Periodic Reporting for period 4 - AVS-ISS (Analysis, Verification, and Synthesis for Infinite-State Systems)
Période du rapport: 2019-08-01 au 2021-01-31
The overall objective of the project is to comprehensively map the algorithmic landscape of verification problems for both discrete and continuous linear dynamical systems, and attendant extensions.
Some 41 peer-reviewed articles were published throughout the course of the action. Our work has substantially enhanced the algorithmic understanding of both discrete and continuous linear dynamical systems; in particular, we have provided algorithms for invariant synthesis and model checking that we expect will be incorporated within program-analysis tools and automated-verification engines in the years to come.
1) The solution of a 30-year old problem of Kannan and Lipton, published in our JACM 2016 paper (Pub#7).
2) The solution of the hyperplane-hitting problem for continuous linear dynamical systems (or equivalently the zero problem for linear differential equations), subject to Schanuel's Conjecture, as published in our LICS 2016 (Pub#2) and ICALP 2016 (Pub#4) papers.
3) An algorithm to decide the existence of, and synthesise, semialgebraic invariants for discrete-time linear dynamical systems, for the point-to-point reachability problem, published in a STACS 2017 paper (Pub#8), with a subsequent invited longer version in the journal Theory of Computing Systems (2019) (Pub#21).
4) The decidability of the longstanding question of structural liveness for linear hybrid systems is decidable, published in our HSCC 2017 paper (Pub#10).
5) The computability of strongest polynomial invariants for affine programs, solving a 40-year-old open problem, published in our LICS 2018 paper (Pub#12). An extension to linear hybrid automata was published in CONCUR 2020 (Pub#30).
6) The computability of strongest families of o-minimal invariants for discrete linear dynamical systems (ICALP 2018) (Pub#13).
7) The solution of the termination problem for linear loops over the integers, answering a famous question of Ashish Tiwari from 2003 (ICALP 2019) (Pub#18).
8) The solution to the "Monniaux Problem" (on automated invariant generation) in our SAS 2019 paper (Pub#24).
9) The most general results on model checking for discrete linear dynamical systems (MFCS 2020 (Pub#26), POPL 2021 (Pub#39), and POPL 2022 (Pub#41)).
10) Advances on the Skolem Problem for linear recurrence sequences (ISSAC 2020 (Pub#27) and LICS 2021 (Pub#35) [which received "distinguished paper award"]).
11) The computability of strongest families of o-minimal invariants for continuous linear dynamical systems (ICALP 2020) (Pub#28).
12) Algorithmic results on reachability under small perturbations for discrete linear dynamical systems (FSTTCS 2020 (Pub#29) and MFCS 2021 (Pub#33)).
13) Moving beyond linear systems: algorithmic results on holonomic systems (MFCS 2021 (Pub#32) and ICALP 2021 (Pub#36)).
14) Algorithmic advances on invariant-generation and ranking-function synthesis for affine and polynomial loops (CONCUR 2020 (Pub#30), MFCS 2021 (Pub#34), CAV 2021 (Pub#38)). The CAV paper also featured a tool, POROUS, for the efficient calculations of invariants.
15) Algorithmic advances on reachability problems for parametric linear dynamical sytems (CONCUR 2021) (Pub#37).
Dissemination has taken place mainly via published peer-reviewed articles, conference presentations, and invited talks at various institutions. As the work is foundational in nature, it has not (yet) led to (industrial) exploitation at the present time.
* Continuous dynamics
* Multimodal systems (and in particular hybrid systems)
* Stochastic aspects
* Robustness aspects