SynCoP 2018

Nathalie Bertrand (Rennes, France)

Population control: how to win when intuition fails?

We consider a population of identical NFA, and view it as a 2-player game: the first player chooses which action to play, and the second one resolves the non- determinism in each copy of the NFA. The objective for the first player is to synchronize all copies to a target state. In this talk, we will report on decidability and complexity of the following parameterized control problem: for every population size, does the first player have a winning strategy ?

Thao Dang (Grenoble, France)

Parameter synthesis for biological systems modelling

In this presentation, we consider the problem of parameter synthesis in view of modelling of biological systems. Models for describing mechanisms and principles of biological processes often involve numerous parameters which are needed to account for imprecision in our knowledge as well as lack of experimental information. We will discuss methods for finding parameters so that a hybrid model satisfies some biological hypothesis expressed using temporal logics, or to make the model fit actual measurements. Some case studies are presented to illustrate the methods.

Marco Faella (Napoli, Italy)

Controller synthesis for Linear Hybrid Systems

Linear Hybrid Automata generalize Timed Automata by allowing for more general real-time dynamics. When discrete transitions are partitioned into controllable and uncontrollable ones, this model can represent the interaction of a switching controller with a plant, subject to disturbances. We will review the state of the art on controller synthesis for this model and demonstrate our NYCS tool.

Pierre Ganty (IMDEA Software Institute, Spain)

Population protocols and predicates

In populations protocols, identical, anonymous, finite-state processes interact pairwise through rendez-vous synchronization. Angluin et al. (PODC 2004) introduced population protocols as a distributed computation model. In that context, an interesting subclass of protocols are the ones computing predicates. Intuitively, a population protocol computes a predicate Φ(N) as follows: instantiate the protocol with N processes and let them interact until they reach a stable unanimity on value true or false. I will present results relative to three natural questions:

• does this protocol computes a predicate?
• does this protocol computes this predicate?
• what predicate does this protocol compute?

Ichiro Hasuo (Tokyo, Japan)

Approximating Reachability Probabilities by (Super-)Martingales

Reachability is a fundamental problem in the analysis of probabilistic systems. It is well-known that reachability probabilities are efficiently computed for finite-state systems by linear programming. However, this LP method does not apply to systems that have infinitely many configurations, such as probabilistic programs and parametric systems. In such a case, we have to rely on a parametric witness (i.e. a function) for over- or under-approximating reachability probabilities. A well-studied class of such witnesses is that of supermartingales. In this talk I will talk about our recent results that refine existing supermartingale-based methods. The technical keys to those results are: choice of a suitable martingale concentration lemma for over-approximation; and a categorical axiomatization of supermartingales by coalgebras and corecursive algebras. The talk is based on my joint work with Natsuki Urabe, Masaki Hara, Bart Jacobs, Toru Takisaka and Yuichiro Oyabu.

Karin Quaas (Leipzig, Germay)

The Precise Complexity of the Reachability Problem for Parametric Timed Automata with a Single Parametric Clock

In parametric timed automata (PTA), clocks can be compared with parameters. The value of a parameter is a priori unknown and it is instantiated during a run by a parameter valuation. The reachability problem is to decide, whether for a given PTA and a target state there exists a parameter valuation and a corresponding run to the target state. Alur, Henzinger, and Vardi (1994) proved that the problem is undecidable for the case that the PTA uses at least three clocks. They also gave a decision procedure for PTA with at most one clock; the precise complexity of the problem was left open. Bundala and Ouaknine recently gave a 2NEXPTIME upper bound and a NEXPTIME lower bound for PTA with one clock. In this talk, we prove that the problem is NEXPTIME-complete. The proof uses a correspondence between PTA and parametric counter automata (established by Bundala and Ouaknine) on the one side, and a correspondence between parametric one-counter automata and classical two-way automata on the other side.
This is joint work with Benedikt Bollig and Arnaud Sangnier.