12,201 research outputs found
Rational stochastic languages
The goal of the present paper is to provide a systematic and comprehensive
study of rational stochastic languages over a semiring K \in {Q, Q +, R, R+}. A
rational stochastic language is a probability distribution over a free monoid
\Sigma^* which is rational over K, that is which can be generated by a
multiplicity automata with parameters in K. We study the relations between the
classes of rational stochastic languages S rat K (\Sigma). We define the notion
of residual of a stochastic language and we use it to investigate properties of
several subclasses of rational stochastic languages. Lastly, we study the
representation of rational stochastic languages by means of multiplicity
automata.Comment: 35 page
Calibrating Generative Models: The Probabilistic Chomsky-SchĂŒtzenberger Hierarchy
A probabilistic ChomskyâSchĂŒtzenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular languages, using analytic tools adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning
Computation of distances for regular and context-free probabilistic languages
Several mathematical distances between probabilistic languages have been investigated in the literature, motivated by applications in language modeling, computational biology, syntactic pattern matching and machine learning. In most cases, only pairs of probabilistic regular languages were considered. In this paper we extend the previous results to pairs of languages generated by a probabilistic context-free grammar and a probabilistic finite automaton.PostprintPeer reviewe
On the Problem of Computing the Probability of Regular Sets of Trees
We consider the problem of computing the probability of regular languages of
infinite trees with respect to the natural coin-flipping measure. We propose an
algorithm which computes the probability of languages recognizable by
\emph{game automata}. In particular this algorithm is applicable to all
deterministic automata. We then use the algorithm to prove through examples
three properties of measure: (1) there exist regular sets having irrational
probability, (2) there exist comeager regular sets having probability and
(3) the probability of \emph{game languages} , from automata theory,
is if is odd and is otherwise
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