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23
Macro Tree Transducers, Attribute Grammars, and MSO Definable Tree Translations
 Inform. and Comput
, 1998
"... A characterization is given of the class of tree translations definable in monadic second order logic (MSO), in terms of macro tree transducers. The first main result is that the MSO definable tree translations are exactly those tree translations realized by macro tree transducers (MTTs) with reg ..."
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Cited by 46 (20 self)
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A characterization is given of the class of tree translations definable in monadic second order logic (MSO), in terms of macro tree transducers. The first main result is that the MSO definable tree translations are exactly those tree translations realized by macro tree transducers (MTTs) with regular lookahead that are single use restricted. For this the single use restriction known from attribute grammars is generalized to MTTs. Since MTTs are closed under regular lookahead, this implies that every MSO definable tree translation can be realized by an MTT. The second main result is that the class of MSO definable tree translations can also be obtained by restricting MTTs with regular lookahead to be finite copying, i.e., to require that each input subtree is processed only a bounded number of times. The single use restriction is a rather strong, static restriction on the rules of an MTT, whereas the finite copying restriction is a more liberal, dynamic restriction on the ...
Bottomup and Topdown Tree Series Transformations
 J. Autom. Lang. Combin
, 2000
"... We generalize bottomup tree transducers and topdown tree transducers to the concept of bottomup tree series transducer and topdown tree series transducer, respectively, by allowing formal tree series as output rather than trees, where a formal tree series is a mapping from output trees to some s ..."
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Cited by 37 (6 self)
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We generalize bottomup tree transducers and topdown tree transducers to the concept of bottomup tree series transducer and topdown tree series transducer, respectively, by allowing formal tree series as output rather than trees, where a formal tree series is a mapping from output trees to some semiring. We associate two semantics with a tree series transducer: a mapping which transforms trees into tree series (for short: tree to tree series transformation or tts transformation), and a mapping which transforms tree series into tree series (for short: tree series transformation or tsts transformation). We show that the standard case of tree transducers is reobtained by choosing the boolean semiring under the tts semantics. Also, for each of the two types of tree series transducers and for both types of semantics, we prove a characterization which generalizes in a straightforward way the corresponding characterization result for the underlying tree transducer class. Mo...
Nary queries by tree automata
 In Proc. of DBPL’05
, 2005
"... www.grappa.univlille3.fr/mostrare We investigate nary node selection queries in trees by successful runs of tree automata. We show that runbased nary queries capture MSO, contribute algorithms for enumerating answers of nary queries, and study the complexity of the problem. We investigate the s ..."
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Cited by 21 (5 self)
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www.grappa.univlille3.fr/mostrare We investigate nary node selection queries in trees by successful runs of tree automata. We show that runbased nary queries capture MSO, contribute algorithms for enumerating answers of nary queries, and study the complexity of the problem. We investigate the subclass of runbased nary queries by unambiguous tree automata.
MSO definable string transductions and twoway finitestate transducers
 ACM Trans. Comput. Logic
, 2001
"... String transductions that are definable in monadic secondorder (mso) logic (without the use of parameters) are exactly those realized by deterministic twoway finite state transducers. Nondeterministic mso definable string transductions (i.e., those definable with the use of parameters) correspond ..."
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Cited by 19 (3 self)
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String transductions that are definable in monadic secondorder (mso) logic (without the use of parameters) are exactly those realized by deterministic twoway finite state transducers. Nondeterministic mso definable string transductions (i.e., those definable with the use of parameters) correspond to compositions of two nondeterministic twoway finite state transducers that have the finite visit property. Both families of mso definable string transductions are characterized in terms of Hennie machines, i.e., twoway finite state transducers with the finite visit property that are allowed to rewrite their input tape.
Macro Tree Translations of Linear Size Increase are MSO Definable
 SIAM J. Comput
, 2001
"... 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 secondorder logic). This gives a ..."
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Cited by 16 (6 self)
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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 secondorder 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.
