972 research outputs found
Random Generation of Unary Finite Automata over the Domain of the Regular Languages
We show that the standard methods for the random generation of finite automata are inadequate if considered over the domain of the regular languages, for small n. We then present a consolidated, practical method for the random generation of unary finite automata over the domain of the regular languages.
Logics for Unranked Trees: An Overview
Labeled unranked trees are used as a model of XML documents, and logical
languages for them have been studied actively over the past several years. Such
logics have different purposes: some are better suited for extracting data,
some for expressing navigational properties, and some make it easy to relate
complex properties of trees to the existence of tree automata for those
properties. Furthermore, logics differ significantly in their model-checking
properties, their automata models, and their behavior on ordered and unordered
trees. In this paper we present a survey of logics for unranked trees
Propagating Regular Counting Constraints
Constraints over finite sequences of variables are ubiquitous in sequencing
and timetabling. Moreover, the wide variety of such constraints in practical
applications led to general modelling techniques and generic propagation
algorithms, often based on deterministic finite automata (DFA) and their
extensions. We consider counter-DFAs (cDFA), which provide concise models for
regular counting constraints, that is constraints over the number of times a
regular-language pattern occurs in a sequence. We show how to enforce domain
consistency in polynomial time for atmost and atleast regular counting
constraints based on the frequent case of a cDFA with only accepting states and
a single counter that can be incremented by transitions. We also prove that the
satisfaction of exact regular counting constraints is NP-hard and indicate that
an incomplete algorithm for exact regular counting constraints is faster and
provides more pruning than the existing propagator from [3]. Regular counting
constraints are closely related to the CostRegular constraint but contribute
both a natural abstraction and some computational advantages.Comment: Includes a SICStus Prolog source file with the propagato
Calibrating Generative Models: The Probabilistic Chomsky-Schützenberger 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
Controlled non uniform random generation of decomposable structures
Consider a class of decomposable combinatorial structures, using different
types of atoms \Atoms = \{\At_1,\ldots ,\At_{|{\Atoms}|}\}. We address the
random generation of such structures with respect to a size and a targeted
distribution in of its \emph{distinguished} atoms. We consider two
variations on this problem. In the first alternative, the targeted distribution
is given by real numbers \TargFreq_1, \ldots, \TargFreq_k such that 0 <
\TargFreq_i < 1 for all and \TargFreq_1+\cdots+\TargFreq_k \leq 1. We
aim to generate random structures among the whole set of structures of a given
size , in such a way that the {\em expected} frequency of any distinguished
atom \At_i equals \TargFreq_i. We address this problem by weighting the
atoms with a -tuple \Weights of real-valued weights, inducing a weighted
distribution over the set of structures of size . We first adapt the
classical recursive random generation scheme into an algorithm taking
\bigO{n^{1+o(1)}+mn\log{n}} arithmetic operations to draw structures from
the \Weights-weighted distribution. Secondly, we address the analytical
computation of weights such that the targeted frequencies are achieved
asymptotically, i. e. for large values of . We derive systems of functional
equations whose resolution gives an explicit relationship between \Weights
and \TargFreq_1, \ldots, \TargFreq_k. Lastly, we give an algorithm in
\bigO{k n^4} for the inverse problem, {\it i.e.} computing the frequencies
associated with a given -tuple \Weights of weights, and an optimized
version in \bigO{k n^2} in the case of context-free languages. This allows
for a heuristic resolution of the weights/frequencies relationship suitable for
complex specifications. In the second alternative, the targeted distribution is
given by a natural numbers such that
where is the number of undistinguished atoms.
The structures must be generated uniformly among the set of structures of size
that contain {\em exactly} atoms \At_i (). We give
a \bigO{r^2\prod_{i=1}^k n_i^2 +m n k \log n} algorithm for generating
structures, which simplifies into a \bigO{r\prod_{i=1}^k n_i +m n} for
regular specifications
Modeling Graph Languages with Grammars Extracted via Tree Decompositions
Work on probabilistic models of natural language tends to focus on strings and trees, but there is increasing interest in more general graph-shaped structures since they seem to be better suited for representing natural language semantics, ontologies, or other varieties of knowledge structures. However, while there are relatively simple approaches to defining generative models over strings and trees, it has proven more challenging for more general graphs. This paper describes a natural generalization of the n-gram to graphs, making use of Hyperedge Replacement Grammars to define generative models of graph languages.9 page(s
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