17,791 research outputs found
Non-deterministic Weighted Automata on Random Words
We present the first study of non-deterministic weighted automata under probabilistic semantics. In this semantics words are random events, generated by a Markov chain, and functions computed by weighted automata are random variables. We consider the probabilistic questions of computing the expected value and the cumulative distribution for such random variables.
The exact answers to the probabilistic questions for non-deterministic automata can be irrational and are uncomputable in general. To overcome this limitation, we propose an approximation algorithm for the probabilistic questions, which works in exponential time in the automaton and polynomial time in the Markov chain. We apply this result to show that non-deterministic automata can be effectively determinised with respect to the standard deviation metric
On the Complexity of the Equivalence Problem for Probabilistic Automata
Checking two probabilistic automata for equivalence has been shown to be a
key problem for efficiently establishing various behavioural and anonymity
properties of probabilistic systems. In recent experiments a randomised
equivalence test based on polynomial identity testing outperformed
deterministic algorithms. In this paper we show that polynomial identity
testing yields efficient algorithms for various generalisations of the
equivalence problem. First, we provide a randomized NC procedure that also
outputs a counterexample trace in case of inequivalence. Second, we show how to
check for equivalence two probabilistic automata with (cumulative) rewards. Our
algorithm runs in deterministic polynomial time, if the number of reward
counters is fixed. Finally we show that the equivalence problem for
probabilistic visibly pushdown automata is logspace equivalent to the
Arithmetic Circuit Identity Testing problem, which is to decide whether a
polynomial represented by an arithmetic circuit is identically zero.Comment: technical report for a FoSSaCS'12 pape
On Zone-Based Analysis of Duration Probabilistic Automata
We propose an extension of the zone-based algorithmics for analyzing timed
automata to handle systems where timing uncertainty is considered as
probabilistic rather than set-theoretic. We study duration probabilistic
automata (DPA), expressing multiple parallel processes admitting memoryfull
continuously-distributed durations. For this model we develop an extension of
the zone-based forward reachability algorithm whose successor operator is a
density transformer, thus providing a solution to verification and performance
evaluation problems concerning acyclic DPA (or the bounded-horizon behavior of
cyclic DPA).Comment: In Proceedings INFINITY 2010, arXiv:1010.611
Learning probability distributions generated by finite-state machines
We review methods for inference of probability distributions generated by probabilistic automata and related models for sequence generation. We focus on methods that can be proved to learn in the inference
in the limit and PAC formal models. The methods we review are state merging and state splitting methods for probabilistic deterministic automata and the recently developed spectral method for nondeterministic probabilistic automata. In both cases, we derive them from a high-level algorithm described in terms of the Hankel matrix of the distribution to be learned, given as an oracle, and then describe how to adapt that algorithm to account for the error introduced by a finite sample.Peer ReviewedPostprint (author's final draft
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