3,225 research outputs found
Automata and rational expressions
This text is an extended version of the chapter 'Automata and rational
expressions' in the AutoMathA Handbook that will appear soon, published by the
European Science Foundation and edited by JeanEricPin
Sound and complete axiomatizations of coalgebraic language equivalence
Coalgebras provide a uniform framework to study dynamical systems, including
several types of automata. In this paper, we make use of the coalgebraic view
on systems to investigate, in a uniform way, under which conditions calculi
that are sound and complete with respect to behavioral equivalence can be
extended to a coarser coalgebraic language equivalence, which arises from a
generalised powerset construction that determinises coalgebras. We show that
soundness and completeness are established by proving that expressions modulo
axioms of a calculus form the rational fixpoint of the given type functor. Our
main result is that the rational fixpoint of the functor , where is a
monad describing the branching of the systems (e.g. non-determinism, weights,
probability etc.), has as a quotient the rational fixpoint of the
"determinised" type functor , a lifting of to the category of
-algebras. We apply our framework to the concrete example of weighted
automata, for which we present a new sound and complete calculus for weighted
language equivalence. As a special case, we obtain non-deterministic automata,
where we recover Rabinovich's sound and complete calculus for language
equivalence.Comment: Corrected version of published journal articl
Towards a Uniform Theory of Effectful State Machines
Using recent developments in coalgebraic and monad-based semantics, we
present a uniform study of various notions of machines, e.g. finite state
machines, multi-stack machines, Turing machines, valence automata, and weighted
automata. They are instances of Jacobs' notion of a T-automaton, where T is a
monad. We show that the generic language semantics for T-automata correctly
instantiates the usual language semantics for a number of known classes of
machines/languages, including regular, context-free, recursively-enumerable and
various subclasses of context free languages (e.g. deterministic and real-time
ones). Moreover, our approach provides new generic techniques for studying the
expressivity power of various machine-based models.Comment: final version accepted by TOC
Parametrized Stochastic Grammars for RNA Secondary Structure Prediction
We propose a two-level stochastic context-free grammar (SCFG) architecture
for parametrized stochastic modeling of a family of RNA sequences, including
their secondary structure. A stochastic model of this type can be used for
maximum a posteriori estimation of the secondary structure of any new sequence
in the family. The proposed SCFG architecture models RNA subsequences
comprising paired bases as stochastically weighted Dyck-language words, i.e.,
as weighted balanced-parenthesis expressions. The length of each run of
unpaired bases, forming a loop or a bulge, is taken to have a phase-type
distribution: that of the hitting time in a finite-state Markov chain. Without
loss of generality, each such Markov chain can be taken to have a bounded
complexity. The scheme yields an overall family SCFG with a manageable number
of parameters.Comment: 5 pages, submitted to the 2007 Information Theory and Applications
Workshop (ITA 2007
Computation of distances for regular and context-free probabilistic languages
Several mathematical distances between probabilistic languages have been investigated in the literature, motivated by applications in language modeling, computational biology, syntactic pattern matching and machine learning. In most cases, only pairs of probabilistic regular languages were considered. In this paper we extend the previous results to pairs of languages generated by a probabilistic context-free grammar and a probabilistic finite automaton.PostprintPeer reviewe
Inertial Frame Independent Forcing for Discrete Velocity Boltzmann Equation: Implications for Filtered Turbulence Simulation
We present a systematic derivation of a model based on the central moment
lattice Boltzmann equation that rigorously maintains Galilean invariance of
forces to simulate inertial frame independent flow fields. In this regard, the
central moments, i.e. moments shifted by the local fluid velocity, of the
discrete source terms of the lattice Boltzmann equation are obtained by
matching those of the continuous full Boltzmann equation of various orders.
This results in an exact hierarchical identity between the central moments of
the source terms of a given order and the components of the central moments of
the distribution functions and sources of lower orders. The corresponding
source terms in velocity space are then obtained from an exact inverse
transformation due to a suitable choice of orthogonal basis for moments.
Furthermore, such a central moment based kinetic model is further extended by
incorporating reduced compressibility effects to represent incompressible flow.
Moreover, the description and simulation of fluid turbulence for full or any
subset of scales or their averaged behavior should remain independent of any
inertial frame of reference. Thus, based on the above formulation, a new
approach in lattice Boltzmann framework to incorporate turbulence models for
simulation of Galilean invariant statistical averaged or filtered turbulent
fluid motion is discussed.Comment: 37 pages, 1 figur
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