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The structure of multiplicatives
Investigating Girard's new propositionnal calculus which aims at a large scale study of computation, we stumble quickly on that question: What is a multiplicative connective? We give here a detailed…
Formal molecular biology
Reversible Communicating Systems
A process algebra RCCS, in the style of CCS, where processes can backtrack is obtained, and it is shown that, given a past, a computation step can be taken back if and only if it leads to a causally equivalent past.
Rule-Based Modelling of Cellular Signalling
- V. Danos, Jérôme Feret, W. Fontana, Russell Harmer, J. Krivine
- Computer ScienceCONCUR
- 3 September 2007
It is shown how causality enables the formalization of the colloquial concept of pathway and, perhaps more surprisingly, how conflict can be used to dissect the signalling dynamics to obtain a qualitative handle on the range of system behaviours.
The measurement calculus
A rigorous mathematical model underlying the one-way quantum computer is developed and a concrete syntax and operational semantics for programs, which are called patterns, are presented, and an algebra of these patterns derived from a denotational semantics are presented.
Scalable Simulation of Cellular Signaling Networks
A radically different method which does not attempt to count species is presented, which uses a representation of the system together with a super-approximation of its 'event horizon' (all events that may happen next), and a specific correction scheme to obtain exact timings.
A new deconstructive logic: linear logic
The method presented is powerful: it allows us to recover as fragments formalisms as seemingly different as Girard's LC and Parigot's λμ, FD, delineates other viable systems as well, and gives means to extend the Krivine/Leivant paradigm of ‘programming-with-proofs’ to classical logic.
Linear logic and elementary time
Bisimulation and cocongruence for probabilistic systems
Internal coarse-graining of molecular systems
- Jérôme Feret, V. Danos, J. Krivine, Russell Harmer, W. Fontana
- Computer ScienceProceedings of the National Academy of Sciences
- 1 April 2009
This work presents a formal (and automated) method for constructing a coarse-grained and self-consistent dynamical system aimed at molecular patterns that are distinguishable by the dynamics of the original system as posited by the rules.