6,068 research outputs found
Observational Equivalence and Full Abstraction in the Symmetric Interaction Combinators
The symmetric interaction combinators are an equally expressive variant of
Lafont's interaction combinators. They are a graph-rewriting model of
deterministic computation. We define two notions of observational equivalence
for them, analogous to normal form and head normal form equivalence in the
lambda-calculus. Then, we prove a full abstraction result for each of the two
equivalences. This is obtained by interpreting nets as certain subsets of the
Cantor space, called edifices, which play the same role as Boehm trees in the
theory of the lambda-calculus
A Correspondence between Maximal Abelian Sub-Algebras and Linear Logic Fragments
We show a correspondence between a classification of maximal abelian
sub-algebras (MASAs) proposed by Jacques Dixmier and fragments of linear logic.
We expose for this purpose a modified construction of Girard's hyperfinite
geometry of interaction which interprets proofs as operators in a von Neumann
algebra. The expressivity of the logic soundly interpreted in this model is
dependent on properties of a MASA which is a parameter of the interpretation.
We also unveil the essential role played by MASAs in previous geometry of
interaction constructions
An extensive English language bibliography on graph theory and its applications
Bibliography on graph theory and its application
Supervisory Control of Fuzzy Discrete Event Systems: A Formal Approach
Fuzzy {\it discrete event systems} (DESs) were proposed recently by Lin and
Ying [19], which may better cope with the real-world problems with fuzziness,
impreciseness, and subjectivity such as those in biomedicine. As a continuation
of [19], in this paper we further develop fuzzy DESs by dealing with
supervisory control of fuzzy DESs. More specifically, (i) we reformulate the
parallel composition of crisp DESs, and then define the parallel composition of
fuzzy DESs that is equivalent to that in [19]; {\it max-product} and {\it
max-min} automata for modeling fuzzy DESs are considered; (ii) we deal with a
number of fundamental problems regarding supervisory control of fuzzy DESs,
particularly demonstrate controllability theorem and nonblocking
controllability theorem of fuzzy DESs, and thus present the conditions for the
existence of supervisors in fuzzy DESs; (iii) we analyze the complexity for
presenting a uniform criterion to test the fuzzy controllability condition of
fuzzy DESs modeled by max-product automata; in particular, we present in detail
a general computing method for checking whether or not the fuzzy
controllability condition holds, if max-min automata are used to model fuzzy
DESs, and by means of this method we can search for all possible fuzzy states
reachable from initial fuzzy state in max-min automata; also, we introduce the
fuzzy -controllability condition for some practical problems; (iv) a number
of examples serving to illustrate the applications of the derived results and
methods are described; some basic properties related to supervisory control of
fuzzy DESs are investigated. To conclude, some related issues are raised for
further consideration
Data-Oblivious Stream Productivity
We are concerned with demonstrating productivity of specifications of
infinite streams of data, based on orthogonal rewrite rules. In general, this
property is undecidable, but for restricted formats computable sufficient
conditions can be obtained. The usual analysis disregards the identity of data,
thus leading to approaches that we call data-oblivious. We present a method
that is provably optimal among all such data-oblivious approaches. This means
that in order to improve on the algorithm in this paper one has to proceed in a
data-aware fashion
Optical computing by injection-locked lasers
A programmable optical computer has remained an elusive concept. To construct
a practical computing primitive equivalent to an electronic Boolean logic, one
should find a nonlinear phenomenon that overcomes weaknesses present in many
optical processing schemes. Ideally, the nonlinearity should provide a
functionally complete set of logic operations, enable ultrafast all-optical
programmability, and allow cascaded operations without a change in the
operating wavelength or in the signal encoding format. Here we demonstrate a
programmable logic gate using an injection-locked Vertical-Cavity
Surface-Emitting Laser (VCSEL). The gate program is switched between the AND
and the OR operations at the rate of 1 GHz with Bit Error Ratio (BER) of 10e-6
without changes in the wavelength or in the signal encoding format. The scheme
is based on nonlinearity of normalization operations, which can be used to
construct any continuous complex function or operation, Boolean or otherwise.Comment: 47 pages, 7 figures in total, 2 tables. Intended for submission to
Nature Physics within the next two week
On the possible Computational Power of the Human Mind
The aim of this paper is to address the question: Can an artificial neural
network (ANN) model be used as a possible characterization of the power of the
human mind? We will discuss what might be the relationship between such a model
and its natural counterpart. A possible characterization of the different power
capabilities of the mind is suggested in terms of the information contained (in
its computational complexity) or achievable by it. Such characterization takes
advantage of recent results based on natural neural networks (NNN) and the
computational power of arbitrary artificial neural networks (ANN). The possible
acceptance of neural networks as the model of the human mind's operation makes
the aforementioned quite relevant.Comment: Complexity, Science and Society Conference, 2005, University of
Liverpool, UK. 23 page
Processing and Transmission of Information
Contains reports on four research projects.Lincoln Laboratory, Purchase Order DDL B-00306U. S. ArmyU. S. NavyU. S. Air Force under Air Force Contract AF19(604)-520
Turing Automata and Graph Machines
Indexed monoidal algebras are introduced as an equivalent structure for
self-dual compact closed categories, and a coherence theorem is proved for the
category of such algebras. Turing automata and Turing graph machines are
defined by generalizing the classical Turing machine concept, so that the
collection of such machines becomes an indexed monoidal algebra. On the analogy
of the von Neumann data-flow computer architecture, Turing graph machines are
proposed as potentially reversible low-level universal computational devices,
and a truly reversible molecular size hardware model is presented as an
example
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