|
Please download my CV with complete list of publications (July 2017): PDF file.
- Synchronization of Bernoulli sequences on
shared letters. Information and Computation, 255(1):1-26, 2017.
DOI -
arXiv -
PDF -
(Show/Hide abstract)
-
(Show/Hide BibTeX references)
The topic of this paper is the distributed and incremental generation of long executions of concurrent systems, uniformly or more generally with weights associated to elementary actions. Synchronizing sequences of letters on alphabets sharing letters are known to produce a trace in the concurrency theoretic sense, i.e., a labeled partially ordered set. We study the probabilistic aspects by considering the synchronization of Bernoulli sequences of letters, under the light of Bernoulli and uniform measures recently introduced for trace monoids. We introduce two algorithms that produce random traces, using only local random primitives. We thoroughly study some specific examples, the path model and the ring model, both of arbitrary size. For these models, we show how to generate any Bernoulli distributed random traces, which includes the case of uniform generation.
@Article{,
author = {Abbes, S.},
title = {Synchronization of Bernoulli sequences on shared letters},
journal = {Information and Computation},
year = 2017,
volume = {255},
number = {1},
pages = {1--26},
doi = {10.1016/j.ic.2017.04.002}
}
- Uniform measures on braid monoids and dual braid
monoids. Journal of Algebra, 473(1):627-666, 2017.
With S. Gouëzel, V. Jugé and J. Mairesse.
DOI -
arXiv -
PDF -
(Show/Hide abstract)
-
(Show/Hide BibTeX references)
We aim at studying the asymptotic properties of typical
positive braids, respectively positive dual braids. Denoting by μk the uniform distribution on positive
(dual) braids of length k , we prove that the sequence
(μk)k converges to a unique probability measure μ∞ on
infinite positive (dual) braids. The key point is that the
limiting measure μ∞ has a Markovian structure which can be
described explicitly using the combinatorial properties of
braids encapsulated in the Möbius polynomial. As a
by-product, we settle a conjecture by Gebhardt and Tawn
(J. Algebra, 2014) on the shape of the Garside normal form of
large uniform braids.
@Article{,
author = {Abbes, S. and Gouëezel, S. and Jug\'e, V. and
Mairesse, J.},
title = {Uniform measures on braid monoids and dual braid monoids},
journal = {Journal of Algebra},
year = 2017,
volume = {473},
number = {1},
pages = {627--666},
doi = {10.1007/s10959-016-0692-6}
}
- A cut-invariant law of large numbers for random
heaps. Journal of Theoretical Probability (Springer),
1-34, 2016.
DOI -
arXiv -
PDF -
(Show/Hide abstract)
-
(Show/Hide BibTeX references)
We consider the framework of Bernoulli measures for heap monoids. We introduce in this framework the notion of asynchronous stopping time, which generalizes the notion of stopping time for classical probabilistic processes. A Strong Bernoulli property is proved. A notion of cut-invariance is formulated for convergent ergodic means. Then a version of the Strong law of large numbers is proved for heap monoids with Bernoulli measures. We study a sub-additive version of the Law of large numbers in this framework.
@Article{,
author = {Abbes, S.},
title = {A cut-invariant law of large numbers for random heaps},
journal = {Journal of Theoretical probability},
year = 2016,
pages = {1--34},
doi = {10.1007/s10959-016-0692-6}
}
- Uniform and Bernoulli measures on the boundary of trace
monoids. Journal of Combinatorial Theory, Series A
135:201-236, 2015. With J. Mairesse.
DOI -
arXiv -
PDF -
(Show/Hide abstract)
-
(Show/Hide BibTeX references)
Trace monoids and heaps of pieces appear in various contexts in combinatorics. They also constitute a model used in computer science to describe the executions of asynchronous systems. The design of a natural probabilistic layer on top of the model has been a long standing challenge. The difficulty comes from the presence of commuting pieces and from the absence of a global clock. In this paper, we introduce and study the class of Bernoulli probability measures that we claim to be the simplest adequate probability measures on infinite traces. For this, we strongly rely on the theory of trace combinatorics with the Möbius polynomial in the key role. These new measures provide a theoretical foundation for the probabilistic study of concurrent systems.
