This document discusses the relationship between P systems and distributed computing. It proposes that P systems can be mapped to distributed computing architectures and implemented on a network of P processors. Each P processor would represent a compartment and communicate with other processors. A set of instructions are proposed for the P processors to simulate P system rules and coordinate their behavior. Open problems remain around how to specify the position of processors joining a system and implement maximal parallelism.

1. On P Systems and Distributed
Computing
Apostolos Syropoulos
Greek Molecular Computing Group
Xanthi, GREECE
gmcg@araneous.gr
– p. 1/15

2. P Systems and Distributing Computing
Is there any relationship between P systems
and distributed computing?
– p. 2/15

3. P Systems and Distributing Computing
Is there any relationship between P systems
and distributed computing?
Distributed simulations of P Systems have
shown that such a link exists.
– p. 2/15

4. P Systems and Distributing Computing
Is there any relationship between P systems
and distributed computing?
Distributed simulations of P Systems have
shown that such a link exists.
Our work aims to make more “formal” this
relationship.
– p. 2/15

5. What is Distributed Computing?
Distributed computing is the process of
running a single computational task on more
than one distinct computers.
– p. 3/15

6. What is Distributed Computing?
Distributed computing is the process of
running a single computational task on more
than one distinct computers.
Distributed Computing = Cluster Computing!
– p. 3/15

7. What is Distributed Computing?
Distributed computing is the process of
running a single computational task on more
than one distinct computers.
Distributed Computing = Cluster Computing!
Distributed computing can utilize
computational resources that would be
otherwise unused.
– p. 3/15

8. What is Distributed Computing?
Distributed computing is the process of
running a single computational task on more
than one distinct computers.
Distributed Computing = Cluster Computing!
Distributed computing can utilize
computational resources that would be
otherwise unused.
SETI@home (SETI at home) is a typical
distributed computing project.
– p. 3/15

9. Basic Characteristics of Distr. Comp.
Network Structure.
Hierarchical
Star
Ring
Multiaccess
Hybrid
– p. 4/15

10. Basic Characteristics of Distr. Comp.
Network Structure.
Hierarchical
Star
Ring
Multiaccess
Hybrid
Programming Tools
– p. 4/15

11. Basic Characteristics of Distr. Comp.
Network Structure.
Hierarchical
Star
Ring
Multiaccess
Hybrid
Programming Tools
File “Systems”
– p. 4/15

12. Basic Characteristics of Distr. Comp.
Network Structure.
Hierarchical
Star
Ring
Multiaccess
Hybrid
Programming Tools
File “Systems”
– p. 4/15

13. Basic Characteristics of Distr. Comp.
Network Structure.
Hierarchical
Star
Ring
Multiaccess
Hybrid
Programming Tools
File “Systems”
– p. 4/15

14. Basic Characteristics of Distr. Comp.
Network Structure.
Hierarchical
Star
Ring
Multiaccess
Hybrid
Programming Tools
File “Systems”
– p. 4/15

15. Basic Characteristics of Distr. Comp.
Network Structure.
Hierarchical
Star
Ring
Multiaccess
Hybrid
Programming Tools
File “Systems”
– p. 4/15

16. Basic Characteristics of Distr. Comp.
Network Structure.
Hierarchical
Star
Ring
Multiaccess
Hybrid
Programming Tools
File “Systems”
– p. 4/15

17. Basic Characteristics of Distr. Comp. cont.
Coordination
– p. 5/15

18. Basic Characteristics of Distr. Comp. cont.
Coordination
Distributed Architectures
client-server architecture
peer-to-peer architecture
– p. 5/15

19. Basic Characteristics of Distr. Comp. cont.
Coordination
Distributed Architectures
client-server architecture
peer-to-peer architecture
– p. 5/15

20. Basic Characteristics of Distr. Comp. cont.
Coordination
Distributed Architectures
client-server architecture
peer-to-peer architecture
– p. 5/15

21. Network Structure
A hierarchical network can be easily
represented as a membrane structure.
– p. 6/15

22. Network Structure
A hierarchical network can be easily
represented as a membrane structure.
A star network structure is a restricted form of
a tree structure; ergo nodes can be
considered as compartments that are placed
inside a skin membrane.
– p. 6/15

