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arXiv · 1109.2536

Power of Randomization in Automata on Infinite Strings

Rohit Chadha·A. Prasad Sistla·Mahesh Viswanathan
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Abstract

Probabilistic Büchi 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 ω-regular languages. Finally, we introduce Hierarchical PBAs, which are syntactically restricted forms of PBAs that are tractable and capture exactly the class of ω-regular languages.

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Rohit Chadha, A. Prasad Sistla, Mahesh Viswanathan. 2011-09-28. Power of Randomization in Automata on Infinite Strings. https://doi.org/10.2168/lmcs-7(3%3A22)2011

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