26,236 research outputs found
Descriptional complexity of multi-continuous grammars
The present paper discusses multi-continuous grammars and their descriptional complexity with respect to the number of nonterminals. It proves that six-nonterminal multi-continuous grammars characterize the family of recursively enumerable languages. In addition, this paper formulates an open problem area closely related to this characterization
Inducing Probabilistic Grammars by Bayesian Model Merging
We describe a framework for inducing probabilistic grammars from corpora of
positive samples. First, samples are {\em incorporated} by adding ad-hoc rules
to a working grammar; subsequently, elements of the model (such as states or
nonterminals) are {\em merged} to achieve generalization and a more compact
representation. The choice of what to merge and when to stop is governed by the
Bayesian posterior probability of the grammar given the data, which formalizes
a trade-off between a close fit to the data and a default preference for
simpler models (`Occam's Razor'). The general scheme is illustrated using three
types of probabilistic grammars: Hidden Markov models, class-based -grams,
and stochastic context-free grammars.Comment: To appear in Grammatical Inference and Applications, Second
International Colloquium on Grammatical Inference; Springer Verlag, 1994. 13
page
Two power-decreasing derivation restrictions in generalized scattered context grammars
The present paper introduces and discusses generalized scattered context grammars that are based upon sequences of productions whose left-hand sides are formed by nonterminal strings, not just single nonterminals. It places two restrictions on the derivations in these grammars. More specifically, let k be a positive integer. The first restriction requires that all rewritten symbols occur within the first k symbols of the first continuous block of nonterminals in the sentential form during every derivation step. The other restriction defines derivations over sentential forms containing no more than k occurrences of nonterminals. As its main result, the paper demonstrates that both restrictions decrease the generative power of these grammars to the power of context-free grammars
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
KMS states on Quantum Grammars
We consider quantum (unitary) continuous time evolution of spins on a lattice
together with quantum evolution of the lattice itself. In physics such
evolution was discussed in connection with quantum gravity. It is also related
to what is called quantum circuits, one of the incarnations of a quantum
computer. We consider simpler models for which one can obtain exact
mathematical results. We prove existence of the dynamics in both Schroedinger
and Heisenberg pictures, construct KMS states on appropriate C*-algebras. We
show (for high temperatures) that for each system where the lattice undergoes
quantum evolution, there is a natural scaling leading to a quantum spin system
on a fixed lattice, defined by a renormalized Hamiltonian.Comment: 22 page
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