57 research outputs found
Connection between the Slave-Particles and X-Operators Path-Integral Representations. a New Perturbative Approach
In the present work it is shown that the family of first-order Lagrangians
for the t-J model and the corresponding correlation generating functional
previously found can be exactly mapped into the slave-fermion decoupled
representation. Next, by means of the Faddeev-Jackiw symplectic method, a
different family of Lagrangians is constructed and it is shown how the
corresponding correlation generating functional can be mapped into the
slave-boson representation. Finally, in order to define the propagation of
fermion modes we discuss two alternative ways to treat the fermionic sector in
the path-integral formalism for the t-J model.Comment: 27 pages, latex, no figures(to be published in Journal of Physics
A:Mathematical and General
Evaluating space measures in P systems
P systems with active membranes are a variant of P systems where membranes can be created by division of existing membranes, thus creating an exponential amount of resources in a polynomial number of steps. Time and space complexity classes for active membrane systems have been introduced, to characterize classes of problems that can be solved by different membrane systems making use of different resources. In particular, space complexity classes introduced initially considered a hypothetical real implementation by means of biochemical materials, assuming that every single object or membrane requires some constant physical space (corresponding to unary notation). A different approach considered implementation of P systems in silico, allowing to store the multiplicity of each object in each membrane using binary numbers. In both cases, the elements contributing to the definition of the space required by a system (namely, the total number of membranes, the total number of objects, the types of different membranes, and the types of different objects) was considered as a whole. In this paper, we consider a different definition for space complexity classes in the framework of P systems, where each of the previous elements is considered independently. We review the principal results related to the solution of different computationally hard problems presented in the literature, highlighting the requirement of every single resource in each solution. A discussion concerning possible alternative solutions requiring different resources is presented
Decision P Systems and the P =NP Conjecture
We introduce decision P systems, which are a class of P
systems with symbol-objects and external output. The main result of
the paper is the following: if there exists an NP–complete problem that
cannot be solved in polynomial time, with respect to the input length, by
a deterministic decision P system constructed in polynomial time, then
P = NP. From Zandron-Ferreti-Mauri’s theorem it follows that if P =
NP, then no NP–complete problem can be solved in polynomial time,
with respect to the input length, by a deterministic P system with active
membranes but without membrane division, constructed in polynomial
time from the input. Together, these results give a characterization of
P = NP in terms of deterministic P systems
Membrane dissolution and division in P
Membrane systems with dividing and dissolving membranes
are known to solve PSPACE problems in polynomial time. However,
we give a P upperbound on an important restriction of such systems. In
particular we examine systems with dissolution, elementary division and
where each membrane initially has at most one child membrane. Even
though such systems may create exponentially many membranes, each
with di erent contents, we show that their power is upperbounded by PJunta de Andalucía TIC-581Ministerio de Educación y Ciencia TIN2006-1342
The Nondeterministic Waiting Time Algorithm: A Review
We present briefly the Nondeterministic Waiting Time algorithm. Our technique
for the simulation of biochemical reaction networks has the ability to mimic
the Gillespie Algorithm for some networks and solutions to ordinary
differential equations for other networks, depending on the rules of the
system, the kinetic rates and numbers of molecules. We provide a full
description of the algorithm as well as specifics on its implementation. Some
results for two well-known models are reported. We have used the algorithm to
explore Fas-mediated apoptosis models in cancerous and HIV-1 infected T cells
A Computational Complexity Theory in Membrane Computing
In this paper, a computational complexity theory within the framework
of Membrane Computing is introduced. Polynomial complexity classes associated with
di erent models of cell-like and tissue-like membrane systems are de ned and the most
relevant results obtained so far are presented. Many attractive characterizations of P 6=
NP conjecture within the framework of a bio-inspired and non-conventional computing
model are deduced.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía P08–TIC-0420
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
A linear-time tissue P system based solution for the 3-coloring problem
In the literature, several examples of the efficiency of cell-like P systems regarding the solution of NPcomplete
problems in polynomial time can be found (obviously, trading space for time). Recently, different
new models of tissue-like P systems have received important attention from the scientific community. In
this paper we present a linear-time solution to an NP-complete problem from graph theory, the 3–coloring
problem, and we discuss the suitability of tissue-like P systems as a framework to address the efficient
solution to intractable problems.Ministerio de Educación y Ciencia TIN2005-09345-C04-01Junta de Andalucía TIC-58
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