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## Publications

Publications (97)

We study several classes of symbolic weighted formalisms: automata (swA), transducers (swT) and visibly pushdown extensions (swVPA, swVPT). They combine the respective extensions of their symbolic and weighted counterparts, allowing a quantitative evaluation of words over a large or infinite input alphabet.We present properties of closure by compos...

We study edit distances between strings, based on weighted operations such as character substitutions, insertions, deletions, and consolidations and fragmentations. The two latter operations transform a sequence of characters into one character and vice-versa. They correspond to the compression and expansion in Dynamic Time-Warping algorithms for s...

In this paper we present Aligned Scores and Performances (ASAP): a new dataset of 222 digital musical scores aligned with 1068 performances (more than 92 hours) of Western classical piano music. The scores are provided as paired MusicXML files and quantized MIDI files, and the performances as paired MIDI files and partially as audio recordings. Sco...

Comparing music score files is an important task for many activities such as collaborative score editing, version control and evaluation of optical music recognition (OMR) or music transcription. Following the Unix diff model for text files, we propose an original procedure for computing the differences between two score files, typically in XML for...

We present a formal language-based framework for MIDI-to-score transcription, the problem of converting a sequence of symbolic musical events with arbitrary timestamps into a structured music score. The framework aims at solving in one pass the two subproblems of rhythm quantization and score production. It relies, throughout the process, on an apr...

We introduce an extension of hedge automata called One-Variable Context-Free Hedge Automata. The class of unranked ordered tree languages they recognize has polynomial membership problem and is preserved by rewrite closure with inverse-monadic rules. We also propose a modeling of primitives of the W3C XQuery Update Facility by mean of parameterized...

The role of an Interactive Music System (IMS) is to accompany musicians during live performances, acting like a real musician. It must react in realtime to audio signals from musicians, according to a timed high-level requirement called mixed score, written in a domain specific language. Such goals imply strong requirements of temporal reliability...

Score-Based Interactive Music Systems are involved in live performances with human musicians, reacting in realtime to audio signals and asynchronous incoming events according to a pre-specified timed scenario called mixed score. Building such a system is a difficult challenge implying strong require- ments of reliability and robustness to unforesee...

We consider an extension of term rewriting rules with context constraints restricting the application of rewriting to positions whose prefix (i.e. the sequence of symbols from the rewrite position up to the root) belongs to a given regular language. This approach, well studied in string rewriting, is similar to node selection mechanisms in XML tran...

We present a tree-based symbolic representation of rhythm notation suitable for processing with purely syntactic theoretical tools such as term rewriting systems or tree automata. Then we propose an equational theory, defined as a set of rewrite rules for transforming these representations. This theory is complete in the sense that from a given rhy...

EFFICACe est un projet de recherche centré sur les outils de composition assistée par ordinateur (CAO), explorant les rapports entre calcul, temps et interactions dans les processus de composition musicale. Nous présentons différents travaux en cours dans le cadre de ce projet, concernant l'application de processus interactifs pour le traitement et...

The role of an interactive music system (IMS) is to accompany musicians during live performances, like a real musician. It reacts in realtime to audio signals from musicians, according to a timed specification called mixed score, written in a domain specific language. Such goals imply strong requirements of temporal reliability and robustness to un...

The IR has the form of an executable code modeling the expected Antescofo's behavior on a given score. We present here a simplified version of Antescofo's IR suitable for our presentation, leaving features such as thread creation, conditional branching, and variable handling outside of the scope of this paper.
In this paper, we define the construct...

This report presents procedures for testing Antescofo, a score-based Interactive Music System (IMS).
It describes common Model-Based Test (MBT) vocabulary and presents methodology and use cases.

We present a tree-based symbolic representation of rhythm notation suitable for processing with purely syntactic theoretical tools such as term rewriting systems or tree automata. Then we propose an equational theory, defined as a set of rewrite rules for transforming these representations. This theory is complete in the sense that from a given rhy...

