33,148 research outputs found
Power of Randomization in Automata on Infinite Strings
Probabilistic B\"uchi Automata (PBA) are randomized, finite state automata
that process input strings of infinite length. Based on the threshold chosen
for the acceptance probability, different classes of languages can be defined.
In this paper, we present a number of results that clarify the power of such
machines and properties of the languages they define. The broad themes we focus
on are as follows. We present results on the decidability and precise
complexity of the emptiness, universality and language containment problems for
such machines, thus answering questions central to the use of these models in
formal verification. Next, we characterize the languages recognized by PBAs
topologically, demonstrating that though general PBAs can recognize languages
that are not regular, topologically the languages are as simple as
\omega-regular languages. Finally, we introduce Hierarchical PBAs, which are
syntactically restricted forms of PBAs that are tractable and capture exactly
the class of \omega-regular languages
Topological Complexity of omega-Powers : Extended Abstract
This is an extended abstract presenting new results on the topological
complexity of omega-powers (which are included in a paper "Classical and
effective descriptive complexities of omega-powers" available from
arXiv:0708.4176) and reflecting also some open questions which were discussed
during the Dagstuhl seminar on "Topological and Game-Theoretic Aspects of
Infinite Computations" 29.06.08 - 04.07.08
The omega-inequality problem for concatenation hierarchies of star-free languages
The problem considered in this paper is whether an inequality of omega-terms
is valid in a given level of a concatenation hierarchy of star-free languages.
The main result shows that this problem is decidable for all (integer and half)
levels of the Straubing-Th\'erien hierarchy
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