We study the expressiveness of polynomial recurrence sequences (PRS), a nonlinear extension of the well-known class of linear recurrence sequences (LRS). A typical example of a sequence definable in PRS but not in LRS is a_n = n!. Our main result is that the sequence u_n = n^n cannot be defined by any PRS. We also discuss the impact of our results on the expressiveness of nonlinear extensions of weighted automata. This is joint work with Michaël Cadilhac, Charles Paperman, Michał Pilipczuk and Géraud Sénizergues.

Monitorability underpins the technique of Runtime Verification because it delineates what properties can be verified at runtime. Although many monitorability definitions exist, few are defined explicitly in terms of the operational guarantees provided by monitors, that is the computational entities carrying out the verification. We view monitorability as a spectrum, where the fewer guarantees that are required of monitors, the more properties become monitorable. Accordingly, we present a monitorability hierarchy based on this trade-off. For regular specifications, we give syntactic characterizations in terms of Hennessy–Milner logic with recursion for its levels. Finally, we map existing monitorability definitions into our hierarchy. Hence our work gives a unified framework that makes the operational assumptions and guarantees of each definition explicit. This provides a rigorous foundation that can inform design choices and correctness claims for runtime verification tools.

I will present a sorting algorithm called adaptive ShiversSort. This recently developed algorithm improves the speed at which it sorts arrays by using the existence of already sorted subarrays. I will focus on the links between this algorithm and the algorithm TimSort, which is a standard algorithm in Python and Java. I will also show that the complexity of adaptive ShiversSort, in terms of comparisons performed, is optimal up to an additive linear factor.

Live stream: https://bbb2.math.univ-paris-diderot.fr/b/yas-gge-2ka

An assume guarantee (AG) specification is of the form “Assumption implies Guarantee”. AG Synthesis is the following problem: given an AG specification, construct a system satisfying it.

In this talk I will discuss the case where both Assumptions and Guarantees are given by Prompt Linear Temporal Logic (Prompt LTL), which is a logic extending LTL by adding bound requirements such as “every request is answered in bounded time”.

The solution to the AG problem for Prompt LTL will be an invitation to the theory of regular cost functions.

Joint work with Bastien Maubert and Moshe Y. Vardi.