A data tree is an unranked ordered tree where each node carries a label from
a finite alphabet and a datum from some infinite domain. We consider the two
variable first order logic FO2(

We describe an intermediate language designed as a medium-level internal
representation of programs of the interactive music system Antescofo. This
representation is independent both of the Antescofo source language and of the
architecture of the execution platform. It is used in tasks such as
verification of timings, model-based conformance testin...

With the advent and availability of powerful personal computing, the computer music research and industry have been focusing on real-time musical interactions between musicians and computers; delegating human-like actions to computers who interact with a musical environment. One common use-case of this kind is Automatic Accompaniment where the syst...

Antescofo is recently developed software for musical score following and mixed music: it automatically, and in real-time, synchronizes electronic instruments with a musician playing on a classical instrument. Therefore, it faces some of the same major challenges as embedded systems. The system provides a programming language used by composers to sp...

Human musicians have since long developed methods and formalisms for ensemble authoring and real-time coordination and synchronization of their actions. Bringing such capabilities to computers and providing them with the ability to take part in musical interactions with human musicians, poses interesting challenges for authoring of time and interac...

Interactive music systems coordinate in real-time an artificial perception of dynamics of human musicians with timely execution of machine reactions. As every human performance will differ from another, it is a challenging task to be able to predict the behavior or such systems in response to any possible performance, and prevent unwanted outcomes....

We define a class of ranked tree automata TABG generalizing both the tree
automata with local tests between brothers of Bogaert and Tison (1992) and with
global equality and disequality constraints (TAGED) of Filiot et al. (2007).
TABG can test for equality and disequality modulo a given flat equational
theory between brother subterms and between s...

We introduce an extension of hedge automata called bidimensional context-free
hedge automata. The class of unranked ordered tree languages they recognize is
shown to be preserved by rewrite closure with inverse-monadic rules. We also
extend the parameterized rewriting rules used for modeling the W3C XQuery
Update Facility in previous works, by the...

Automatic accompaniment systems are comprised of re- altime score following systems that in reaction to recogni- tion of events in a score from a human performer, launch necessary actions for the accompaniment section. While the realtime detection of score events out of live musi- cians’ performance has been widely addressed in the lit- erature, sc...

We present a procedure for the verification of cryptographic protocols based on a new method for automatic implicit induction theorem proving for specifications made of conditional and constrained rewrite rules. The method handles axioms between constructor terms which are used to introduce explicit destructor symbols for the specification of crypt...

We present a procedure for checking sufficient completeness of conditional and constrained term rewriting systems containing axioms for constructors which may be constrained (by e.g. equalities, disequalities, ordering, membership, …). Such axioms allow to specify complex data structures like e.g. sets, sorted lists or powerlists. Our approach is i...

We investigate the problem of deciding first-order theories of finite trees with several distinguished congruence relations, each of them given by some equational axioms. We give an automata-based solution for the case where the different equational axiom systems are linear and variable-disjoint (this includes the case where all axioms are ground),...

This document presents the study of several models of state machines, all of them extending the same formalism: the classical tree automata, and their application in various reasoning tasks, such as static analysis of programs or systems, typing, verification of the consistency of specifications, model checking... Trees are a natural data structure...

Motivated by the problem of verification of imperative tree transformation programs, we study the combination, called controlled term rewriting systems (CntTRS), 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 p...

We introduce the class of rigid tree automata (RTA), an extension of standard bottom-up 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...

XML became the de facto standard for the data representation and exchange on the internet. Regarding XML documents access control policy definition, OASIS ratified the XACML standard. It is a declarative language allowing the specification of authorizations as rules. Furthermore, it is common to formally represent XML documents as labeled trees and...

We define tree automata with global constraints (TAGC), generalizing the well-known class of tree automata with global equality and disequality constraints (14) (TAGED). TAGC can test for equality and disequality between sub- terms whose positions are defined by the states reached dur- ing a computation. In particular, TAGC can check that all the s...

The configuration of firewalls is highly error prone and automated solution are needed in order to analyze its correctness. We propose a formal and automatic method for checking whether a firewall reacts correctly with respect to a security policy given in an high level declarative language. When errors are detected, some feedback is returned to th...

