eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-29
107:1
107:15
10.4230/LIPIcs.ICALP.2020.107
article
Invariants for Continuous Linear Dynamical Systems
Almagor, Shaull
1
https://orcid.org/0000-0001-9021-1175
Kelmendi, Edon
2
Ouaknine, Joël
3
2
Worrell, James
2
Department of Computer Science, Technion, Haifa, Israel
Department of Computer Science, Oxford University, UK
Max Planck Institute for Software Systems, Saarland Informatics Campus, Saarbrücken, Germany
Continuous linear dynamical systems are used extensively in mathematics, computer science, physics, and engineering to model the evolution of a system over time. A central technique for certifying safety properties of such systems is by synthesising inductive invariants. This is the task of finding a set of states that is closed under the dynamics of the system and is disjoint from a given set of error states. In this paper we study the problem of synthesising inductive invariants that are definable in o-minimal expansions of the ordered field of real numbers. In particular, assuming Schanuel’s conjecture in transcendental number theory, we establish effective synthesis of o-minimal invariants in the case of semi-algebraic error sets. Without using Schanuel’s conjecture, we give a procedure for synthesizing o-minimal invariants that contain all but a bounded initial segment of the orbit and are disjoint from a given semi-algebraic error set. We further prove that effective synthesis of semi-algebraic invariants that contain the whole orbit, is at least as hard as a certain open problem in transcendental number theory.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol168-icalp2020/LIPIcs.ICALP.2020.107/LIPIcs.ICALP.2020.107.pdf
Invariants
continuous linear dynamical systems
continuous Skolem problem
safety
o-minimality