Frédéric Servais

Visibly Pushdown Transducers

Visibly pushdown automata have been recently introduced by Alur and Madhusudan as a subclass of pushdown automata. This class enjoys nice properties such as closure under all Boolean operations and the decidability of language inclusion. Along the same line, we introduce here visibly pushdown transducers as a subclass of pushdown transducers. We study properties of those transducers and identify subclasses with useful properties like decidability of type checking as well as preservation of regularity of visibly pushdown languages.

Minimal coverability set for Petri nets: Karp and Miller algorithm with pruning

This paper presents the Monotone-Pruning algorithm (MP) for computing the minimal coverability set of Petri nets. The original Karp and Miller algorithm (K&M) unfolds the reachability graph of a Petri net and uses acceleration on branches to ensure termination. The MP algorithm improves the K&M algorithm by adding pruning between branches of the K&M tree. This idea was first introduced in the Minimal Coverability Tree algorithm (MCT), however it was recently shown to be incomplete. The MP algorithm can be viewed as the MCT algorithm with a slightly more aggressive pruning strategy which ensures completeness. Experimental results show that this algorithm is a strong improvement over the K&M algorithm.

From Two-Way to One-Way Finite State Transducers

Any two-way finite state automaton is equivalent to some one-way finite state automaton. This well-known result, shown by Rabin and Scott and independently by Shepherdson, states that two-way finite state automata (even non-deterministic) characterize the class of regular languages. It is also known that this result does not extend to finite string transductions: (deterministic) two-way finite state transducers strictly extend the expressive power of (functional) one-way transducers. In particular deterministic two-way transducers capture exactly the class of MSO-transductions of finite strings. In this paper, we address the following definability problem: given a function defined by a two-way finite state transducer, is it definable by a one-way finite state transducer? By extending Rabin and Scotts proof to transductions, we show that this problem is decidable. Our procedure builds a one-way transducer, which is equivalent to the two-way transducer, whenever one exists.

Visibly pushdown transducers with look-ahead

Visibly Pushdown Transducers (VPT) form a subclass of pushdown transducers. In this paper, we investigate the extension of VPT with visibly pushdown look-ahead (VPTla ). Their transitions are guarded by visibly pushdown automata that can check whether the well-nested subword starting at the current position belongs to the language they define. First, we show that VPTla are not more expressive than VPT, but are exponentially more succinct. Second, we show that the class of deterministic VPTla corresponds exactly to the class of functional VPT, yielding a simple characterization of functional VPT. Finally, we show that while VPTla are exponentially more succinct than VPT, checking equivalence of functional VPTla is, as for VPT, ExpT-C. As a consequence, we show that any functional VPT is equivalent to an unambiguous one.

Streamability of Nested Word Transductions

We consider the problem of evaluating in streaming (i.e. in a single left-to-right pass) a nested word transduction with a limited amount of memory. A transduction T is said to be height bounded memory (HBM) if it can be evaluated with a memory that depends only on the size of T and on the height of the input word. We show that it is decidable in coNPTime for a nested word transduction defined by a visibly pushdown transducer (VPT), if it is HBM. In this case, the required amount of memory may depend exponentially on the height of the word. We exhibit a sufficient, decidable condition for a VPT to be evaluated with a memory that depends quadratically on the height of the word. This condition defines a class of transductions that strictly contains all determinizable VPTs.

Definability problems for graph query languages

Given a graph, a relation on its nodes, and a query language Q of interest, we study the Q-definability problem which amounts to deciding whether there exists a query in Q defining precisely the given relation over the given graph. Previous research has identified the complexity of FO- and CQ-definability. In this paper, we consider the definability problem for regular paths and conjunctive regular path queries (CRPQs) over labelled graphs.

Distributed Streaming with Finite Memory

We introduce three formal models of distributed systems for query evaluation on massive databases: Distributed Streaming with Register Automata (DSAs), Distributed Streaming with Register Transducers (DSTs), and Distributed Streaming with Register Transducers and Joins (DSTJs). These models are based on the key-value paradigm where the input is transformed into a dataset of key-value pairs, and on each key a local computation is performed on the values associated with that key resulting in another set of key-value pairs. Computation proceeds in a constant number of rounds, where the result of the last round is the input to the next round, and transformation to key-value pairs is required to be generic. The dierence between the three models is in the local computation part. In DSAs it is limited to making one pass over its input using a register automaton, while in DSTs it can make two passes: in the first pass it uses a finitestate automaton and in the second it uses a register transducer. The third model DSTJs is an extension of DSTs, where local computations are capable of constructing the Cartesian product of two sets. We obtain the following results: (1) DSAs can evaluate first-order queries over bounded degree databases; (2) DSTs can evaluate semijoin algebra queries over arbitrary databases; (3) DSTJs can evaluate the whole relational algebra over arbitrary databases; (4) DSTJs are strictly stronger than DSTs, which in turn, are strictly stronger than DSAs; (5) within DSAs, DSTs and DSTJs there is a strict hierarchy w.r.t. the number of rounds.

Minimal Coverability Set for Petri Nets: Karp and Miller Algorithm with Pruning

This paper presents the Monotone-Pruning algorithm (MP) for computing the minimal coverability set of Petri nets. The original Karp and Miller algorithm (K&M) unfolds the reachability graph of a Petri net and uses acceleration on branches to ensure termination. The MP algorithm improves the K&M algorithm by adding pruning between branches of the K&M tree. This idea was first introduced in the Minimal Coverability Tree algorithm (MCT), however it was recently shown to be incomplete. The MP algorithm can be viewed as the MCT algorithm with a slightly more aggressive pruning strategy which ensures completeness. Experimental results show that this algorithm is a strong improvement over the K&M algorithm.

XEvolve: an XML schema evolution framework

This paper presents XEvolve, a framework that unifies streaming validation of XML documents, and efficient testing of equivalence and inclusion of specifications for various XML schema languages. For these purposes, this framework relies on Visibly Pushdown Automata (VPA) as a unifying model for the various schema languages. Schemas are first translated into VPA; standard algorithms for VPA can be then used to validate documents as well as to test equivalence or inclusion of schemas. In general, inclusion and equivalence are tested in exponential-time. However, when the given specifications are provided as DTD or XSD, these tests have a polynomial-time complexity with respect to the automaton size. Moreover, in this case the memory foot-print of the validation does not depend on the size of the input document but only on its depth.

Expressiveness of Visibly Pushdown Transducers

Visibly pushdown transducers (VPTs) are visibly pushdown automata extended with outputs. Theyhave been introduced to model transformations of nested words, i.e. words with a call/return struc-ture. As trees and more generally hedges can be linearized into (well) nested words, VPTs are anatural formalism to express tree transformations evaluated in streaming. This paper aims at charac-terizing precisely the expressive power of VPTs with respect to other tree transducer models.