@Article{,
author = {Abbes, S. and Mairesse, J.},
title = {Uniform and Bernoulli measures on the boundary of trace monoids},
journal = {Journal of Combinatorial Theory, Series A},
year = 2015,
number = {135},
pages = {201--236},
doi = {10.1016/j.jcta.2015.05.003}
}
- Markov two-components processes. Logical
Methods in Computer Science 9(2:14):1-34, 2013.
DOI -
arXiv -
PDF -
(Show/Hide abstract)
-
(Show/Hide BibTeX references)
We propose Markov two-components processes (M2CP) as a probabilistic model of asynchronous systems based on the trace semantics for concurrency. Considering an asynchronous system distributed over two sites, we introduce concepts and tools to manipulate random trajectories in an asynchronous framework: stopping times, an Asynchronous Strong Markov property, recurrent and transient states and irreducible components of asynchronous probabilistic processes. The asynchrony assumption implies that there is no global totally ordered clock ruling the system. Instead, time appears as partially ordered and random. We construct and characterize M2CP through a finite family of transition matrices. M2CP have a local independence property that guarantees that local components are independent in the probabilistic sense, conditionally to their synchronization constraints. A synchronization product of two Markov chains is introduced, as a natural example of M2CP.
@Article{abbes13,
author = {Abbes, S.},
title = {Markov two-components processes},
journal = {Logical Methods in Computer Science},
year = 2013,
month = {June},
number = {9(2:14)},
pages = {1--34},
doi = {10.2168/LMCS-9(2:14)2013}
}
- On countable completions of quotient ordered
semigroups. Semigroup Forum 77(3):482-499, 2008.
DOI -
HAL -
PDF -
(Show/Hide abstract)
-
(Show/Hide BibTeX references)
We study the commutativity of two operations: quotienting
and completing. Completing refers to the countable chain
completion, known to exist for every partial order, and
quotienting is with respect to a semigroup congruence. The two
operations are shown to commute in a suitable framework. We
apply the results for studying the semigroup structure and
topological semigroup structure on the completion.
@Article{abbes08,
author = {Abbes, S.},
title = {{On Countable Completions of Quotient Ordered Semigroups}},
journal = {Semigroup Forum},
year = 2008,
month = {December},
number = {77},
volume = {3},
pages = {482--499}
}
- Probabilistic true-concurrency models: Markov nets and a
Law of large numbers. Theoretical Computer Science
390(2-3):129-170, 2008. With A. Benveniste.
DOI -
HAL -
PDF -
(Show/Hide
abstract) -
(Show/Hide BibTeX references)
We introduce the model of Markov nets, a probabilistic
extension of safe Petri nets under the true-concurrency
semantics. This means that traces, not firing sequences, are
given a probability. This model builds upon our previous work
on probabilistic event structures. We use the notion of
branching cell for event structures and show that the latter
provides the adequate notion of local state, for nets. We
prove a Law of Large Numbers (LLN) for Markov nets, which
constitutes the main contribution of the paper. This LLN
allows characterizing in a quantitative way the asymptotic
behavior of Markov nets.
@Article{abbes07b,
author = {Abbes, S. and Benveniste, A.},
title = {{Probabilistic true-concurrency models: Markov nets
and a law of large numbers}},
journal = {Theoretical Computer Science},
year = 2008,
volume = {390},
number = {2-3},
pages = {129-170}
}
- A projective formalism applied to topological and
probabilistic event structures.
Mathematical Structures in Computer Science
17(4):819-837, 2007.
