995 research outputs found
Analytic aspects of the shuffle product
There exist very lucid explanations of the combinatorial origins of rational
and algebraic functions, in particular with respect to regular and context free
languages. In the search to understand how to extend these natural
correspondences, we find that the shuffle product models many key aspects of
D-finite generating functions, a class which contains algebraic. We consider
several different takes on the shuffle product, shuffle closure, and shuffle
grammars, and give explicit generating function consequences. In the process,
we define a grammar class that models D-finite generating functions
Context-free pairs of groups I: Context-free pairs and graphs
Let be a finitely generated group, a finite set of generators and
a subgroup of . We call the pair context-free if the set of all
words over that reduce in to an element of is a context-free
language. When is trivial, itself is called context-free; context-free
groups have been classified more than 20 years ago in celebrated work of Muller
and Schupp as the virtually free groups.
Here, we derive some basic properties of such group pairs. Context-freeness
is independent of the choice of the generating set. It is preserved under
finite index modifications of and finite index enlargements of . If
is virtually free and is finitely generated then is context-free. A
basic tool is the following: is context-free if and only if the
Schreier graph of with respect to is a context-free graph
Applications of Evolutionary Algorithms in Formal Languages
Starting from the model proposed by means of Grammatical Evolution, we extend the applicability of the parallel and cooperative searching processes of Evolutionary Algorithms to a new topic: Tree Adjoining Grammar parsing. We evolved derived trees using a string-tree-representation.We also used a linear matching function to compare the yield of a derived tree with a given input. The running tests presented several encouraging results. A post running analysis allowed us to propose several research directions for extending the currently known computational mechanisms in the mildly context sensitive class of languages
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
mARC: Memory by Association and Reinforcement of Contexts
This paper introduces the memory by Association and Reinforcement of Contexts
(mARC). mARC is a novel data modeling technology rooted in the second
quantization formulation of quantum mechanics. It is an all-purpose incremental
and unsupervised data storage and retrieval system which can be applied to all
types of signal or data, structured or unstructured, textual or not. mARC can
be applied to a wide range of information clas-sification and retrieval
problems like e-Discovery or contextual navigation. It can also for-mulated in
the artificial life framework a.k.a Conway "Game Of Life" Theory. In contrast
to Conway approach, the objects evolve in a massively multidimensional space.
In order to start evaluating the potential of mARC we have built a mARC-based
Internet search en-gine demonstrator with contextual functionality. We compare
the behavior of the mARC demonstrator with Google search both in terms of
performance and relevance. In the study we find that the mARC search engine
demonstrator outperforms Google search by an order of magnitude in response
time while providing more relevant results for some classes of queries
Tracing monadic computations and representing effects
In functional programming, monads are supposed to encapsulate computations,
effectfully producing the final result, but keeping to themselves the means of
acquiring it. For various reasons, we sometimes want to reveal the internals of
a computation. To make that possible, in this paper we introduce monad
transformers that add the ability to automatically accumulate observations
about the course of execution as an effect. We discover that if we treat the
resulting trace as the actual result of the computation, we can find new
functionality in existing monads, notably when working with non-terminating
computations.Comment: In Proceedings MSFP 2012, arXiv:1202.240
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