# Victor MarsaultUniversité Gustave Eiffel & CNRS · Laboratoire d'Informatique Gaspard-Monge

Victor Marsault

Ph.D

## About

31

Publications

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733

Citations

## Publications

Publications (31)

In this paper we show that enumerating the set MM(G,R), defined below, cannot be done with polynomial-delay in its input G and R, unless P=NP. R is a regular expression over an alphabet $\Sigma$, G is directed graph labeled over $\Sigma$, and MM(G,R) contains walks of G. First, consider the set Match(G,R) containing all walks G labeled by a word (o...

We consider the Distinct Shortest Walks problem. Given two vertices s and t of a graph database D and a regular path query, we want to enumerate all walks of minimal length from s to t that carry a label that conforms to the query. Usual theoretical solutions turn out to be inefficient when applied to graph models that are closer to real-life syste...

RPQs (regular path queries) are an important building block of most query languages for graph databases. They are generally evaluated under homomorphism semantics; in particular only the endpoints of the matched walks are returned. However, practical applications often need the full matched walks to compute aggregate values. In those cases, homomor...

Property graphs have reached a high level of maturity, witnessed by multiple robust graph database systems as well as the ongoing ISO standardization effort aiming at creating a new standard Graph Query Language (GQL). Yet, despite documented demand, schema support is limited both in existing systems and in the first version of the GQL Standard. It...

GQL (Graph Query Language) is being developed as a new ISO standard for graph query languages to play the same role for graph databases as SQL plays for relational. In parallel, an extension of SQL for querying property graphs, SQL/PGQ, is added to the SQL standard; it shares the graph pattern matching functionality with GQL. Both standards (not ye...

The formalism of RPQs (regular path queries) is an important building block of most query languages for graph databases. RPQs are generally evaluated under homomorphism semantics; in particular only the endpoints of the matched walks are returned. Practical applications often need the full matched walks to compute aggregate values. In those cases,...

The development of practical query languages for graph databases runs well ahead of the underlying theory. The ISO committee in charge of database query languages is currently developing a new standard called Graph Query Language (GQL) as well as an extension of the SQL Standard for querying property graphs represented by a relational schema, calle...

As graph databases become widespread, the International Organi-
zation for Standardization (ISO) and International Electrotechni-
cal Commission (IEC) have approved a project to create GQL, a
standard property graph query language. This complements the
SQL/PGQ project, which specifies how to define graph views over
a SQL tabular schema, and to run...

As graph databases become widespread, JTC1 -- the committee in joint charge of information technology standards for the International Organization for Standardization (ISO), and International Electrotechnical Commission (IEC) -- has approved a project to create GQL, a standard property graph query language. This complements a project to extend SQL...

Let p/q be a rational number. Numeration in base p/q is defined by a function
that evaluates each finite word over A_p={0,1,...,p-1} to some rational number.
We let N_p/q denote the image of this evaluation function. In particular, N_p/q
contains all nonnegative integers and the literature on base p/q usually
focuses on the set of words that are ev...

This work is a contribution to the study of rewrite games. Positions are finite words, and the possible moves are defined by a finite number of local rewriting rules. We introduce and investigate taking-and-merging games, that is, where each rule is of the form a^k->epsilon.
We give sufficient conditions for a game to be such that the losing positi...

The paper describes the present and the future of graph updates in Cypher, the language of the Neo4j property graph database and several other products. Update features include those with clear analogs in relational databases, as well as those that do not correspond to any relational operators. Moreover, unlike SQL, Cypher updates can be arbitraril...

Let $b$ be an integer strictly greater than $1$. Each set of nonnegative
integers is represented in base $b$ by a language over $\{0, 1, \dots, b -
1\}$. The set is said to be $b$-recognisable if it is represented by a regular
language. It is known that ultimately periodic sets are $b$-recognisable, for
every base $b$, and Cobham's theorem implies...

This work contributes to the study of rewrite games where positions are words and the moves are local rewriting rules of the form u->v belonging to a finite set. We introduce and investigate taking-and-merging games where each rule is of the form a^k->epsilon. We give sufficient conditions for a game to be such that the losing positions (resp. the...

The Cypher property graph query language is an evolving language, originally designed and implemented as part of the Neo4j graph database, and it is currently used by several commercial database products and researchers. We describe Cypher 9, which is the first version of the language governed by the openCypher Implementers Group. We first introduc...

