Thesis
My research focus on publications in Theoretical Computer Science.
It consists of some contributions of the theory of automata with multiplicities.
This structure has many applications to connected sciences (Computer Sciences,
Mathematics, Physics, etc). A particular type of automata with multiplicities is
the automaton with epsilon-transitions denoted by k-epsilon-automaton.
In the first part, we give an algebraic method for removing the epsilon-transitions
of the k-epsilon-automaton in order to obtain an equivalent k automaton with the same behaviour.
We discuss two aspects of the star problem (by infinite sums and by equations).
The theory of minimization allows to minimize a k-automaton in the sense of reducing to the smallest
among the number of states. It can be used with some modification to solve other problems such as the
splitting of modules. We have used the algorithm of decomposition to split a Boolean function which
constitute the non-linear element of the cryptographic algorithm and to split a A-module where A is
the Hecke algebra as \(q=0\). These algorithms are added to the library MuPAD-combinat.
MuPAD-Combinat
The structures studied in the context of my PhD research as the concept of semi-ring, module, automata with multiplicities
and other combinatorial structures can be manipulated in the
MuPAD language using the library
MuPAD-Combinat . MuPAD-Combinat is an open system of algebraic combinatory.
It currently contains functions that deal with the usual combinatorial classes (partitions, tables and decomposable classe),
Schubert polynomials, the symmetric group and weighted automata. It provides the user with tools to build new classes and
combinatorial algebras. Its development has started since spring 2001 and officially incorporated in the MuPAD library since
version 2.5.0. The library MuPAD-Combinat offers many features of algebraic combinatory.
The package WeightedAutomaton of the MuPAD-Combinat library contains a set of procedures for manipulating automata with
multiplicities. To build an automaton using this package, you must provide the dimension of this automaton (number of states),
the alphabet A, the input vector, the transition matrices for each letter of the alphabet and the output vector.
Current research work
Currently, my research activities includes the domain of application related to automata with multiplicities.
We demenstrate that we can use this kind of automata for the specification of the Publish/Subscribe
architecture system. En fact, the dynamicity and the evolution of the Publish/Subscribe architecture
system generate changes and disturbances in the structure and the behavior of the system.
This dynamic character makes difficult to have a correct Publish/Subscribe model with respect to
its architectural style. It is so delicate to identify the whole system’s elements and to understand
all its concerned relations. A specification tool is needed for supporting the dynamic aspect of the
system and an evaluation tool of its change to determine which properties are affected and which
inconsistencies can occur. We use the automata with multiplicities for the specification of our system.
We use the model checking SPIN for the validation of our system and to specify the properties relating to
the structure and the behavior of a dynamic system.
Supervision of research
I participate in co-supervision of two masters degree in Computer Science
|
1.
|
Siwar KHELIFI, Specification and verification of the structural and behavioural properties of Publish/Subscribe architectures.
Defended on January 31, 2009 at Faculty of Economics and Management of Sfax.
|
|
2.
|
Nesrine OULEDABDALLAH, Sensor Networks and Population Protocols: Application of the diffusion and improved with the rendezvous model.
Will be defended on 9 January, 2010 at Faculty of Economics and Management of Sfax.
|
I Supervise also a master degree in Computer Science
|
1.
|
Issam GAIED, ACME-Refinement: a new approach to describe software architectures.
Will be Defended on January 15, 2010 at the Higher Institut of Computer Science and Multimedia of Gabes.
|
