Difference between revisions of "Jobs/M2 AD 2015 Syntactic Monoids"

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{{Job
 
{{Job
|Reference id=2015 AD Syntactic Monoids
+
|Reference id=M2 AD 2015 Syntactic Monoids
|Title=Syntactic Monoids
+
|Title= Syntactic Monoids
  +
|Dates=5-6 months in 2015
  +
|Research field=Automata Theory
  +
|Related project=Vaucanson
  +
|Advisor=Akim Demaille
  +
|General presentation of the field=The classical theory of automata, of transducers and of rational expressions, admits a very elegant and extremely useful extension (eg, in natural language processing) taking into account the concept of weighting. The weights are then taken in a semi-ring, which can be classical (⟨𝔹, ∨, ∧⟩, ⟨ℤ, +, ×⟩, ⟨ℚ, +, ×⟩, etc..), tropical (⟨ℤ min, +⟩, etc..), or yet of another type (e.g. rational expressions).
  +
  +
The field 𝔽₂ is a particular interest, and shows quite a few unique properties, as demonstrated by the current active research under various names (e.g., "Symmetric Difference Automata").
  +
  +
Vcsn is a project led by Alexandre Duret-Lutz and Akim Demaille (LRDE). It is a platform for the manipulation of automata, transducers and weighted rational expressions. It is written in C++11 avoiding the classical object-oriented programming in favor of generic programming (template) for more performance. Vcsn is an heir of the Vaucanson 2 project which was developed in partnership with Jacques Sakarovitch (Telecom ParisTech) and Sylvain Lombardy (LaBRI).
  +
  +
|Prerequisites=* good programmer in some language
  +
* acquaintance with C++
  +
* facilities with theoretical matters
  +
|Objectives=The objective of this internship is exploit the existing features of Vcsn to apply them to 𝔽₂ in a first step, and then, in a second step, to use Vcsn as a tool to explore novel results.
  +
|References=Some references
  +
* [http://www.amazon.com/Elements-Automata-Theory-Jacques-Sakarovitch/dp/0521844258 Jacques Sakarovitch, “Elements of Automata Theory,” Cambridge University Press.]
  +
* [http://publications.lrde.epita.fr/201307-CIAA Akim Demaille, Alexandre Duret-Lutz, Sylvain Lombardy, Jacques Sakarovitch. “Implementation Concepts in Vaucanson 2,” CIAA’13.]
  +
* [http://www.cs.sun.ac.za/~jaco/PUBS/index.html#vzg13 L. van Zijl, J. Geldenhuys, “ Symmetric Difference NFA: the state of the art”]
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|Contact=<akim at lrde . epita . fr>
  +
|Compensation=1000 € gross/month
  +
|Type=Master Internship
 
|Language=en
 
|Language=en
 
}}
 
}}

Revision as of 14:25, 29 October 2014

Syntactic Monoids
Reference id

M2 AD 2015 Syntactic Monoids

Dates

5-6 months in 2015

Research field

Automata Theory

Related project

Vaucanson

Advisor

Akim Demaille

General presentation of the field

The classical theory of automata, of transducers and of rational expressions, admits a very elegant and extremely useful extension (eg, in natural language processing) taking into account the concept of weighting. The weights are then taken in a semi-ring, which can be classical (⟨𝔹, ∨, ∧⟩, ⟨ℤ, +, ×⟩, ⟨ℚ, +, ×⟩, etc..), tropical (⟨ℤ min, +⟩, etc..), or yet of another type (e.g. rational expressions).

The field 𝔽₂ is a particular interest, and shows quite a few unique properties, as demonstrated by the current active research under various names (e.g., "Symmetric Difference Automata").

Vcsn is a project led by Alexandre Duret-Lutz and Akim Demaille (LRDE). It is a platform for the manipulation of automata, transducers and weighted rational expressions. It is written in C++11 avoiding the classical object-oriented programming in favor of generic programming (template) for more performance. Vcsn is an heir of the Vaucanson 2 project which was developed in partnership with Jacques Sakarovitch (Telecom ParisTech) and Sylvain Lombardy (LaBRI).

Prerequisites
  • good programmer in some language
  • acquaintance with C++
  • facilities with theoretical matters
Objectives

The objective of this internship is exploit the existing features of Vcsn to apply them to 𝔽₂ in a first step, and then, in a second step, to use Vcsn as a tool to explore novel results.

Benefit for the candidate
References

Some references

Place LRDE: How to get to us
Compensation

1000 € gross/month

Future work opportunities
Contact

<akim at lrde . epita . fr> <akim at lrde . epita . fr>