arXiv subjects

Michael Blondin

Publications and source records attributed to Michael Blondin.

22 records · Page 2Linked to original sources

arXiv2018

Large Flocks of Small Birds: On the Minimal Size of Population Protocols

Population protocols are a well established model of distributed computation by mobile finite-state agents with very limited storage. A classical result establishes that population protocols compute exactly predicates definable in Presburger arithmetic. We initiate the study of the minimal amount of memory required to compute a given predicate as a function of its size. We present results on the predicates $x \geq n$ for $n \in \mathbb{N}$, and more generally on the predicates corresponding to systems of linear inequalities. We show that they can be computed by protocols with $O(\log n)$ states (or, more generally, logarithmic in the coefficients of the predicate), and that, surprisingly, some families of predicates can be computed by protocols with $O(\log\log n)$ states. We give essentially matching lower bounds for the class of 1-aware protocols.

cs.DC↗

arXiv2017

Well Behaved Transition Systems

The well-quasi-ordering (i.e., a well-founded quasi-ordering such that all antichains are finite) that defines well-structured transition systems (WSTS) is shown not to be the weakest hypothesis that implies decidability of the coverability problem. We show coverability decidable for monotone transition systems that only require the absence of infinite antichains and call well behaved transitions systems (WBTS) the new strict superclass of the class of WSTS that arises. By contrast, we confirm that boundedness and termination are undecidable for WBTS under the usual hypotheses, and show that stronger monotonicity conditions can enforce decidability. Proofs are similar or even identical to existing proofs but the surprising message is that a hypothesis implicitely assumed minimal for twenty years in the theory of WSTS can meaningfully be relaxed, allowing more orderings to be handled in an abstract way.

cs.LO↗

arXiv2016

Approaching the Coverability Problem Continuously

The coverability problem for Petri nets plays a central role in the verification of concurrent shared-memory programs. However, its high EXPSPACE-complete complexity poses a challenge when encountered in real-world instances. In this paper, we develop a new approach to this problem which is primarily based on applying forward coverability in continuous Petri nets as a pruning criterion inside a backward coverability framework. A cornerstone of our approach is the efficient encoding of a recently developed polynomial-time algorithm for reachability in continuous Petri nets into SMT. We demonstrate the effectiveness of our approach on standard benchmarks from the literature, which shows that our approach decides significantly more instances than any existing tool and is in addition often much faster, in particular on large instances.

cs.LO↗

arXiv2014

Reachability in Two-Dimensional Vector Addition Systems with States is PSPACE-complete

Determining the complexity of the reachability problem for vector addition systems with states (VASS) is a long-standing open problem in computer science. Long known to be decidable, the problem to this day lacks any complexity upper bound whatsoever. In this paper, reachability for two-dimensional VASS is shown PSPACE-complete. This improves on a previously known doubly exponential time bound established by Howell, Rosier, Huynh and Yen in 1986. The coverability and boundedness problems are also noted to be PSPACE-complete. In addition, some complexity results are given for the reachability problem in two-dimensional VASS and in integer VASS when numbers are encoded in unary.

cs.FL↗