We consider problems of access control for update of XML documents. In the context of XML programming, types can be viewed as hedge automata, and static type checking amounts to verify that a program always converts valid source documents into also valid output documents. Given a set of update operations we are particularly interested by checking s...

Computation with a term rewrite system (TRS) consists in the application of its rules from a given starting term until a normal form is reached, which is considered the result of the computation. The unique normalization (UN) property for a TRS \(\mathcal{R}\) states that any starting term can reach at most one normal form when \(\mathcal{R}\) is u...

In this paper, we develop an analysis of the Needham-Schroeder Public-KeyProtocol (NSPK) using a P system approach. This analysis is used to validate theprotocol and exhibits, as expected, a well known logical attack. The novelty of ourapproach is to use MGS, a P system like formalism, to find the attack by a systematicstate exploration.

We introduce the class of Rigid Tree Automata (RTA), an extension of standard bottom-up automata on ranked trees with dis- tinguished 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...

Preservation of regularity by a term rewriting system (TRS) states that the set of reachable terms from a tree automata (TA) language (aka regular term set) is also a TA language. It is an important and useful property, and there have been many works on identifying classes of TRS ensuring it; unfortunately, regularity is not preserved for restricte...

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. Constr...

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. Constr...

We consider rewriting systems for unranked ordered terms, i.e. trees where the number of successors of a node is not determined by its label, and is not a priori bounded. The rewriting systems are defined such that variables in the rewrite rules can be substituted by hedges (sequences of terms) instead of just terms. Consequently, this notion of re...

Tree automata with one memory have been introduced in 2001. They generalize both pushdown (word) automata and the tree automata with constraints of equality between brothers of Bogaert and Tison. Though it has a decidable emptiness problem, the main weakness of this model is its lack of good closure properties. We propose a generalization of the vi...

This paper presents new classes of tree automata combining automata with equality test and automata modulo equational theories. We believe that these classes have a good potential for application in e.g. software verification. These tree automata are obtained by extending the standard Horn clause representations with equational conditions and rewri...

Tree automata with one memory have been introduced in 2001. They generalize both pushdown (word) automata and the tree automata with constraints of equality between brothers of Bogaert and Tison. Though it has a decidable emptiness problem, the main weakness of this model is its lack of good closure properties.
We propose a generalization of the vi...

We investigate some preservation properties for classes of regular languages of unranked ordered terms under an appropriate gen- eralization of term rewriting subsuming both standard term rewriting and word rewriting. The considered classes include languages of hedge automata (HA) and some extension (called CF-HA) with context-free languages in tra...

We consider the problem of formal automatic verification of cryptographic protocols when some data, like poorly chosen passwords, can be guessed by dictionary attacks. First, we define a theory of these attacks and propose an inference system modeling the deduction capabilities of an intruder. This system extends a set of well-studied deduction rul...

We prove that the properties of reachability, joinability and confluence are undecidable for flat TRSs. Here, a TRS is flat if the heights of the left and right-hand sides of each rewrite rule are at most one.

We present a procedure for checking sufficient completeness for conditional and constrained term rewriting systems containing axioms for constructors which may be constrained (by e.g. equalities, disequalities, ordering, membership...). Such axioms allow to specify complex data structures like e.g. sets, sorted lists or powerlists. Our approach is...

We present a new method for automatic implicit induction theorem proving, and its application for the verification of a key distribution cryptographic protocol. The method can handle axioms between constructor terms, a feature generally not supported by other induction procedure. We use such axioms in order to specify explicit destructors represent...

We present a procedure for checking sufficient completeness for conditional and constrained term rewriting systems with axioms for constructors which may be constrained (by e.g. equalities, disequalities, ordering, membership...). Such axioms allow to specify complex data structures like e.g. sets, sorted lists or powerlists. Our method is integrat...

