2,981 research outputs found
Calibrating Generative Models: The Probabilistic Chomsky-SchĂĽtzenberger Hierarchy
A probabilistic Chomsky–Schützenberger 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
Coding-theorem Like Behaviour and Emergence of the Universal Distribution from Resource-bounded Algorithmic Probability
Previously referred to as `miraculous' in the scientific literature because
of its powerful properties and its wide application as optimal solution to the
problem of induction/inference, (approximations to) Algorithmic Probability
(AP) and the associated Universal Distribution are (or should be) of the
greatest importance in science. Here we investigate the emergence, the rates of
emergence and convergence, and the Coding-theorem like behaviour of AP in
Turing-subuniversal models of computation. We investigate empirical
distributions of computing models in the Chomsky hierarchy. We introduce
measures of algorithmic probability and algorithmic complexity based upon
resource-bounded computation, in contrast to previously thoroughly investigated
distributions produced from the output distribution of Turing machines. This
approach allows for numerical approximations to algorithmic
(Kolmogorov-Chaitin) complexity-based estimations at each of the levels of a
computational hierarchy. We demonstrate that all these estimations are
correlated in rank and that they converge both in rank and values as a function
of computational power, despite fundamental differences between computational
models. In the context of natural processes that operate below the Turing
universal level because of finite resources and physical degradation, the
investigation of natural biases stemming from algorithmic rules may shed light
on the distribution of outcomes. We show that up to 60\% of the
simplicity/complexity bias in distributions produced even by the weakest of the
computational models can be accounted for by Algorithmic Probability in its
approximation to the Universal Distribution.Comment: 27 pages main text, 39 pages including supplement. Online complexity
calculator: http://complexitycalculator.com
Advances and applications of automata on words and trees : executive summary
Seminar: 10501 - Advances and Applications of Automata on Words and Trees. The aim of the seminar was to discuss and systematize the recent fast progress in automata theory and to identify important directions for future research. For this, the seminar brought together more than 40 researchers from automata theory and related fields of applications. We had 19 talks of 30 minutes and 5 one-hour lectures leaving ample room for discussions. In the following we describe the topics in more detail
Advances and applications of automata on words and trees : abstracts collection
From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 "Advances and Applications of Automata on Words and Trees" was held in Schloss Dagstuhl - Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available
Probabilistic regular graphs
Deterministic graph grammars generate regular graphs, that form a structural
extension of configuration graphs of pushdown systems. In this paper, we study
a probabilistic extension of regular graphs obtained by labelling the terminal
arcs of the graph grammars by probabilities. Stochastic properties of these
graphs are expressed using PCTL, a probabilistic extension of computation tree
logic. We present here an algorithm to perform approximate verification of PCTL
formulae. Moreover, we prove that the exact model-checking problem for PCTL on
probabilistic regular graphs is undecidable, unless restricting to qualitative
properties. Our results generalise those of EKM06, on probabilistic pushdown
automata, using similar methods combined with graph grammars techniques.Comment: In Proceedings INFINITY 2010, arXiv:1010.611
Flexible RNA design under structure and sequence constraints using formal languages
The problem of RNA secondary structure design (also called inverse folding)
is the following: given a target secondary structure, one aims to create a
sequence that folds into, or is compatible with, a given structure. In several
practical applications in biology, additional constraints must be taken into
account, such as the presence/absence of regulatory motifs, either at a
specific location or anywhere in the sequence. In this study, we investigate
the design of RNA sequences from their targeted secondary structure, given
these additional sequence constraints. To this purpose, we develop a general
framework based on concepts of language theory, namely context-free grammars
and finite automata. We efficiently combine a comprehensive set of constraints
into a unifying context-free grammar of moderate size. From there, we use
generic generic algorithms to perform a (weighted) random generation, or an
exhaustive enumeration, of candidate sequences. The resulting method, whose
complexity scales linearly with the length of the RNA, was implemented as a
standalone program. The resulting software was embedded into a publicly
available dedicated web server. The applicability demonstrated of the method on
a concrete case study dedicated to Exon Splicing Enhancers, in which our
approach was successfully used in the design of \emph{in vitro} experiments.Comment: ACM BCB 2013 - ACM Conference on Bioinformatics, Computational
Biology and Biomedical Informatics (2013
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