---
res:
bibo_abstract:
- "The Continuous Skolem Problem asks whether a real-valued function satisfying
a linear differen-\r\ntial equation has a zero in a given interval of real numbers.
This is a fundamental reachability\r\nproblem for continuous linear dynamical
systems, such as linear hybrid automata and continuous-\r\ntime Markov chains.
Decidability of the problem is currently open – indeed decidability is open\r\neven
for the sub-problem in which a zero is sought in a bounded interval. In this paper
we show\r\ndecidability of the bounded problem subject to Schanuel’s Conjecture,
a unifying conjecture in\r\ntranscendental number theory. We furthermore analyse
the unbounded problem in terms of the\r\nfrequencies of the differential equation,
that is, the imaginary parts of the characteristic roots.\r\nWe show that the
unbounded problem can be reduced to the bounded problem if there is at most\r\none
rationally linearly independent frequency, or if there are two rationally linearly
independent\r\nfrequencies and all characteristic roots are simple. We complete
the picture by showing that de-\r\ncidability of the unbounded problem in the
case of two (or more) rationally linearly independent\r\nfrequencies would entail
a major new effectiveness result in Diophantine approximation, namely\r\ncomputability
of the Diophantine-approximation types of all real algebraic numbers.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Ventsislav K
foaf_name: Chonev, Ventsislav K
foaf_surname: Chonev
foaf_workInfoHomepage: http://www.librecat.org/personId=36CBE2E6-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: Joël
foaf_name: Ouaknine, Joël
foaf_surname: Ouaknine
- foaf_Person:
foaf_givenName: James
foaf_name: Worrell, James
foaf_surname: Worrell
bibo_doi: 10.4230/LIPIcs.ICALP.2016.100
bibo_volume: 55
dct_date: 2016^xs_gYear
dct_language: eng
dct_publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik@
dct_title: On the skolem problem for continuous linear dynamical systems@
...