5,817 research outputs found
Speech Recognition by Composition of Weighted Finite Automata
We present a general framework based on weighted finite automata and weighted
finite-state transducers for describing and implementing speech recognizers.
The framework allows us to represent uniformly the information sources and data
structures used in recognition, including context-dependent units,
pronunciation dictionaries, language models and lattices. Furthermore, general
but efficient algorithms can used for combining information sources in actual
recognizers and for optimizing their application. In particular, a single
composition algorithm is used both to combine in advance information sources
such as language models and dictionaries, and to combine acoustic observations
and information sources dynamically during recognition.Comment: 24 pages, uses psfig.st
Eilenberg Theorems for Free
Eilenberg-type correspondences, relating varieties of languages (e.g. of
finite words, infinite words, or trees) to pseudovarieties of finite algebras,
form the backbone of algebraic language theory. Numerous such correspondences
are known in the literature. We demonstrate that they all arise from the same
recipe: one models languages and the algebras recognizing them by monads on an
algebraic category, and applies a Stone-type duality. Our main contribution is
a variety theorem that covers e.g. Wilke's and Pin's work on
-languages, the variety theorem for cost functions of Daviaud,
Kuperberg, and Pin, and unifies the two previous categorical approaches of
Boja\'nczyk and of Ad\'amek et al. In addition we derive a number of new
results, including an extension of the local variety theorem of Gehrke,
Grigorieff, and Pin from finite to infinite words
The separation problem for regular languages by piecewise testable languages
Separation is a classical problem in mathematics and computer science. It
asks whether, given two sets belonging to some class, it is possible to
separate them by another set of a smaller class. We present and discuss the
separation problem for regular languages. We then give a direct polynomial time
algorithm to check whether two given regular languages are separable by a
piecewise testable language, that is, whether a sentence can
witness that the languages are indeed disjoint. The proof is a reformulation
and a refinement of an algebraic argument already given by Almeida and the
second author
Uniform Random Sampling of Traces in Very Large Models
This paper presents some first results on how to perform uniform random walks
(where every trace has the same probability to occur) in very large models. The
models considered here are described in a succinct way as a set of
communicating reactive modules. The method relies upon techniques for counting
and drawing uniformly at random words in regular languages. Each module is
considered as an automaton defining such a language. It is shown how it is
possible to combine local uniform drawings of traces, and to obtain some global
uniform random sampling, without construction of the global model
Sequential and asynchronous processes driven by stochastic or quantum grammars and their application to genomics: a survey
We present the formalism of sequential and asynchronous processes defined in
terms of random or quantum grammars and argue that these processes have
relevance in genomics. To make the article accessible to the
non-mathematicians, we keep the mathematical exposition as elementary as
possible, focusing on some general ideas behind the formalism and stating the
implications of the known mathematical results. We close with a set of open
challenging problems.Comment: Presented at the European Congress on Mathematical and Theoretical
Biology, Dresden 18--22 July 200
- …