TBA

### March 13, 2017

*TBA*

**Ioana boureanu**

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# Seminars 2016-17

Contact : seminar@lacl.fr
# On monday, at 2pm - UPEC CMC - Room P2-131

### March 13, 2017

*TBA*

**Ioana boureanu**
(University of Surrey)

### March 6, 2017

*TBA*

**Nicolas Perrin**
(UPMC)

### February 27, 2017

*TBA*

**Serge Haddad**
(LSV)

### February 20, 2017

*TBA*

**Aymerick Savary**
(LACL)

### January 30, 2017

*Deterministic Automaton and Logically Definable Sets of Numbers*

**Arthur Milchior**
(LACL)

### January 23, 2017

*Let’s compute through infinite time!*

**Sabrina Ouazzani**
(LACL)

### January 16, 2017

*Semilinear Sets, Register Machines, and Integer Vector Addition (P) Systems*

**Sergiu Ivanov**

### January 9, 2017

*Controlling a Population*

**Blaise Genest**
(IRISA CNRS)

### November 28, 2016

*Robustness against Consistency Models with Atomic Visibility*

**Bernardi Giovanni**
(IRIF)

### November 21, 2016

*Un théorème de Dixon pour les groupes d’automates*

**Thibaud Godin**
(IRIF)

TBA

TBA

TBA

TBA

For a fixed base b, any integer can be encoded as a finite word of alphabet of digits. In dimension d>0, a vector of d integers is encoded as a word of alphabet of vector of d digits. A set of vector of integers is thus encoded as a language whose alphabet is the set of vector of digits. Thus, an automaton whose alphabet is the set of vector of digits recognizes a set of integers. Similarly, a Büchi automaton recognizes a set of vector of real.

It is then natural to consider algorithms which decide whether the set of vectors of numbers accepted by a finite automaton admits some properties. For example, Honkala proved in 1986 that it is decidable whether an automaton recognize a FO[N,+,<]-definable set of integers. Muchnik proved a similar result for automata recognizing sets of vectors of reals. A polynomial-time algorithm was then given by Leroux in 2006, and a quasi-linear time algorithm for the case of dimension 1 was given in 2013 by Marsault and Sakarovitch.

We state that it is decidable in linear time:

-whether a set of reals recognized by a given finite minimal weak Büchi automaton is FO[R,+,<]-definable.

-whether a set of vectors recognized by a minimal finite deterministic automaton can be defined in some logics less expressive than FO[N,+], such as FO[N,<,mod].

Furthermore, formulas which defines those sets can be computed in linear time and cubic time respectively.

Furthermore, is shown that it is decidable whether a set of vector of real or of integers accepted by a (weak Büchi) automaton:

-is definable in a logic which admits quantifier-elimination. For example, if the set is definable in FO[R,+,<], FO[R,Z,+,<,mod,floor] where mod is the set of modular predicate, FO[N,<,mod] or FO[<].

-satisfies a first-order formula in some formalism. For example, whether a set is a submonoid/subsemigroup of (R^d,+)

In this talk, I intend to:

-introduce automata recognizing set of vector of numbers,

-characterize the set of numbers which are FO[N,<,mod]- and FO[R,+,<]-definable,

-introduce and generalizes the methods used by Honkala, Muchnik and Marsault-Sakarovitch

-explain how how those methods can be applied to the above-mentioned problems.

In this talk, we present infinite time Turing machines (ITTM), from

the original definition of the model to some new infinite time

algorithms.

We will present algorithmic techniques that allow to highlight some

properties of the ITTM-computable ordinals. In particular, we will

study gaps in ordinal computation times, that is to say, ordinal times

at which no infinite time program halts.

In this talk we will consider membrane (P) systems working with

multisets with integer multiplicities. We will focus on a model in

which rule applicability is not influenced by the contents of the

membrane. We show that this variant is closely related to blind

register machines and integer vector addition systems. Furthermore, we

describe the computational power of these models in terms of linear and

semilinear sets of integer vectors.

We introduce a new setting where a population of agents, each modelled by a finite-state system, are controlled uniformly: the controller applies the same action to every agent. The framework is largely inspired by the control of a biological system, namely a population of yeasts, where the controller may only change the environment common to all cells. In this talk, we will describe a sure synchronization problem for such populations: no matter how individual agents react to the actions of the controller, the controller aims at driving all agents synchronously to a goal set of states. The agents are naturally represented by a non-deterministic finite state automaton, the same for every agent, and the whole system is encoded as a 2-player game. The first player chooses actions, and the second player resolves non-determinism for each agent. The game with *m* agents is called the m-population game. A natural parametrized control problem, given the automaton representing the agents, is whether player one wins the m-population game for any population size m. We show that if the answer is negative, there exists a cut-off, that is, a population size m0 such that for populations of size *m < m0* there exists a winning controller, and there is none for populations of size *m >m0*. Surprisingly, we show that this cut-off can be doubly exponential in the number of states of the NFA. While this suggests a high complexity for the parameterized control problem, we actually show that it can be solved in EXPTIME and is PSPACE-hard.

To achieve scalability, modern Internet services often rely on

distributed databases with consistency models for transactions

weaker than serializability.

At present, application programmers often lack techniques to ensure

that the weakness of these consistency models does not violate

application correctness.

In this talk I will present criteria to check whether applications

that rely on a database providing only weak consistency are robust,

i.e., behave as if they used a database providing serializability,

and I will focus on a consistency model called Parallel Snapshot Isolation.

The results I will outline handle systematically and uniformly several

recently proposed weak consistency models, as well as a mechanism for

strengthening consistency in parts of an application.

As every finite group is a subgroup of some permutation group, the most natural idea to generate random finite groups is to pick some random permutations and consider the group they generate. However, Dixon proved that this approach fails, as it generically leads to generate the symmetric are the alternating group.

Mealy automata, on the other hand, are a powerful tool to generate groups and have been used to solve several important group theoretic conjectures. In particular, any finite group can be generated by a Mealy automaton, hence the idea of doing random generation by drawing random automata.

In this talk we will present this method and prove an analogue to Dixon’s theorem for a certain class of Mealy automata. Then we will discuss how to avoid this convergence of the distribution of generated groups.