We present a new procedure for testing sufficient completeness for conditional and constrained term rewriting systems in presence of constrained axioms for constructors. Such axioms allow to specify complex data structures like e.g. sets or sorted lists. Our approach is based on tree grammars with constraints, a formalism which permits an exact rep...

In this paper, we develop an analysis of the Needham-Schroeder Public-Key Protocol in the framework of membrane computing. This analysis is used to validate the protocol and exhibits, as expected, a well known logical attack. The novelty of our approach is to use multiset rewriting in a nest of membranes. The use of membranes enables to tight the c...

We develop an analysis of the Needham-Schroeder public key protocol in the framework of membrane computing. This analysis is used to validate the protocol and exhibits, as expected, a well known logical attack. The novelty of our approach is to use multiset rewriting in a nest of membranes. The use of membranes enables us to make airtight the condi...

We present a non-deterministic polynomial time procedure to decide the problem of insecurity, in the presence of a bounded number of sessions, for cryptographic protocols containing explicit destructor symbols, like decryption and projection. These operators are axiomatized by an arbitrary convergent rewrite system satisfying some syntactic restric...

We consider the problem of automating proofs of cryptographic protocols when some data, like poorly chosen passwords, can be guessed by dictionary attacks. First, we define a theory of these attacks: we introduce an inference system modeling the guessing capabilities of an intruder. This system extends the classical Dolev-Yao rules. Using proof rew...

In this paper, we develop a new approach for mechanizing induction on complex data structures (like bags, sorted lists, trees, powerlists. . . ) by adapting and generalizing works in tree automata with constraints. The key idea of our approach is to compute a tree grammar with constraints which describes the initial model of the given specification...

In this paper, we develop a new approach for mechanizing induction on complex data structures (like bags, sorted lists, trees, powerlists. . . ) by adapting and generalizing works in tree automata with constraints. The key idea of our approach is to compute a tree grammar with constraints which describes the initial model of the given specification...

In this paper, we develop an analysis of the Needham-Schroeder Public-Key Protocol (NSPK) using a P system approach. This analysis is used to validate the protocol and exhibits, as expected, a well known logical attack. The novelty of our approach is to use MGS, a P system like formalism, to find the attack by a systematic state exploration.

We consider the problem of automating proofs of cryptographic protocols when some data, like poorly chosen passwords, can be guessed by dictionary attacks. First, we define a theory of these attacks: we introduce an inference system modeling the guessing capabilities of an intruder. This system extends the classical Dolev--Yao rules. Using proof re...

We consider the problem of automating proofs of cryptographic protocols whensome data, like poorly chosen passwords, can be guessed by dictionary attacks. First, we denea theory of these attacks: we introduce an inference system modeling the guessing capabilities ofan intruder. This system extends the classical Dolev{Yao rules. Using proof rewritin...

We investigate the resolution of a class of symbolic constraints modulo an equationaltheory presented by a convergent rewriting system. These constraints are combinations ofrstorderequations and so-called intruder constraints which can be seen as restricted second-orderunication problems. We propose an inference system based on basic narrowing tech...

We prove that ground reducibility is EXPTIME-complete in the
general case. EXPTIME-hardness is proved by encoding the computations of
an alternating Turing machine whose space is polynomially bounded. It is
more difficult to show that ground reducibility belongs to DEXPTIME. We
associate first an automaton with disequality constraints
A<sub>R,t</su...

Ground reachability, ground joinability and confluence are shown undecidable for flat term rewriting systems, i.e. systems in which all left and right members of rule have depth at most one.

Contents Introduction 9 Preliminaries 13 1 Recognizable Tree Languages and Finite Tree Automata 17 1.1 Finite Tree Automata . . . . . . . . . . . . . . . . . . . . . . . . 18 1.2 The Pumping Lemma for Recognizable Tree Languages . . . . . 26 1.3 Closure Properties of Recognizable Tree Languages . . . . . . . . 27 1.4 Tree Homomorphisms . . . . . ....