DOI -
HAL -
PDF -
(Show/Hide
abstract) -
(Show/Hide BibTeX references)
This paper introduces projective systems for topological and
probabilistic event structures.
The projective formalism is used for studying the domain of
configurations of a prime event structure and its space of maximal
elements. This is done from both a topological and a probabilistic
viewpoint. We give probability measure extension theorems in
this framework.
@Article{abbes07a,
author = {Abbes, S.},
title = {A projective formalisme applied to topological and probabilistic event structures},
journal = {Mathematical Structures in Computer Science},
year = 2007,
volume = 17,
number = 4,
pages = {819--837}}
- Projective topology on bifinite domains and applications.
Theoretical Computer Science 365(3):171-183,
2006. With K. Keimel.
DOI -
HAL -
PDF -
(Show/Hide abstract) -
(Show/Hide BibTeX references)
We revisit extension results from continuous valuations to
Radon measures for bifinite domains. In the framework of
bifinite domains, the Prokhorov theorem (existence of
projective limits of Radon measures) appears as a natural
tool, and helps building a bridge between Measure theory and
Domain theory. The study we present also fills a gap in the
literature concerning the coincidence between projective and
Lawson topology for bifinite domains. Motivated by
probabilistic considerations, we study the extension of
measures in order to define Borel measures on the space of
maximal elements of a bifinite domain.
@Article{abbes06c,
author = {Abbes, S. and Keimel, K.},
title = {Projective topology on bifinite domains and applications},
journal = {Theoretical Computer Science},
year = 2006,
volume = 365,
number = 3,
pages = {171--183}}
- A Cartesian closed category of event structures with
quotients. Discrete Mathematics and Theoretical Computer
Science 8(1):249-272, 2006.
HAL -
PDF -
(Show/Hide abstract) -
(Show/Hide BibTeX references)
We introduce a new class of morphisms for event
structures. The category obtained is cartesian closed, and a
natural notion of quotient event structure is defined within
it. We study in particular the topological space of maximal
configurations of quotient event structures. We introduce
the compression of event structures as an example of quotient:
the compression of an event structure E is a minimal event
structure with the same space of maximal configurations as E.
@Article{abbes06b,
author = {Abbes, S.},
title = {A Cartesian closed category of event structures with
quotients},
journal = {Discrete Mathematics and Theoretical Computer Science},
year = 2006,
volume = 8,
number = 1,
pages = {249--272}}
- Probabilistic models for true-concurrency: branching
cells and distributed probabilities for event structures.
Information and Computation 204(2):231-274, 2006. With A. Benveniste.
DOI -
HAL -
PDF -
(Show/Hide
abstract) -
(Show/Hide BibTeX references)
This paper is devoted to probabilistic models for
concurrent systems under their true-concurrency
semantics. Here we address probabilistic event structures. We
consider a new class of event structures, called locally
finite, that extend confusion-free event structure. In locally
finite event structures, maximal configurations can be tiled
with branching cells: branching cells are minimal and finite
sub-structures capturing the choices performed while scanning
a maximal configuration. The probabilistic event structures
that we introduce have the property that concurrent processes
are independent in the probabilistic sense.
@Article{abbes06a,
author = {Abbes, S. and Benveniste, A.},
title = {Probabilistic true-concurrency models: branching cells and distributed probabilities for event structures},
journal = {Information and Computation},
year = 2006,
volume = 204,
number = 2,
pages = {231--274}}
- Toward uniform random generation in 1-safe Petri
nets. In Random generation of combinatorial structures - GASCOM 2016, J.-M. Fédou and L. Ferrari, editors, Electronic Notes in Discrete Mathematics, volume 59, p. 3-17, 2017.
