Periodic Reporting for period 3 - AVS-ISS (Analysis, Verification, and Synthesis for Infinite-State Systems)
Reporting period: 2018-02-01 to 2019-07-31
The overall objective is to comprehensively map the algorithmic landscape of verification problems for both discrete and continuous linear dynamical systems, and attendant extensions.
1) The solution of a 30-year old problem of Kannan and Lipton, published in our JACM 2016 paper.
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 and ICALP 2016 papers.
3) An algorithm for 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. We were subsequently invited to submit an extended
version of this work to the journal Theory of Computing Systems, and our paper has been accepted subject to minor corrections.
4) The decidability of the longstanding question of structural liveness for linear hybrid systems is decidable, published in out HSCC 2017 paper.
We are expecting some major advances in the area of automated invariant synthesis by the end of the project.