denotes the size of the tree s). The challenge here is the space complexity; we use a compressed representation of M’s output trees for input s, inspired by =-=[19]-=-, and then check if t is contained using a recursive procedurein which nodes needed for backtracking are compressed using a trie, similar to Aho’s compression of index strings in [1]. Then, we genera... |

10 |
Generalized syntax directed translation, tree transducers and linear space
- BAKER
- 1978
(Show Context)
Citation Context ... nondeletion condition used for total deterministic mtts, but it is sufficient for our purpose. In order to speak more formally, here we define the notion of computation tree (following the method of =-=[3]-=-, but extending it to deal with accumulating parameters). For any finite set P , we define the ranked alphabet P = {p (1) | p ∈ P }. Let M = (Q, Σ, ∆, q0, R) be an mttcf and s ∈ TΣ. The set COMP(M, s)... |

10 |
Complexity of recognition in intermediatelevel languages
- Rounds
- 1973
(Show Context)
Citation Context ...-complete by [2] and [10], respectively. Another subclass of our class is that of OI-macro languages, which are equivalent to the indexed languages [1], by [13]. This class is known to be NP-complete =-=[23]-=-. Hence, our class is NP-hard too (even already at level 2). Our first main result is that output languages of the mtt-hierarchy are NP-complete; thus, the complexity remains in NP when going from ind... |

9 |
The complexity of languages generated by attribute grammars
- Engelfriet
- 1986
(Show Context)
Citation Context ...ages (or, equivalently, the yields of context-free-tree languages under IO-derivation) and the string languages generated by attribute grammars. Both of these classes are LOG(CFL)-complete by [2] and =-=[10]-=-, respectively. Another subclass of our class is that of OI-macro languages, which are equivalent to the indexed languages [1], by [13]. This class is known to be NP-complete [23]. Hence, our class is... |

7 | Output string languages of compositions of deterministic macro tree transducers
- Engelfriet, Maneth
(Show Context)
Citation Context ...roof. The closure under LT immediately follows from the following known results: MT = DtMT ; T (Corollary 6.12 of [12]), T ; LT = DtQREL ; T (Lemma 2.11 of [9]), and DtMT ; DtQREL ⊆ DtMT (Lemma 11 of =-=[11]-=-). By Lemma 2.11 of [9] and Theorem 2.9 of [8], T ; LT ⊆ LT ; T, which implies that T(F ) is also closed under LT. By the decomposition MT = DtT ; LMT (page 138 of [12]), MT(F ) ⊆ LMT(T(F )). By apply... |

4 |
Time and space complexity of inside-out macro languages
- Asveld
- 1981
(Show Context)
Citation Context ...ssue, we (1) instead of solving the membership problem for all mtts, only deal with mtts in the above mentioned non-deleting normal form, and which are linear with respect to the input variables, and =-=(2)-=- exploit the compressed representation of outputs of mtts [19] for manipulating the output set. Note that due to nondeterminism we cannot anymore obtain some of the useful normal forms (nonerasing, wh... |

2 |
Grammars without erasing rules. the OI case
- Leguy
- 1981
(Show Context)
Citation Context ... mtts without input: think of ⟨q, xi⟩ as a nonterminal Nq, or equivalently, think of macro grammars [13] or indexed grammars [1], with trees instead of strings in right-hand sides), it has been shown =-=[16]-=- that there is no non-erasing normal form: erasing grammars are strictly more powerful than non-erasing ones. To see where the difficulty arises, let us consider the following example of a determinist... |