23. Network Structure
A hierarchical network can be easily
represented as a membrane structure.
A star network structure is a restricted form of
a tree structure; ergo nodes can be
considered as compartments that are placed
inside a skin membrane.
But in general a network structure is actually
a graph.
– p. 6/15

24. Network Structure
A hierarchical network can be easily
represented as a membrane structure.
A star network structure is a restricted form of
a tree structure; ergo nodes can be
considered as compartments that are placed
inside a skin membrane.
But in general a network structure is actually
a graph.
Only P systems with a graph membrane
structure are suitable to describe the network
structure of any system.
– p. 6/15

25. Graph-structured P Systems
The membrane structure is replaced by a
relation in {1, . . . , m} × {1, . . . , m}, describing
the network structure of the system
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26. Graph-structured P Systems
The membrane structure is replaced by a
relation in {1, . . . , m} × {1, . . . , m}, describing
the network structure of the system
The new symbol “toj” should be used to
directly place an object from the host
compartment to compartment j.
– p. 7/15

27. Graph-structured P Systems
The membrane structure is replaced by a
relation in {1, . . . , m} × {1, . . . , m}, describing
the network structure of the system
The new symbol “toj” should be used to
directly place an object from the host
compartment to compartment j.
The rule is applicable only if (i, j) ∈ gm or
(j, i) ∈ gm, where gm is the relation describing
the network structure.
– p. 7/15

28. P Systems and Distr. Progr.
P systems have at least the computational
power of Turing machines.
– p. 8/15

29. P Systems and Distr. Progr.
P systems have at least the computational
power of Turing machines.
In addition, it is possible to encode any
general recursive function as P system.
– p. 8/15

30. P Systems and Distr. Progr.
P systems have at least the computational
power of Turing machines.
In addition, it is possible to encode any
general recursive function as P system.
Thus, we can implement “simple” functional
programming languages on P hardware.
– p. 8/15

31. On P hardware
Designing a new kind of hardware is not any
easy process.
– p. 9/15

32. On P hardware
Designing a new kind of hardware is not any
easy process.
First, we need to design the hardware.
– p. 9/15

33. On P hardware
Designing a new kind of hardware is not any
easy process.
First, we need to design the hardware.
Second, we need to implement it in silico or to
implement it in the form of a virtual machine.
– p. 9/15

34. P processors
Each processor implements the functionality
of a compartment of a particular P system.
– p. 10/15

35. P processors
Each processor implements the functionality
of a compartment of a particular P system.
Each P-processor must be able to
communicate with other P-processors.
– p. 10/15

36. P processors
Each processor implements the functionality
of a compartment of a particular P system.
Each P-processor must be able to
communicate with other P-processors.
Thus, P-processors will form a network.
– p. 10/15

37. P Processor Intructions
send d, i Send all “d’s” to processor “i”
isalive i Is P-processor i is alive
intro o, n, i Introduce to the ith compartment
n copies of o
addrule R, i Associate rule R with processor i
delrule R, i Disassociate rule R from
processor i
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38. P Processor Intructions cont.
replace o, o′
, i Replace each occurrence of o in
compartment i with o′
delete o, i Delete each occurrence of o in
compartment i
ifempty o, i If the compartment i is empty,
then place a copy of o at it
halt n, i Halt processor i after n cycles
ihalt i Immediately halt processor i
– p. 12/15

39. P Processor Intructions cont.
joinsys i Processor i joins the system
exec Start execution
noop A do-nothing instuction
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40. Open Problems
How do we specify the specify the possition
of a P-processor that joins a system?
– p. 14/15

41. Open Problems
How do we specify the specify the possition
of a P-processor that joins a system?
How do we enumerate the various
P-processors?
– p. 14/15

42. Open Problems
How do we specify the specify the possition
of a P-processor that joins a system?
How do we enumerate the various
P-processors?
How do we implement the maximal
parallelism principle?
– p. 14/15

43. That’s all!
Thank you very much for your attention!
– p. 15/15