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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
Rigid Tree Automata and Applications
, 2011
"... 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 ar ..."
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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.
Decidable Classes of Tree Automata MIXING LOCAL AND GLOBAL CONSTRAINTS MODULO FLAT THEORIES
, 2013
"... ..."
Random Generation of Positive TAGEDs
, 2010
"... 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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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.
The emptiness problem for tree automata . . .
"... 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 computatio ..."
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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.
DECIDABLE CLASSES OF TREE AUTOMATA MIXING LOCAL AND GLOBAL CONSTRAINTS MODULO FLAT THEORIES ∗
, 2012
"... Vol. 9(2:01)2013, pp. 1–39 www.lmcsonline.org ..."
Florent Jacquemard Chargé de recherche Codirecteur de thèse
, 2011
"... Sujet de la thèse: Automates d'arbres à contraintes globales pour la vérification de propriétés de sécurité Thèse présentée et soutenue à Cachan le 07/12/2010 devant le jury composé de: ..."
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Sujet de la thèse: Automates d'arbres à contraintes globales pour la vérification de propriétés de sécurité Thèse présentée et soutenue à Cachan le 07/12/2010 devant le jury composé de: