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- Publisher
- Association for Computing Machinery
- Copyright
- Copyright © 2017 by ACM Inc.
- ISSN
- 2372-3491
- DOI
- 10.1145/3157831.3157833
- Publisher site
- See Article on Publisher Site
Abstract
Undecidability Results for Probabilistic Automata Nathanael Fijalkow, Alan Turing Institute of Data Science and University of Warwick, UK The model of probabilistic automata was introduced by Rabin in 1963. Ever since, undecidability results were obtained for this model, showing that although simple, it is very expressive. This paper provides streamlined constructions implying the most important negative results, including the celebrated inapproximability result of Condon and Lipton. 1. INTRODUCTION AND DEFINITIONS By way of introducing the model of probabilistic automata de ned by Rabin [Rabin 1963], we highlight its characteristic features. As a starting point, we model processes: ” with nitely many states, each of them representing a con guration of the process, ” evolving at discrete time steps, meaning that one transition is red at each time unit leading from a state to another, ” with probabilistic behaviour, i.e. the choice of transition follows a xed probabilistic distribution. We let Q denote the nite set of states. A (probabilistic) distribution over Q is a P function : Q ! [0, 1] such that q2Q (q) = 1. The set of distributions over Q is denoted D(Q). Reactive and generative processes. An important distinction to be made for probabilistic
Journal
ACM SIGLOG News – Association for Computing Machinery
Published: Nov 3, 2017