Abstract
Hybrid automata have been introduced in both control engineering and
computer science as a formal model for the dynamics of hybrid
discrete-continuous systems. While computability issues
concerning safety properties have been extensively studied,
liveness properties have remained largely uninvestigated.
In this article, we investigate decidability of state recurrence and
of progress properties.
First, we show that state recurrence and progress are in general
undecidable for polynomial hybrid automata. Then, we demonstrate
that they are closely related for hybrid automata subject to a
simple model of noise, even though these automata are infinite-state
systems. Based on this, we augment a semi-decision procedure for
recurrence with a semi-decision method for length-boundedness of
paths in such a way that we obtain an automatic verification method
for progress properties of linear and polynomial hybrid automata
that may only fail on pathological, practically uninteresting cases.
These cases are such that satisfaction of the desired progress
property crucially depends on the complete absence of noise, a
situation unlikely to occur in real hybrid systems.
| Original language | English |
|---|---|
| Title of host publication | Theoretical Aspects of Computer Software, TACS 2001 |
| Publisher | Springer |
| Publication date | 2001 |
| Pages | 340-359 |
| Publication status | Published - 2001 |