当前位置：
X-MOL 学术
›
arXiv.cs.FL
›
论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Reachability in two-parametric timed automata with one parameter is EXPSPACE-complete
arXiv - CS - Formal Languages and Automata Theory Pub Date : 2020-11-13 , DOI: arxiv-2011.07091 Stefan G\"oller and Mathieu Hilaire
arXiv - CS - Formal Languages and Automata Theory Pub Date : 2020-11-13 , DOI: arxiv-2011.07091 Stefan G\"oller and Mathieu Hilaire
Parametric timed automata (PTA) are an extension of timed automata in which
clocks can be compared against parameters. The reachability problem asks for
the existence of an assignment of the parameters to the non-negative integers
such that reachability holds in the underlying timed automaton. The
reachability problem for PTA is long known to be undecidable, already over
three parametric clocks. A few years ago, Bundala and Ouaknine proved that for PTA over two parametric
clocks and one parameter the reachability problem is decidable and also showed
a lower bound for the complexity class PSPACE^NEXP. Our main result is that the
reachability problem for two-parametric timed automata with one parameter is
EXPSPACE-complete. Our contribution is two-fold. For the EXPSPACE lower bound we make use of deep results from complexity
theory, namely a serializability characterization of EXPSPACE (based on
Barrington's Theorem) and a logspace translation of numbers in chinese
remainder representation to binary representation. For the EXPSPACE upper bound, we give a careful exponential time reduction
from PTA over two parametric clocks and one parameter to a slight subclass of
parametric one-counter automata (POCA) over one parameter based on a minor
adjustment of a construction due to Bundala and Ouaknine. We provide a series
of techniques to partition a fictitious run of a POCA into several carefully
chosen subruns that allow us to prove that it is sufficient to consider a
parameter value of exponential magnitude only. This allows us to show a
doubly-exponential upper bound on the value of the only parameter of a PTA over
two parametric clocks and one parameter. We hope that extensions of our
techniques lead to finally establishing decidability of the long-standing open
problem of reachability in parametric timed automata with two parametric clocks
(and arbitrarily many parameters).
更新日期：2020-11-17
京公网安备 11010802027423号