Exact and Approximate Determinization of Discounted-Sum Automata

@article{Boker2014ExactAA,
  title={Exact and Approximate Determinization of Discounted-Sum Automata},
  author={Udi Boker and Thomas A. Henzinger},
  journal={Log. Methods Comput. Sci.},
  year={2014},
  volume={10}
}
A discounted-sum automaton (NDA) is a nondeterministic finite automaton with edge weights, valuing a run by the discounted sum of visited edge weights. More precisely, the weight in the i-th position of the run is divided by $\lambda^i$, where the discount factor $\lambda$ is a fixed rational number greater than 1. The value of a word is the minimal value of the automaton runs on it. Discounted summation is a common and useful measuring scheme, especially for infinite sequences, reflecting the… 
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References

SHOWING 1-10 OF 21 REFERENCES
Determinizing Discounted-Sum Automata
TLDR
It is proved that the class of NDAs with integral discount factors enjoys closure under the algebraic operations min, max, addition, and subtraction, which is not the case for general NDAs nor for deterministic NDAs.
Approximate Determinization of Quantitative Automata
TLDR
This work defines approximate determinization with respect to a distance function, and provides an alternative construction that is singly exponential in the discount factor, in the precision, and in the number of states, and proves matching lower bounds, showing exponential dependency on each of these three parameters.
Alternating Weighted Automata
TLDR
It is shown that alternation brings more expressive power than nondeterminism for limit average and discounted sum, and the expressive power of the various classes of alternating and nondeterministic weighted automata over infinite words is compared.
Expressiveness and Closure Properties for Quantitative Languages
TLDR
It is shown that the set of words with value greater than a threshold can be non-omega-regular for deterministic limit-average and discounted-sum automata, while this set is always omega-regular when the threshold is isolated, and it is proved that the omega- regular language is robust against small perturbations of the transition weights.
Quantitative Languages Defined by Functional Automata
TLDR
This paper investigates functional weighted automata for four different measures: the sum, the mean, the discounted sum of weights along edges and the ratio between rewards and costs, and shows that functionality is decidable for the four measures.
An Approximate Determinization Algorithm for Weighted Finite-State Automata
TLDR
A new approximate determinization algorithm is designed that produces a deterministic weighted finite-state automaton that preserves the strings of a weighted language but not necessarily their weights, and can reduce automatic speech recognition memory requirements by 25—35% with negligible effects on recognition time and accuracy.
What's Decidable about Weighted Automata?
TLDR
It follows from Krob's results that the universality problem is decidable for weighted automata with weights in N ∪ {∞}, and that the equality problem is undecidable when the weights are in N €∞.
Quantitative languages
TLDR
A notion of quantitative simulation that is decidable and implies language inclusion is introduced, and it is shown that most classes of weighted automata cannot be determinized.
Handbook of Weighted Automata
TLDR
This book covers all the main aspects of weighted automata and formal power series methods, ranging from theory to applications, and presents a detailed survey of the state of the art and pointers to future research.
...
...