37,917 research outputs found
A Symbolic Transformation Language and its Application to a Multiscale Method
The context of this work is the design of a software, called MEMSALab,
dedicated to the automatic derivation of multiscale models of arrays of micro-
and nanosystems. In this domain a model is a partial differential equation.
Multiscale methods approximate it by another partial differential equation
which can be numerically simulated in a reasonable time. The challenge consists
in taking into account a wide range of geometries combining thin and periodic
structures with the possibility of multiple nested scales.
In this paper we present a transformation language that will make the
development of MEMSALab more feasible. It is proposed as a Maple package for
rule-based programming, rewriting strategies and their combination with
standard Maple code. We illustrate the practical interest of this language by
using it to encode two examples of multiscale derivations, namely the two-scale
limit of the derivative operator and the two-scale model of the stationary heat
equation.Comment: 36 page
From Finite Automata to Regular Expressions and Back--A Summary on Descriptional Complexity
The equivalence of finite automata and regular expressions dates back to the
seminal paper of Kleene on events in nerve nets and finite automata from 1956.
In the present paper we tour a fragment of the literature and summarize results
on upper and lower bounds on the conversion of finite automata to regular
expressions and vice versa. We also briefly recall the known bounds for the
removal of spontaneous transitions (epsilon-transitions) on non-epsilon-free
nondeterministic devices. Moreover, we report on recent results on the average
case descriptional complexity bounds for the conversion of regular expressions
to finite automata and brand new developments on the state elimination
algorithm that converts finite automata to regular expressions.Comment: In Proceedings AFL 2014, arXiv:1405.527
A General Framework for the Derivation of Regular Expressions
The aim of this paper is to design a theoretical framework that allows us to
perform the computation of regular expression derivatives through a space of
generic structures. Thanks to this formalism, the main properties of regular
expression derivation, such as the finiteness of the set of derivatives, need
only be stated and proved one time, at the top level. Moreover, it is shown how
to construct an alternating automaton associated with the derivation of a
regular expression in this general framework. Finally, Brzozowski's derivation
and Antimirov's derivation turn out to be a particular case of this general
scheme and it is shown how to construct a DFA, a NFA and an AFA for both of
these derivations.Comment: 22 page
A Computational Interpretation of Context-Free Expressions
We phrase parsing with context-free expressions as a type inhabitation
problem where values are parse trees and types are context-free expressions. We
first show how containment among context-free and regular expressions can be
reduced to a reachability problem by using a canonical representation of
states. The proofs-as-programs principle yields a computational interpretation
of the reachability problem in terms of a coercion that transforms the parse
tree for a context-free expression into a parse tree for a regular expression.
It also yields a partial coercion from regular parse trees to context-free
ones. The partial coercion from the trivial language of all words to a
context-free expression corresponds to a predictive parser for the expression
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