---
res:
bibo_abstract:
- "The continuous evolution of a wide variety of systems, including continous-time
Markov chains and linear hybrid automata, can be\r\ndescribed in terms of linear
differential equations. In this paper we study the decision problem of whether
the solution x(t) of a system of linear differential equations dx/dt = Ax reaches
a target halfspace infinitely often. This recurrent reachability problem can\r\nequivalently
be formulated as the following Infinite Zeros Problem: does a real-valued function
f:R≥0 --> R satisfying a given linear\r\ndifferential equation have infinitely
many zeros? Our main decidability result is that if the differential equation
has order at most 7, then the Infinite Zeros Problem is decidable. On the other
hand, we show that a decision procedure for the Infinite Zeros Problem at order
9 (and above) would entail a major breakthrough in Diophantine Approximation,
specifically an algorithm for computing the Lagrange constants of arbitrary real
algebraic numbers to arbitrary precision.@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: 10.1145/2933575.2934548
dct_date: 2016^xs_gYear
dct_language: eng
dct_publisher: IEEE@
dct_title: On recurrent reachability for continuous linear dynamical systems@
...