Characterization of Properties and Relations defined in Monadic Second Order Logic on the Nodes of Trees
, 1997
"... . A formula from monadic second order (mso) logic with one free variable can be used to define a property of the nodes of a tree. Similarly, an mso formula with two free variables can be used to define a binary relation between the nodes of a tree. It is proved that a node relation is mso definable ..."
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Cited by 14 (1 self)
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. A formula from monadic second order (mso) logic with one free variable can be used to define a property of the nodes of a tree. Similarly, an mso formula with two free variables can be used to define a binary relation between the nodes of a tree. It is proved that a node relation is mso definable iff it can be computed by a finitestate treewalking automaton, provided the automaton can test mso definable properties of the nodes of the tree; if the relation is a function, the automaton is deterministic. It is also proved that a node property is mso definable iff it can be computed by an attribute grammar of which all attributes have finitely many values. mso definable node properties are computable in linear time, mso definable node relations in quadratic time, and mso definable node functions in linear time. 1 Introduction It is shown in [Buc, Elg] that a set of strings can be defined in monadic second order logic if and only if it can be recognized by a finitestate automaton. Th...
Extended Multi BottomUp Tree Transducers
"... Abstract. Extended multi bottomup tree transducers are de ned and investigated. They are an extension of multi bottomup tree transducers by arbitrary, not just shallow, lefthand sides of rules; this includes rules that do not consume input. It is shown that such transducers can compute any transf ..."
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Cited by 9 (5 self)
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Abstract. Extended multi bottomup tree transducers are de ned and investigated. They are an extension of multi bottomup tree transducers by arbitrary, not just shallow, lefthand sides of rules; this includes rules that do not consume input. It is shown that such transducers can compute any transformation that is computed by a linear extended topdown tree transducer. Moreover, the classical composition results for bottomup tree transducers are generalized to extended multi bottomup tree transducers. Finally, a characterization in terms of extended topdown tree transducers is presented. 1
S.: The equivalence problem for deterministic MSO tree transducers is decidable
 Inf. Process. Lett
, 2006
"... Abstract. It is decidable for deterministic MSO definable graphtostring or graphtotree transducers whether they are equivalent on a contextfree set of graphs. It is well known that the equivalence problem for nondeterministic (oneway) finite state transducers is undecidable, even when they cann ..."
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Cited by 8 (1 self)
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Abstract. It is decidable for deterministic MSO definable graphtostring or graphtotree transducers whether they are equivalent on a contextfree set of graphs. It is well known that the equivalence problem for nondeterministic (oneway) finite state transducers is undecidable, even when they cannot read or write the empty string [Gri68]. In contrast, equivalence is decidable for deterministic finite state transducers, even for twoway transducers [Gur82]. The question arises whether these results can be generalized from strings to transducers working on more complex structures like, e.g., trees or graphs. There is no accepted notion of finite state transducer working on graphs; instead, it is believed that transductions expressed in monadic secondorder logic (MSO) are the natural counterpart of finite state transductions on graphs. The idea is to define an output graph by interpreting fixed MSO formulas on a given input graph. In fact, if the input and output graphs of such an MSO graph transducer are strings, then the resulting transductions (in the deterministic case) are precisely the deterministic twoway finite state transductions [EH01]. Hence, by the above, equivalence is decidable for deterministic MSO string transducers. A nondeterministic MSO graph
Attribute Grammars for Unranked Trees as a query language for structured documents
"... Document specification languages, like for instance XML, model documents using extended contextfree grammars. These di#er from standard contextfree grammars in that they allow arbitrary regular expressions on the righthand side of productions. To query such documents, we introduce a new form ..."
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Cited by 7 (3 self)
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Document specification languages, like for instance XML, model documents using extended contextfree grammars. These di#er from standard contextfree grammars in that they allow arbitrary regular expressions on the righthand side of productions. To query such documents, we introduce a new form of attribute grammars (extended AGs) that work directly over extended contextfree grammars rather than over standard contextfree grammars. Viewed as a query language, extended AGs are particularly relevant as they can take into account the inherent order of the children of a node in a document.