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ENSTA ParisTech
Postdoc position - Designing a SAT modulo ODE solver
ENSTA ParisTech
ENSTA ParisTech belongs to the foremost graduate schools of engineering in France.
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Publié: il y a 16 jours
Date limite d'inscription: mars 01
Localisation: Palaiseau, France
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Postdoc position - Designing a SAT modulo ODE solver

  • Keywords: SAT/SMT solvers, Interval analysis, Constraint programming
  • Lab: U2IS, ENSTA ParisTech, 828 boulevard des maréchaux 91762 Palaiseau Cedex
  • Advisors: Julien Alexandre dit Sandretto, Alexandre Chapoutot, and Sylvain Conchon (Université Paris-Sud)
  • Duration: 12 months. An extension for a second year is possible.
  • Expected start time Immediately.
  • Salary: The indicative net monthly salary is between 2200€ and 2400€, depending on experience.

Scientific context and job description.

Control-command systems are made of software part and continuous-time dynamics which closely related in order to produce an automatic behavior. They are member of the important class of cyber-physical systems (CPS). In order to provide guarantee on this behavior, formal verification methods can be applied to produce a mathematical proof that the system designed fulfill some (functional) requirements. Nevertheless, the challenge in applying formal verification methods on CPS is the need to take into account its continuous-time part (usually described by ordinary differential equations) and its discrete-time part, i.e., the software part, (generally described by a transition system).

In previous work, on formal verification of CPS, SAT module ODE solvers [5, 7, 6] have been defined to tackle this challenge. These solvers embed theory solver to deal with QF_NRA logic and specialized solver to take care of ODEs. We want to take a fresh look at this approach so the aim of this postdoc project is to

•           define the logic fragment suitable to verify CPS;

•           develop a new SAT modulo ODE solver taking advantage of the latest development of SMT Solver [4]; and ODE solver [3, 2, 1]


The candidate

•           must have obtained a PhD degree in Computer Science or related area, with excellent grades.

•           is required to have a very strong background in theoretical Computer Science, logic and formal methods.

•           must be capable of programming in the most popular programming languages, including C, C++, Ocaml, Bash.

•           should demonstrate commitment, team working and a critical mind.

•           must have a good knowledge of the English language is necessary.

Note that previous experience in formal verification by model checking and/or numerical methods for ODE, is a plus but not essential.

Candidate should send by email, the following documents in PDF,

•           Academic CV with an established research record

•           Covering letter stating why you consider yourself suitable for the post (maximum 2 pages A4)

•           References do not need to be included with the application, but shortlisted applicants will need to send 2 reference letters before interview.

with a title "Application to Postdoc SAT modulo ODE", to

•           Julien Alexandre dit Sandretto – alexandre@ensta.fr

•           Alexandre Chapoutot – chapoutot@ensta.fr

•           Sylvain Conchon – sylvain.conchon@lri.fr

Closing date for application: the 1st of March 2019


[1]        J. Alexandre dit Sandretto and A. Chapoutot. DynBEX: a Differential Constraint Library for Studying Dynamical Systems (Poster). In Conference on Hybrid Systems: Computation and Control, 2016.

[2]        J. Alexandre dit Sandretto and A. Chapoutot. Validated Explicit and Implicit Runge-Kutta Methods. Reliable Computing electronic edition, 22, 2016.

[3]        O. Bouissou, A. Chapoutot, and A. Djoudi. Enclosing temporal evolution of dynamical systems using numerical methods. In NASA Formal Methods, number 7871 in LNCS, pages 108–123. Springer, 2013.

[4]        L. M. de Moura and D. Jovanovic. A model-constructing satisfiability calculus. In Verification, Model Checking, and Abstract Interpretation, 14th International Conference, VMCAI 2013, Rome, Italy, January 20-22, 2013. Proceedings, pages 1–12, 2013.

[5]        A. Eggers, N. Ramdani, N. Nedialkov, and M. Fränzle. Improving the sat modulo ode approach to hybrid systems analysis by combining different enclosure methods. Software and Systems Modeling, pages 1–28, 2012.

[6]        S. Gao, S. Kong, and E. M. Clarke. dreal: An smt solver for nonlinear theories over the reals. In International Conference on Automated Deduction, volume 7898 of LNCS, pages 208–214. Springer, 2013.

[7]        D. Ishii, K. Ueda, and H. Hosobe. An interval-based sat modulo ode solver for model checking nonlinear hybrid systems. International Journal on Software Tools for Technology Transfer, 13(5):449–461, 2011.

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