
On Computing the Total Variation Distance of Hidden Markov Models
We prove results on the decidability and complexity of computing the tot...
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A Nivat Theorem for Weighted Alternating Automata over Commutative Semirings
In this paper, we give a Nivatlike characterization for weighted altern...
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Testing Membership for Timed Automata
Given a timed automata which admits thick components and a timed word x,...
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Genetic Algorithm for the Weight Maximization Problem on Weighted Automata
The weight maximization problem (WMP) is the problem of finding the word...
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Approximate Bisimulation Minimisation
We propose polynomialtime algorithms to minimise labelled Markov chains...
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Approximating probabilistic models as weighted finite automata
Weighted finite automata (WFA) are often used to represent probabilistic...
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Quantitative Matrix Simulation
We introduce notions of simulation between semiringweighted automata as...
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The BigO Problem for Labelled Markov Chains and Weighted Automata
Given two weighted automata, we consider the problem of whether one is bigO of the other, i.e., if the weight of every finite word in the first is not greater than some constant multiple of the weight in the second. We show that the problem is undecidable, even for the instantiation of weighted automata as labelled Markov chains. Moreover, even when it is known that one weighted automaton is bigO of another, the problem of finding or approximating the associated constant is also undecidable. Our positive results show that the bigO problem is polynomialtime solvable for unambiguous automata, coNPcomplete for unlabelled weighted automata (i.e., when the alphabet is a single character) and decidable, subject to Schanuel's conjecture, when the language is bounded (i.e., a subset of w_1^*… w_m^* for some finite words w_1,…,w_m). On labelled Markov chains, the problem can be restated as a ratio total variation distance, which, instead of finding the maximum difference between the probabilities of any two events, finds the maximum ratio between the probabilities of any two events. The problem is related to ϵdifferential privacy, for which the optimal constant of the bigO notation is exactly (ϵ).
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