-
Selection by year
-
Selection by authors
-
Complete lists
akshay:hal-01245037
S. Akshay, B. Genest, V. Karelovic, N. Vyas. On Regularity of unary Probabilistic Automata. In STACS 2016, STACS 2016, Orléans, France, 2016.
Download [help]
Download paper:
Adobe portable document (pdf) 
Copyright notice:
This material is presented to ensure timely dissemination of scholarly and
technical work. Copyright and all rights therein are retained by authors or
by other copyright holders. All persons copying this information are expected
to adhere to the terms and constraints invoked by each author's
copyright. These works may not be reposted without the explicit permission of
the copyright holder.
This page is automatically generated by bib2html v216, © INRIA 2002-2007, Projet Lagadic
Abstract
The quantitative verification of Probabilistic Automata (PA) is undecidable in general. Unary PA are a simpler model where the choice of action is fixed. Still, the quantitative verification problem is open and known to be as hard as Skolem's problem, a problem on linear recurrence sequences, whose decidability is open for at least 40 years. In this paper, we approach this problem by studying the languages generated by unary PAs (as defined below), whose regularity would entail the decidability of quantitative verification. Given an initial distribution, we represent the trajectory of a unary PA over time as an infinite word over a finite alphabet, where the n th letter represents a probability range after n steps. We extend this to a language of trajectories (a set of words), one trajectory for each initial distribution from a (possibly infinite) set. We show that if the eigenvalues of the transition matrix associated with the unary PA are all distinct positive real numbers, then the language is effectively regular. Further, we show that this result is at the boundary of regularity, as non-regular languages can be generated when the restrictions are even slightly relaxed. The regular representation of the language allows us to reason about more general properties, e.g., robustness of a regular property in a neighbourhood around a given distribution
Contact
Blaise Genest http://perso.crans.org/~genest/
BibTex Reference
@InProceedings{akshay:hal-01245037,
Author = {Akshay, S. and Genest, B. and Karelovic, V. and Vyas, N.},
Title = {On Regularity of unary Probabilistic Automata},
BookTitle = {STACS 2016},
Series = {STACS 2016},
Address = {Orléans, France},
Year = {2016}
}
EndNote Reference [help]
Get EndNote Reference (.ref)