## Section: New Results

### Encoding constrained transition systems

Participants : Kaustuv Chaudhuri, Joëlle Despeyroux.

Joëlle Despeyroux and Kaustuv Chaudhuri have given an encoding of the synchronous stochastic -calculus in a hybrid extension of intuitionistic linear logic (called HyLL). Precisely, they have shown that focused partial sequent derivations in the encoding are in bijection with stochastic traces. The modal worlds are used to represent the rates of stochastic interactions, and the connectives of hybrid logic are used to represent the constraints in the stochastic transition rules. These results have been submitted to a journal [31] and an extended report is available from HAL [21] .

One of the most successful applications of the stochastic -calculus has been in representing signal transduction networks in cellular biology. An interesting application of this work would therefore be the direct representations of biological processes in HyLL, the original motivation for this line of investigation. Furthermore, other stochastic systems can, at least in principle, be similarly encoded in HyLL, giving us the linguistic ability to compare and combine systems represented using different stochastic formalisms.