590 research outputs found
On external presentations of infinite graphs
The vertices of a finite state system are usually a subset of the natural
numbers. Most algorithms relative to these systems only use this fact to select
vertices.
For infinite state systems, however, the situation is different: in
particular, for such systems having a finite description, each state of the
system is a configuration of some machine. Then most algorithmic approaches
rely on the structure of these configurations. Such characterisations are said
internal. In order to apply algorithms detecting a structural property (like
identifying connected components) one may have first to transform the system in
order to fit the description needed for the algorithm. The problem of internal
characterisation is that it hides structural properties, and each solution
becomes ad hoc relatively to the form of the configurations.
On the contrary, external characterisations avoid explicit naming of the
vertices. Such characterisation are mostly defined via graph transformations.
In this paper we present two kind of external characterisations:
deterministic graph rewriting, which in turn characterise regular graphs,
deterministic context-free languages, and rational graphs. Inverse substitution
from a generator (like the complete binary tree) provides characterisation for
prefix-recognizable graphs, the Caucal Hierarchy and rational graphs. We
illustrate how these characterisation provide an efficient tool for the
representation of infinite state systems
Streamability of nested word transductions
We consider the problem of evaluating in streaming (i.e., in a single
left-to-right pass) a nested word transduction with a limited amount of memory.
A transduction T is said to be height bounded memory (HBM) if it can be
evaluated with a memory that depends only on the size of T and on the height of
the input word. We show that it is decidable in coNPTime for a nested word
transduction defined by a visibly pushdown transducer (VPT), if it is HBM. In
this case, the required amount of memory may depend exponentially on the height
of the word. We exhibit a sufficient, decidable condition for a VPT to be
evaluated with a memory that depends quadratically on the height of the word.
This condition defines a class of transductions that strictly contains all
determinizable VPTs
Finite-Valued Weighted Automata
Any weighted automaton (WA) defines a relation from finite words to values: given an input word, its set of values is obtained as the set of values computed by each accepting run on that word. A WA is k-valued if the relation it defines has degree at most k, i.e., every set of values associated with an input word has cardinality at most k. We investigate the class of quantitative languages defined by k-valued automata, for all parameters k. We consider several measures to associate values with runs: sum, discounted-sum, and more generally values in groups.
We define a general procedure which decides, given a bound k and a WA over a group, whether this automaton is k-valued. We also show that any k-valued WA over a group, under some general conditions, can be decomposed as a union of k unambiguous WA. While inclusion and equivalence are undecidable problems for arbitrary sum-automata, we show, based on this decomposition, that they are decidable for k-valued sum-automata, and k-valued discounted sum-automata over inverted integer discount factors. We finally show that the quantitative Church problem is undecidable for k-valued sum-automata, even given as finite unions of deterministic sum-automata
Particle separation by phase modulated surface acoustic waves
High efficiency isolation of cells or particles from a heterogeneous mixture is a critical processing step in lab-on-a-chip devices. Acoustic techniques offer contactless and label-free manipulation, preserve viability of biological cells, and provide versatility as the applied electrical signal can be adapted to various scenarios. Conventional acoustic separation methods use time-of-flight and achieve separation up to distances of quarter wavelength with limited separation power due to slow gradients in the force. The method proposed here allows separation by half of the wavelength and can be extended by repeating the modulation pattern and can ensure maximum force acting on the particles. In this work, we propose an optimised phase modulation scheme for particle separation in a surface acoustic wave microfluidic device. An expression for the acoustic radiation force arising from the interaction between acoustic waves in the fluid was derived. We demonstrated, for the first time, that the expression of the acoustic radiation force differs in surface acoustic wave and bulk devices, due to the presence of a geometric scaling factor. Two phase modulation schemes are investigated theoretically and experimentally. Theoretical findings were experimentally validated for different mixtures of polystyrene particles confirming that the method offers high selectivity. A Monte-Carlo simulation enabled us to assess performance in real situations, including the effects of particle size variation and non-uniform acoustic field on sorting efficiency and purity, validating the ability to separate particles with high purity and high resolution
MSO definable string transductions and two-way finite state transducers
String transductions that are definable in monadic second-order (mso) logic
(without the use of parameters) are exactly those realized by deterministic
two-way finite state transducers. Nondeterministic mso definable string
transductions (i.e., those definable with the use of parameters) correspond to
compositions of two nondeterministic two-way finite state transducers that have
the finite visit property. Both families of mso definable string transductions
are characterized in terms of Hennie machines, i.e., two-way finite state
transducers with the finite visit property that are allowed to rewrite their
input tape.Comment: 63 pages, LaTeX2e. Extended abstract presented at 26-th ICALP, 199
A Generalization of Girod's Bidirectional Decoding Method to Codes with a Finite Deciphering Delay
Girod's encoding method has been introduced in order to efficiently decode from both directions messages encoded by using finite prefix codes. In the present paper, we generalize this method to finite codes with a finite deciphering delay. In particular, we show that our decoding algorithm can be realized by a deterministic finite transducer. We also investigate some properties of the underlying unlabeled graph
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