Section: New Results

Tree automata theory

Participants : Stéphane Demri, Florent Jacquemard, Luc Segoufin.

Most of our results for this section concerns data words and data trees. Those are words and trees where each position contains a data value together with the classical label. Data trees can be seen as a model for XML data. We have studied automata model using registers or memory or allowing constraints that can involve data comparisons in its transitions.

Register Automata.

These extend the classical model of finite automata with auxiliary registers storing data values for later comparison.

We have introduced a new model of automata over data trees and shown the decidability of its emptiness problem [30] . These automata were used for obtaining decidability results for the static analysis for some fragments of XPath presented in the previous section.

Automata with counters.

In [39] , a survey chapter on the verification of infinite-state systems is presented that is focused on the verification of counter systems. Verification problems for vector addition systems and recursive Petri nets are considered. Moreover, we introduce subclasses of counter systems for which reachability questions can be solved in Presburger arithmetic viewed as a means to symbolically represent sets of tuples of natural numbers.

Automata with isomorphism tests among subtrees.

We have also considered some models described by tree automata enriched with a feature testing for isomorphisms between subtrees. Such constraints could be used for testing monadic key constraints over XML documents. For these models, the main challenge is to establish the decidability of the non-emptiness of the language specified by a given automaton [18] .

Rewriting Controlled by Selection Automata.

Motivated by the problem of static analysis of XML update programs, we have studied [33] the combination, called controlled term rewriting systems (CTRS), of term rewriting rules with constraints selecting the possible rewrite positions. These constraints are specified, for each rewrite rule, by a selection automaton which defines a set of positions in a term based on tree automata computations. We have established several decidability and complexity results for several cases of the reachability and regular model checking problems for this tree transformation formalism.