Every rational number p/q defines a rational base numeration system in which
every integer has a unique finite representation, up to leading zeroes. This
work is a contribution to the study of the set of the representations of
integers. This prefix-closed subset of the free monoid is naturally represented
as a highly non-regular tree. Its nodes are...

Cypher is a query language for property graphs. It was originally designed and implemented as part of the Neo4j graph database, and it is currently used in a growing number of commercial systems, industrial applications and research projects. In this work, we provide denotational semantics of the core fragment of the read-only part of Cypher, which...

Let $\frac{p}{q}$ be a rational number. Numeration in base $\frac{p}{q}$ is defined by a function that evaluates each finite word over $A_p=\{0,1,\ldots,{p-1}\}$ to a rational number in some set $N_{\frac{p}{q}}$. In particular, $N_{\frac{p}{q}}$ contains all integers and the literature on base $\frac{p}{q}$ usually focuses on the set of words that...

Given an integer base $b>1$, a set of integers is represented in base $b$ by a language over $\{0,1,...,b-1\}$. The set is said to be $b$-recognisable if its representation is a regular language. It is known that eventually periodic sets are $b$-recognisable in every base $b$, and Cobham's theorem implies the converse: no other set is $b$-recognisa...

The signature of a labelled tree (and hence of its prefix-closed branch language) is the sequence of the degrees of the nodes of the tree in the breadth-first traversal. In a previous work, we have characterised the signatures of the regular languages. Here, the trees and languages that have the simplest possible signatures, namely the periodic one...

We present here the notion of signature of trees and of languages, and its relationships with the theory of numeration systems. The signature of an ordered infinite tree (of bounded degree) is an infinite (bounded) sequence of integers, the sequence of the degrees of the nodes taken in the visit order of the canonical breadth-first traversal of the...

The signature of a labelled tree (and hence of its prefix-closed branch language) is the sequence of the degrees of the nodes of the tree in the breadth-first traversal. In a previous work, we have characterised the signatures of the regular languages. Here, the trees and languages that have the simplest possible signatures, namely the periodic one...

Ce mémoire aborde et résout des problèmes assez différents, ayant tous trait à la numération, avec une certaine unité conceptuelle quant aux moyens mis en œuvre pour les résoudre: la théorie des automates. Nous considérons d'abord les bases entières et présentons un algorithme quasi-linéaire et structurel permettant de décider si le langage accepté...

We introduce the notion of surminimisation of a finite deterministic automaton; it consists in performing a transition relabelling before executing the minimisation and it produces an automaton smaller than a sole minimisation would. While the classical minimisation process preserves the accepted language, the surminimisation process preserves its...

We present here the notion of breadth-first signature and its relationship
with numeration system theory. It is the serialisation into an infinite word of
an ordered infinite tree of finite degree. We study which class of languages
corresponds to which class of words and,more specifically, using a known
construction from numeration system theory, w...

We present here the notion of breadth-first signature and its relationship with numeration system theory. It is the serialisation into an infinite word of an ordered infinite tree of finite degree. We study which class of languages corresponds to which class of words and,more specifically, using a known construction from numeration system theory, w...

This work introduces the idea of breadth-first generation of infinite trees
and languages. It is orthogonal to usual descriptions by classical objects such
as automata and grammars which refer more naturally to a depth-first approach.
This idea is brought into play with periodic inputs, a case that comes from the
study of rational base number syste...

This work is a contribution to the study of set of the representations of integers in a rational base number system. This prefix-closed subset of the free monoid is naturally represented as a highly non regular tree whose nodes are the integers and whose subtrees are all distinct. With every node of that tree is then associated a minimal infinite w...

It is decidable if a set of numbers, whose representation in a base b is a
regular language, is ultimately periodic. This was established by Honkala in
1986.
We give here a structural description of minimal automata that accept an
ultimately periodic set of numbers. We then show that it can verified in linear
time if a given minimal automaton meets...

In this work, it is proved that a set of numbers closed under addition and
whose representations in a rational base numeration system is a rational
language is not a finitely generated additive monoid.
A key to the proof is the definition of a strong combinatorial property on
languages : the bounded left iteration property. It is both an unnatural...