Brief look back at the membrane computing model

1. G R O UP 1
MEMBRANE COMPUTING

2. WHAT IS COMPUTING ?

3. What is Computing ?
 Computing is any goal-oriented activity
requiring, benefiting form, or creating
algorithmic processes.
 Computing includes :
 Designing, developing and building
hardware and software systems.
 Processing, structuring and managing
various kinds of information.
 Doing scientific research on and with
computers etc.

4.  The models of computing ->
 Von Neuman Model (Instruction driven
Model) :
• Personal Computers, Laptops
 Pattern driven Model :
• Artificial intelligence
 Data driven Model :
• Machine learning, Soft Computing
 Natural Computing :
• Molecular Computing, Quantum
computing

6. What is Natural Computing ?
 Studying of the models of computation
inspired by biological systems.
 Nature is a major source of inspiration;
 Natural phenomena can be translated into
computing paradigms.
 Natural processes can be (and are) used as
carriers of computational operations.
 The best thing is in natural computing,
best solution emerge rather than being
designed.

7.  Some approaches in Natural Computing use the
methods of formal language theory ;
 L-systems :
• Development of multicellular organisms. (plants)
• Founded by Aristid Lindenmayer in 1968.
 Cellular Automata:
• Discrete model studied in Computability theory,
Mathematics, Physics, Complexity science,
Theoretical biology and Microstructure modeling.
• Founded by Stephen Wolfram in 1983 based on the
work of V. Neuman, Stanislaw Ulam.
 H-systems:
• DNA
• Founded by Tom Head in 1987.
 Membrane computing(P-systems):
• Founded by Gheorghe Paun in 1998.

9. Membrane
Computing
“ The paradigmatic idea of
membrane computing is to
see whether we can mimic
the living cell – its structure
and functioning.”
-Gheorghe Păun

10. What is Membrane Computing ?
Challenges :
 Is a ‘living cell’ computing?
 Can we abstract a computing device
from the cell structure and functioning ?
 How computationally powerful is this
device?
 Is it possible to implement computations
in living cells?

11.  ‘Living cells’ have usually a large number of
compartments hosting a huge variety of
biochemical reactions.
 So a living cell is doing computations too.
 Membrane Computing[MC] is an area within
computer science that seeks to discover new
computational models from the study of the
biological cells, particularly the cellular
membranes.
 MC is a generalization of DNA computing:
Within different regions of space different but not
unrelated computations can be performed.
 MC is a branch of molecular computing initiated
by ‘Gheorghe Paun’ in 1998.

12.  Biologically inspired, but a computational rather
than a biological model.
 MC identifiers an unconventional computer
model called P-systems (abstracts from the way
living cell process chemical compounds in their
compartmental structure.)
 Membranes organized as Venn diagrams/tree
structure where one membrane contains other
membranes.
 Dynamics of the system governed by the set of
rules associated with each membrane.
 Rules specify how objects evolve/move into
neighboring membranes how membranes can
dissolved/divided/created.

13.  Rules are used in nondeterministic, maximal
parallel manner define transition between
configurations.
 A P-system can be used as :
acceptor of configurations or generator of
configurations. (from a fixed initial configuration)

14. Dynamics of P-systems :
 Each region contains a multi set of objects and a
set of rules.
 The objects are represented by symbols from a
given alphabet.
 We start with and initial configuration :
An initial membrane structure and some initial multi set
of objects placed inside the region of the system.
 We apply the rules in nondeterministic maximal
parallel manner in each step, each region, each
object that can be evolved according to some
rule must do it.

15.  A computation is said successful if it halts, that is ,
it reaches a configuration where no rules can be
applied.
 The result of a successful computation may be
the multi sets formed either by the object
contained in a specific output membrane or by
the objects sent out of the system during the
computations.
 A non-halting computation yields no result.

16. Language acceptor/generator :
 A P-system ‘p’ starts with an initial configuration
z= 1
𝑛1
𝑎 … … 𝑘
𝑛𝑘
𝑎 in the input membrane.
 At each step, a maximal multi sets of rules are
non-deterministically selected and applied in
parallel.
 The string ‘z’ is accepted if the system eventually
halts. (a configuration is halting if no rule is
applicable.)
 A string ‘w’ is generated if found in originally
empty output membrane.

17. b->d
d->de
(ff->f)>(f->∂)
af
a->ab
a->b∂
f->ff
e-𝑒 𝑜𝑢𝑡
(1)
(2)
(3)

18. Applications of Membrane Computing
 Most of the applications of membrane computing
use cell-like P systems and tissue-like P systems and
the general protocol.
 General protocol is a P system written which
models a given process, capturing the objects,
compartments, and evolution rules.
 After that a program is written to simulate this P
system. In this way, applications of membrane
computing is can be separated into 04
categories.
1. Bio Applications
2. Computer Science Applications
3. Applications to Linguistics

19. Bio Applications
1) P system models for Mechanosensitive
Channels.
2) P systems for Biological Dynamics.
3) Modeling respiration in Bacteria and
Photosynthesis/Respiration.
4) Modeling call-meditated immunity by means of
P-systems.
5) A membrane computing model on
photosynthesis.
6) Modeling ‘P53’ pathway by using multi set
processing.

20. Computer Science Applications
1) Static sorting P-systems.
2) Membrane based devices used in computer
graphics.
3) An analysis of public key protocol with
membranes.
4) Membrane algorithms.
5) Computationally hard problems addressed
through P-systems.
6) Membrane computing software.

21. Application to Linguistics
1) Linguistics membrane systems.
2) Parsing with P-automata.

23.  Membrane computing provides computational
models that abstracts from the living cell structure and
functioning.
 Such models have been proved to be
computationally powerful and efficient.
 Membrane computing defines an abstract framework
about distribute architectures communication parallel
information processing.
 Such features are relevant both for computer science
and biology.
 Membrane systems have been developed so far as a
purely generative devices in the context of the formal
language theory.
 They lack a well-defined semantics for reasoning
about real systems.
 Non-determinism and maximal parallelism are not
always desirable features.