DOI - arXiv -
HAL - (Show/Hide BibTeX references)
@InProceedings{,
author = {Abbes, S.},
title = "Toward uniform random generation in 1-safe {P}etri nets ",
series = "Electronic Notes in Discrete Mathematics ",
editor = "F\'edou, J.-M. and Ferrari, L.",
volume = "59",
pages = "3--17",
year = "2017",
booktitle = "Random Generation of Combinatorial Structures -- GASCom 2016",
doi = "10.1016/j.endm.2017.05.002"}
- Uniform generation in trace monoids. In G. Italiano,
G. Pighizzini and D. Sannella
(Eds), MFCS
2015, Mathematical Foundations of Computer Science 2015,
Part 1. Volume 9234 of LNCS, Springer, p. 63-75, 2015. With J. Mairesse.
DOI -
arXiv -
(Show/Hide BibTeX references)
@InProceedings{,
author = {Abbes, S. and Mairesse, J.},
title = {Uniform generation in trace monoids},
booktitle = {Mathematical Foundations of Computer Science 2015 (MFCS
2015), part 1},
editor = {Italiano, G. and Pighizzini, G. and Sannella, D.},
year = 2015,
volume = 9234,
series= {LNCS},
publisher={Springer},
pages = {63--75}}
- Concurrency, sigma-algebras and probabilistic
fairness. In L. de Alfaro,
editor, FOSSACS
2009, 12th Conference on Foundation of
Software Science and Computation Structures, member
of ETAPS
2009, York (UK), volume 5504 of LNCS,
p. 380-394, 2009. With A. Benveniste.
DOI -
PDF -
(Show/Hide BibTeX references)
@InProceedings{,
author = {Abbes, S. and Benveniste, A.},
title = {Concurrency, sigma-algebras and probabilistic fairness},
booktitle = {12th~Conference on Foundations of Software Science and
Computation Structures (FOSSACS 09)},
editor = {de Alfaro, L.},
year = 2009,
volume = 5504,
series= {LNCS},
pages = {380--394},
address = {York (UK)}}
Extended version (2008):
HAL -
PDF
- Branching cells as local states for event structures and nets:
probabilistic applications. In V. Sassone,
editor, FOSSACS 2005, Conference on Foundations of
Software Science and Computation Structures, member of
ETAPS
2005, Edimbourgh (UK), volume 3441 of LNCS,
p. 95-109, 2005. With A. Benveniste.
DOI -
HAL -
PDF -
(Show/Hide BibTeX references)
@InProceedings{,
author = {Abbes, S. and Benveniste, A.},
title = {Branching cells as local states for event
structures and nets: probabilistic applications},
booktitle = {Conference on Foundations of Software Science and
Computation Structures (FOSSACS 05)},
editor = {Sassone, V.},
year = 2005,
volume = 3441,
series= {LNCS},
pages = {95--109},
address = {Edimburgh (UK)}}
Extended version: preprint IRISA PI 1651, 2004 - IRISA archive
- The (true) concurrent Markov property and some
applications to Markov nets. In G. Ciardo and
P. Darondeau, editors, ICATPN'05, International
Conference on Theory and Applications of Petri Nets,
Miami (FL, USA), volume 3536 of LNCS, p. 70-89, 2005.
DOI -
HAL -
PDF -
(Show/Hide BibTeX references)
@InProceedings{,
author = {Abbes, S.},
title = {{The (true) concurrent Markov property and some
applications to Markov nets}},
booktitle = {International Conference on Theory and Applications of
Petri Nets (ICATPN~05)},
editor = {Ciardo, G. and Darondeau, P.},
year = 2005,
volume = 3536,
series= {LNCS},
pages = {70--89},
address = {Miami (FL, USA)}}
- Combinatorics and probability: measure of maximal entropy,
uniform measure, random generation.
- Models of algebraic combinatorics: heap monoids
(Viennot's "heaps of pieces" which correspond to "right-angled"
Coxeter-Tits monoids), positive braid monoids.
- Limits of finite combinatorial structures. Weak convergence of
uniform distributions.
- Random generation in concurrent systems: trace monoids, trace languages,
Petri nets.
|
|