Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time-bounded Reachability for Hybrid Automata: Complexity and Fixpoints   In this paper, we study thetime-bounded reachability problem for rectangular
hybrid automata with non-negative rates (RHA+). This problem was recently shown
to be decidable [Brihaye et al, ICALP11] (even though the unbounded
reachability problem for even very simple classes of hybrid automata is
well-known to be undecidable). However, [Brihaye et al, ICALP11] does not
provide a precise characterisation of the complexity of the time-bounded
reachability problem. The contribution of the present paper is threefold.
First, we provide a new NExpTime algorithm to solve the timed-bounded
reachability problem on RHA+. This algorithm improves on the one of [Brihaye et
al, ICALP11] by at least one exponential. Second, we show that this new
algorithm is optimal, by establishing a matching lower bound: time-bounded
reachability for RHA+ is therefore NExpTime-complete. Third, we extend these
results in a practical direction, by showing that we can effectively compute
fixpoints that characterise the sets of states that are reachable (resp.
co-reachable) within T time units from a given starting state.

18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
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The categories of this paper are: eess
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat