Results 1  10
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11
Rigid Tree Automata
, 2008
"... 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: two subtrees reaching the same rigid state in a run must be equal. RTA are ab ..."
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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: two subtrees reaching the same rigid state in a run must be equal. RTA are able to perform local and global tests of equality between subtrees, nonlinear tree pattern matching, and restricted 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 that is decidable whether a given tree belongs to the rewrite closure of a RTA language under a restricted family of term rewriting systems, whereas this closure is not a 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. Finally, a comparison of RTA with several classes of tree automata with local and global equality tests, and with dag automata is also provided.
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
Automated Induction with Constrained Tree Automata ⋆,⋆⋆
"... Abstract. We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values), and may express syntactic equality, disequality, o ..."
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Cited by 7 (2 self)
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Abstract. We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values), and may express syntactic equality, disequality, ordering and also membership in a fixed tree language. Constrained equational axioms between constructor terms are supported and can be used in order to specify complex data structures like sets, sorted lists, trees, powerlists... Our procedure is based on tree grammars with constraints, a formalism which can describe exactly the initial model of the given specification (when it is sufficiently complete and terminating). They are used in the inductive proofs first as an induction scheme for the generation of subgoals at induction steps, second for checking validity and redundancy criteria by reduction to an emptiness problem, and third for defining and solving membership constraints. We show that the procedure is sound and refutationally complete. It generalizes former test set induction techniques and yields natural proofs for several nontrivial examples presented in the paper, these examples are difficult (if not impossible) to specify and carry on automatically with other induction procedures. 1
Satisfiability of a spatial logic with tree variables
 In Proc. 21st Int. Workshop on Computer Science Logic (CSL
, 2007
"... Abstract. We investigate in this paper the spatial logic TQL for querying semistructured data, represented as unranked ordered trees over an infinite alphabet. This logic consists of usual Boolean connectives, spatial connectives (derived from the constructors of a tree algebra), tree variables and ..."
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Abstract. We investigate in this paper the spatial logic TQL for querying semistructured data, represented as unranked ordered trees over an infinite alphabet. This logic consists of usual Boolean connectives, spatial connectives (derived from the constructors of a tree algebra), tree variables and a fixpoint operator for recursion. Motivated by XMLoriented tasks, we investigate the guarded TQL fragment. We prove that for closed formulas this fragment is MSOcomplete. In presence of tree variables, this fragment is strictly more expressive than MSO as it allows for tree (dis)equality tests, i.e. testing whether two subtrees are isomorphic or not. We devise a new class of tree automata, called TAGED, which extends tree automata with global equality and disequality constraints. We show that the satisfiability problem for guarded TQL formulas reduces to emptiness of TAGED. Then, we focus on bounded TQL formulas: intuitively, a formula is bounded if for any tree, the number of its positions where a subtree is captured by a variable is bounded. We prove this fragment to correspond with a subclass of TAGED, called bounded TAGED, for which we prove emptiness to be decidable. This implies the decidability of the bounded guarded TQL fragment. Finally, we compare bounded TAGED to a fragment of MSO extended with subtree isomorphism tests. 1
Unranked tree automata with sibling equalities and disequalities
, 2006
"... We propose an extension of the tree automata with constraints between direct subtrees (Bogaert and Tison, 1992) to unranked trees. Our approach uses MSOformulas to capture the possibility of comparing unboundedly many direct subtrees. Our main result is that the nonemptiness problem for the deter ..."
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We propose an extension of the tree automata with constraints between direct subtrees (Bogaert and Tison, 1992) to unranked trees. Our approach uses MSOformulas to capture the possibility of comparing unboundedly many direct subtrees. Our main result is that the nonemptiness problem for the deterministic automata, as in the ranked setting, is decidable. It turns out that the main difficulty is indeed the absence of the rank, as it gives a certain bound on the number of distinct subtrees needed in order to satisfy an equality or disequality constraint. We overcome this difficulty by finding such a bound via a bruteforce method.
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"... Combining approaches for the security of infinite state systems Nancy Grand Est THEME SYM c t i v it y e p o r t ..."
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Combining approaches for the security of infinite state systems Nancy Grand Est THEME SYM c t i v it y e p o r t
ProjectTeam SECSI Sécurité des systèmes d’information
"... c t i v it y e p o r t 2007 Table of contents ..."
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