8,709 research outputs found
Computing with cells: membrane systems - some complexity issues.
Membrane computing is a branch of natural computing which abstracts computing models from the structure and the functioning of the living cell. The main ingredients of membrane systems, called P systems, are (i) the membrane structure, which consists of a hierarchical arrangements of membranes which delimit compartments where (ii) multisets of symbols, called objects, evolve according to (iii) sets of rules which are localised and associated with compartments. By using the rules in a nondeterministic/deterministic maximally parallel manner, transitions between the system configurations can be obtained. A sequence of transitions is a computation of how the system is evolving. Various ways of controlling the transfer of objects from one membrane to another and applying the rules, as well as possibilities to dissolve, divide or create membranes have been studied. Membrane systems have a great potential for implementing massively concurrent systems in an efficient way that would allow us to solve currently intractable problems once future biotechnology gives way to a practical bio-realization. In this paper we survey some interesting and fundamental complexity issues such as universality vs. nonuniversality, determinism vs. nondeterminism, membrane and alphabet size hierarchies, characterizations of context-sensitive languages and other language classes and various notions of parallelism
Beyond Generalized Multiplicities: Register Machines over Groups
Register machines are a classic model of computing, often seen as a canonical
example of a device manipulating natural numbers. In this paper, we de ne register
machines operating on general groups instead. This generalization follows the research
direction started in multiple previous works. We study the expressive power of register
machines as a function of the underlying groups, as well as of allowed ingredients (zero
test, partial blindness, forbidden regions). We put forward a fundamental connection
between register machines and vector addition systems. Finally, we show how registers
over free groups can be used to store and manipulate strings
On the Syntax of Logic and Set Theory
We introduce an extension of the propositional calculus to include abstracts
of predicates and quantifiers, employing a single rule along with a novel
comprehension schema and a principle of extensionality, which are substituted
for the Bernays postulates for quantifiers and the comprehension schemata of ZF
and other set theories. We prove that it is consistent in any finite Boolean
subset lattice. We investigate the antinomies of Russell, Cantor, Burali-Forti,
and others, and discuss the relationship of the system to other set theoretic
systems ZF, NBG, and NF. We discuss two methods of axiomatizing higher order
quantification and abstraction, and then very briefly discuss the application
of one of these methods to areas of mathematics outside of logic.Comment: 34 pages, accepted, to appear in the Review of Symbolic Logi
Graph Subsumption in Abstract State Space Exploration
In this paper we present the extension of an existing method for abstract
graph-based state space exploration, called neighbourhood abstraction, with a
reduction technique based on subsumption. Basically, one abstract state
subsumes another when it covers more concrete states; in such a case, the
subsumed state need not be included in the state space, thus giving a
reduction. We explain the theory and especially also report on a number of
experiments, which show that subsumption indeed drastically reduces both the
state space and the resources (time and memory) needed to compute it.Comment: In Proceedings GRAPHITE 2012, arXiv:1210.611
Branching rules of semi-simple Lie algebras using affine extensions
We present a closed formula for the branching coefficients of an embedding p
in g of two finite-dimensional semi-simple Lie algebras. The formula is based
on the untwisted affine extension of p. It leads to an alternative proof of a
simple algorithm for the computation of branching rules which is an analog of
the Racah-Speiser algorithm for tensor products. We present some simple
applications and describe how integral representations for branching
coefficients can be obtained. In the last part we comment on the relation of
our approach to the theory of NIM-reps of the fusion rings of WZW models with
chiral algebra g_k. In fact, it turns out that for these models each embedding
p in g induces a NIM-rep at level k to infinity. In cases where these NIM-reps
can be be extended to finite level, we obtain a Verlinde-like formula for
branching coefficients.Comment: 11 pages, LaTeX, v2: one reference added, v3: Clarified proof of
Theorem 2, completely rewrote and extended Section 5 (relation to CFT), added
various references. Accepted for publication in J. Phys.
Complexity of Simulating R Systems by P Systems
We show multiple ways to simulate R systems by non-cooperative P systems
with atomic control by promoters and/or inhibitors, or with matter-antimatter annihi-
lation rules, with a slowdown by a factor of constant. The descriptional complexity is
also linear with respect to that of simulated R system. All these constants depend on
how general the model of R systems is, as well as on the chosen control ingredients of
P systems. Special attention is paid to the di erences in the mode of rule application in
these models
Real Separated Algebraic Curves, Quadrature Domains, Ahlfors Type Functions and Operator Theory
The aim of this paper is to inter-relate several algebraic and analytic
objects, such as real-type algebraic curves, quadrature domains, functions on
them and rational matrix functions with special properties, and some objects
from Operator Theory, such as vector Toeplitz operators and subnormal
operators. Our tools come from operator theory, but some of our results have
purely algebraic formulation. We make use of Xia's theory of subnormal
operators and of the previous results by the author in this direction. We also
correct (in Section 5) some inaccuracies in two papers by the author in Revista
Matematica Iberoamericana (1998).Comment: 43 pages, 2 figures; zip archiv
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