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Tree automata with global constraints
 In 12th Int. Conf. in Developments in Lang. Theory (DLT), vol. 5257 of LNCS
, 2008
"... Abstract. A tree automaton with global tree equality and disequality constraints, TAGED for short, is an automaton on trees which allows to test (dis)equalities between subtrees which may be arbitrarily faraway. In particular, it is equipped with an (dis)equality relation on states, so that whenever ..."
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Abstract. A tree automaton with global tree equality and disequality constraints, TAGED for short, is an automaton on trees which allows to test (dis)equalities between subtrees which may be arbitrarily faraway. In particular, it is equipped with an (dis)equality relation on states, so that whenever two subtrees t and t ′ evaluate (in an accepting run) to two states which are in the (dis)equality relation, they must be (dis)equal. We study several properties of TAGEDs, and prove decidability of emptiness of several classes. We give two applications of TAGEDs: decidability of an extension of Monadic Second Order Logic with tree isomorphism tests and of unification with membership constraints. These results significantly improve the results of [10]. 1
C.: Rigid tree automata
, 2008
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Cited by 12 (1 self)
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Applying Tree Languages in Proof Theory
 In AdrianHoria Dediu and Carlos MartínVide, editors, Language and Automata Theory and Applications (LATA) 2012, volume 7183 of Lecture Notes in Computer Science
, 2012
"... Abstract. We introduce a new connection between formal language theory and proof theory. One of the most fundamental proof transformations in a class of formal proofs is shown to correspond exactly to the computation of the language of a certain class of tree grammars. Translations in both direction ..."
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Cited by 9 (7 self)
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Abstract. We introduce a new connection between formal language theory and proof theory. One of the most fundamental proof transformations in a class of formal proofs is shown to correspond exactly to the computation of the language of a certain class of tree grammars. Translations in both directions, from proofs to grammars and from grammars to proofs, are provided. This correspondence allows theoretical as well as practical applications. 1
Rigid Tree Automata and ApplicationsI
"... cFT/RD/MAPS/AMS/SLE dFT/RD We introduce the class of Rigid Tree Automata (RTA), an extension of standard bottomup automata on ranked trees with distinguished states called rigid. Rigid states define a restriction on the computation of RTA on trees: RTA can test for equality in subtrees reaching th ..."
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cFT/RD/MAPS/AMS/SLE dFT/RD We introduce the class of Rigid Tree Automata (RTA), an extension of standard bottomup automata on ranked trees with distinguished states called rigid. Rigid states define a restriction on the computation of RTA on trees: RTA can test for equality in subtrees reaching the same rigid state. RTA are able to perform local and global tests of equality between subtrees, nonlinear tree pattern matching, and some inequality and disequality tests as well. Properties like determinism, pumping lemma, Boolean closure, and several decision problems are studied in detail. In particular, the emptiness problem is shown decidable in linear time for RTA whereas membership of a given tree to the language of a given RTA is NPcomplete. Our main result is the decidability of whether a given tree belongs to the rewrite closure of an RTA language under a restricted family of term rewriting systems, whereas this closure is not an RTA language. This result, one of the first on rewrite closure of languages of tree automata with constraints, is enabling the extension of model checking procedures based on finite tree automata techniques, in particular for the verification of communicating processes with several local non rewritable memories, like security protocols. Finally, a comparison of RTA with several classes of tree automata with local and global equality tests, with dag automata and Horn clause formalisms is also provided.
International Journal of Foundations of Computer Science c © World Scientific Publishing Company Tree Automata With Global Constraints
, 2010
"... We define tree automata with global equality and disequality constraints (TAGED). TAGEDs can test (dis)equalities between subtrees which may be arbitrarily faraway. In particular, they are equipped with an equality relation and a disequality relation on states, so that whenever two subtrees t and t ..."
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We define tree automata with global equality and disequality constraints (TAGED). TAGEDs can test (dis)equalities between subtrees which may be arbitrarily faraway. In particular, they are equipped with an equality relation and a disequality relation on states, so that whenever two subtrees t and t ′ evaluate (in an accepting run) to two states which are in the (dis)equality relation, they must be (dis)equal. We study several properties of TAGEDs, and prove emptiness decidability of for several expressive subclasses of TAGEDs.
ProjectTeam MOSTRARE Modeling Tree Structures, Machine Learning, and Information Extraction
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ProjectTeam mostrare Modeling Tree Structures, Machine Learning, and Information Extraction
"... c t i v it y e p o r t 2009 Table of contents ..."
J & user=10 & coverDate=03
, 2011
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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GLOBAL CONSTRAINTS MODULO FLAT THEORIES ∗
, 2012
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Barcelona
"... We define tree automata with global constraints (TAGC), generalizing the wellknown class of tree automata with global equality and disequality constraints [14] (TAGED). TAGC can test for equality and disequality between subterms whose positions are defined by the states reached during a computati ..."
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We define tree automata with global constraints (TAGC), generalizing the wellknown class of tree automata with global equality and disequality constraints [14] (TAGED). TAGC can test for equality and disequality between subterms whose positions are defined by the states reached during a computation. In particular, TAGC can check that all the subterms reaching a given state are distinct. This constraint is related to monadic key constraints for XML documents, meaning that every two distinct positions of a given type have different values. We prove decidability of the emptiness problem for TAGC. This solves, in particular, the open question of decidability of emptiness for TAGED. We further extend our result by allowing global arithmetic constraints for counting the number of occurrences of some state or the number of different subterms reaching some state during a computation. We also allow local equality and disequality tests between sibling positions and the extension to unranked ordered trees. As a consequence of our results for TAGC, we prove the decidability of a fragment of the monadic second order logic on trees extended with predicates for equality and disequality between subtrees, and cardinality. 1