Section: Highlights of the Year

Highlights of the Year

Reaching approximate agreement in a distributed system among a set of local input values is a problem that often is repeatedly solved in artificial and natural distributed systems. Time efficient algorithms for this problem are thus of great theoretical and practical relevance. In [28] we studied the performance of such algorithms in dynamic networks. We showed lower time complexity bounds, demonstrating that already relatively simple broadcast and averaging algorithms achieve optimal time complexity. The results also imply new tight lower time complexity bounds for approximate agreement in classic distributed computing models with stable network architectures; solving a previously open problem.

• obtaining [34], on the one hand, bi-directional translations between Contextual nets and BNs and correspondences between results on synchronism sensitivities. Taking advantage of CPN semantics enabling more behaviour than the generalized asynchronous updating mode, we propose an encoding of BNs that ensures correct abstraction of any multivalued refinement; and

• [20], [32] investigating update modes for discrete networks. It is commonly expected that Boolean networks produce an over-approximation of behaviours (reachable configurations), and that subsequent refinements would only prune some impossible transitions. However, we show that even generalized asynchronous updating of Boolean networks, which subsumes the usual updating modes including synchronous and fully asynchronous, does not capture all transitions doable in a multi-valued or timed refinement. We introduce a new semantics for interpreting BNs which meets with a correct abstraction of any multivalued refinements, with any update mode. This semantics subsumes all the usual updating modes, while enabling new behaviours achievable by more concrete models. Moreover, it appears that classical dynamical analyses of reachability and attractors have a simpler computational complexity: – reachability can be assessed in a polynomial number of iterations (instead of being PSPACE-complete with update modes); – attractors are hypercubes, and deciding the existence of attractors with a given upper-bounded dimension is in NP (instead of PSPACE-complete with update modes). The computation of iterations is in NP in the very general case, and is linear when local functions are monotonic, or with some usual representations of functions of BNs (binary decision diagrams, Petri nets, automata networks, etc.). In brief, the most permissive semantics of BNs enables a correct abstract reasoning on dynamics of BNs, with a greater tractability than previously introduced update modes. These works open new perspectives in concurrent semantics, and at the same time will allow to capture hitherto inaccessible phenotypes and pathways in biological networks.