## Macro Tree Translations of Linear Size Increase are MSO Definable (2001)

Venue: | SIAM J. Comput |

Citations: | 16 - 6 self |

### BibTeX

@ARTICLE{Engelfriet01macrotree,

author = {Joost Engelfriet and Sebastian Maneth},

title = {Macro Tree Translations of Linear Size Increase are MSO Definable},

journal = {SIAM J. Comput},

year = {2001},

volume = {32},

pages = {2003}

}

### OpenURL

### Abstract

Abstract. The first main result is that if a macro tree translation is of linear size increase, i.e., if the size of every output tree is linearly bounded by the size of the corresponding input tree, then the translation is MSO definable (i.e., definable in monadic second-order logic). This gives a new characterization of the MSO definable tree translations in terms of macro tree transducers: they are exactly the macro tree translations of linear size increase. The second main result is that given a macro tree transducer, it can be decided whether or not its translation is MSO definable, and if it is then an equivalent MSO transducer can be constructed. Similar results hold for attribute grammars, which define a subclass of the macro tree translations.

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Citation Context ...generation of graphs by context-free graph grammars [5, 7, 22, 15] (see also [35]). Taking trees as logical structure, another type of tree transducer is obtained: the MSO tree transducer, studied in =-=[3, 18]-=- (for strings, see [17]). An important part of tree transducer theory is to compare the formal power of these different models of transformation of tree-structured objects and to provide effective tra... |

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Citation Context ...ntext-free graph grammars [5, 7, 22, 15] (see also [35]). Taking trees as logical structure, another type of tree transducer is obtained: the MSO tree transducer, studied in [3, 18] (for strings, see =-=[17]-=-). An important part of tree transducer theory is to compare the formal power of these different models of transformation of tree-structured objects and to provide effective translations between these... |

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Citation Context ...of of our first main result, as discussed above), (2) for an MTT it is decidable whether or not it is finite copying (the proof is based on the fact that the finiteness of ranges of MTTs is decidable =-=[11]-=-), and (3) from [18, 3] it follows that given a finite copying MTT, an equivalent MSO tree transducer can be constructed. Note that very often membership in a subclass is undecidable (such as regulari... |

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Citation Context ... use restricted” MTTs and for finite copying MTTs in Corollary 7.3 of [18], and for nondeleting MTTs that are finite copying and linear in the parameters in Theorem 5 of [19] (based on Theorem 8.1 of =-=[9]-=-). Theorem 7.7. The output tree languages of MTTs of linear size increase applied to the regular tree languages are the tree languages generated by (HR or NR) contextfree graph grammars. 7.4. Open Pro... |

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Citation Context ...ree transformation. We are interested in models of such transformations: tree transducers. Well-known examples of tree transducers are top-down tree transducers [45, 47, 1, 31] and attribute grammars =-=[16, 26, 27]-=- (motivated by syntax-directed semantics and compilers, cf. [34, 36, 39, 52]), unranked tree transducers [42, 2] and pebble tree transducers [44] (motivated by the transformation of XML documents, cf.... |

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Citation Context ... that is independent of the device that defines the whole class, i.e., a “semantic” rather than “syntactic” characterization, such as our linear size increase characterization. As another example, in =-=[6]-=- it is shown that an NR (node replacement) context-free graph language can be generated by an HR (hyperedge replacement) context-free graph grammar if and only if the number of edges of its graphs is ... |

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Citation Context ...ion of ‘finite contribution’. Intuitively, an MTT R is of finite contribution if there is a bound on the number of output nodes contributed by a single node u of the input tree. In the terminology of =-=[49]-=-, the node u is called the ‘origin’ of the nodes of the output tree that it contributes; so, finite contribution means that there is a bound on the number of nodes that have the same origin. In [49] i... |

1 |
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Citation Context ...rchy, but rather it remains the class of MSO definable tree translations, i.e., is LSI ∩ � n MTT n = MSOTT ? Since compositions of MTTs can be realized by high-level tree transducers (and vice versa) =-=[24]-=- this question is equivalent to: Are linear size increase high-level tree translations MSO definable? Again, this question could also be considered for polynomial instead of linear size increase. Rece... |