5,160 research outputs found
Spectral learning of general weighted automata via constrained matrix completion
Student Paper Awards NIPS 2012Many tasks in text and speech processing and computational biology require estimating
functions mapping strings to real numbers. A broad class of such functions
can be defined by weighted automata. Spectral methods based on the singular
value decomposition of a Hankel matrix have been recently proposed for
learning a probability distribution represented by a weighted automaton from a
training sample drawn according to this same target distribution. In this paper, we
show how spectral methods can be extended to the problem of learning a general
weighted automaton from a sample generated by an arbitrary distribution. The
main obstruction to this approach is that, in general, some entries of the Hankel
matrix may be missing. We present a solution to this problem based on solving a
constrained matrix completion problem. Combining these two ingredients, matrix
completion and spectral method, a whole new family of algorithms for learning
general weighted automata is obtained. We present generalization bounds for a
particular algorithm in this family. The proofs rely on a joint stability analysis of
matrix completion and spectral learning.Peer ReviewedAward-winningPostprint (published version
Exact and Approximate Determinization of Discounted-Sum Automata
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
, where the discount factor 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 assumption that earlier weights are more
important than later weights. Unfortunately, determinization of NDAs, which is
often essential in formal verification, is, in general, not possible. We
provide positive news, showing that every NDA with an integral discount factor
is determinizable. We complete the picture by proving that the integers
characterize exactly the discount factors that guarantee determinizability: for
every nonintegral rational discount factor , there is a
nondeterminizable -NDA. We also prove 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. For general NDAs, we look into approximate determinization,
which is always possible as the influence of a word's suffix decays. We show
that the naive approach, of unfolding the automaton computations up to a
sufficient level, is doubly exponential in the discount factor. We provide an
alternative construction for approximate determinization, which is singly
exponential in the discount factor, in the precision, and in the number of
states. We also prove matching lower bounds, showing that the exponential
dependency on each of these three parameters cannot be avoided. All our results
hold equally for automata over finite words and for automata over infinite
words
*-Continuous Kleene -Algebras for Energy Problems
Energy problems are important in the formal analysis of embedded or
autonomous systems. Using recent results on star-continuous Kleene
omega-algebras, we show here that energy problems can be solved by algebraic
manipulations on the transition matrix of energy automata. To this end, we
prove general results about certain classes of finitely additive functions on
complete lattices which should be of a more general interest.Comment: In Proceedings FICS 2015, arXiv:1509.0282
Kleene Algebras and Semimodules for Energy Problems
With the purpose of unifying a number of approaches to energy problems found
in the literature, we introduce generalized energy automata. These are finite
automata whose edges are labeled with energy functions that define how energy
levels evolve during transitions. Uncovering a close connection between energy
problems and reachability and B\"uchi acceptance for semiring-weighted
automata, we show that these generalized energy problems are decidable. We also
provide complexity results for important special cases
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