This paper presents the results cited in Section 4.3, especially Theorem 33

Contents Introduction 9 Preliminaries 13 1 Recognizable Tree Languages and Finite Tree Automata 17 1.1 Finite Tree Automata . . . . . . . . . . . . . . . . . . . . . . . . 18 1.2 The Pumping Lemma for Recognizable Tree Languages . . . . . 26 1.3 Closure Properties of Recognizable Tree Languages . . . . . . . . 27 1.4 Tree Homomorphisms . . . . . ....

trees are ground terms over F . Evaluate expressions or compute attributes over abstract trees than over syntactical trees. The following transformation associates with a syntactical tree t its corresponding abstract tree A(t).

Contents Introduction 9 Preliminaries 13 1 Recognizable Tree Languages and Finite Tree Automata 17 1.1 Finite Tree Automata . . . . . . . . . . . . . . . . . . . . . . . . 18 1.2 The Pumping Lemma for Recognizable Tree Languages . . . . . 26 1.3 Closure Properties of Recognizable Tree Languages . . . . . . . . 27 1.4 Tree Homomorphisms . . . . . ....

We propose a direct and fully automated translation from standard security protocol descriptions to rewrite rules. This compilation defines non-ambiguous operational semantics for protocols and intruder behavior: they are rewrite systems executed by applying a variant of ac-narrowing. The rewrite rules are processed by the theorem-prover daTac. Mul...

We show that rigid reachability, the non-symmetric form of rigid E-unification, is already undecidable in the case of a single constraint. From this we infer the undecidability of a new and rather restricted kind of second-order unification. We also show that certain decidable subclasses of the problem which are PTIME-complete in the equational cas...

In this paper we prove decidability results of restricted fragments of simultaneous rigid reachability or SRR, that is the nonsymmetrical form of simultaneous rigid E-unification or SREU. The absence of symmetry enforces us to use different methods, than the ones that have been successful in the context of SREU (for example word equations). The met...

We show that unification in certain extensions of shallow equational theories is decidable. Our extensions generalize the known classes of shallow or standard equational theories. In order to prove decidability of unification in the extensions, a class of Horn clause sets called sorted shallow equational theories is introduced. This class is a natu...

Colloque sans acte à diffusion restreinte.

We show that rigid reachability, the non-symmetric form of rigid E-unification, is undecidable already in the case of a single constraint. From this we infer the undecidability of a new rather
restricted kind of second-order unification. We also show that certain decidable subclasses of the problem which are P-complete in the equational case become...

We show that unification in certain extensions of shallow equational theories is decidable. Our extensions generalize the known classes of shallow or standard equational theories. In order to prove decidability of unification in the extensions, a class of Horn clause sets called sorted shallow equational theories is introduced. This class is a natu...

A linear term rewriting system
R\mathcal{R}is growing when, for every rule l→r ∈
R\mathcal{R}, each variable which is shared by l and r occurs at depth one in l. We show that the set of ground terms having a normal form w.r.t. a growing rewrite system is recognized by a finite tree automaton. This implies in particular that reachability and seque...

Using the automata with constraints, we give an algorithm for the decision of ground reducibility of a term t w.r.t. a rewriting system R. The complexity of the algorithm is doubly exponential in the maximum of the depths of t and R and the cardinal of R. Introduction Ground reducibility of a term t w.r.t. a term rewriting system R is the property...

We define a new class of tree automata which generalizes both the encompassment automata of [3] and the automata with tests between brothers of [2]. We give a pumping lemma for these automata, which implies that the emptiness of the corresponding language is decidable. Then, we show how to decide emptiness by means of a "cleaning" algorithm, which...

We define a new class of tree automata which generalizes both the encompassment automata of [3] and the automata with tests between brothers of [2]. We give a pumping lemmafor these automata, which implies that the emptiness of the corresponding language is decidable.Then, we show how to decide emptiness by means of a "cleaning" algorithm, whichlea...

We investigate the problem of deciding first-order theories of finite trees with several distinguished congruence relations, each of them given by some equational axioms. We give an automata-based solution for the case where the different equational axiom systems are linear and variable-disjoint (this includes the case where all axioms are ground),...