P Systems and Distributed Computing

On P Systems and Distributed

Computing

Apostolos Syropoulos

Greek Molecular Computing Group

Xanthi, GREECE

[email protected]

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P Systems and Distributing Computing

Is there any relationship between P systemsand distributed computing?

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Distributed simulations of P Systems haveshown that such a link exists.

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Distributed simulations of P Systems haveshown that such a link exists.

Our work aims to make more “formal” thisrelationship.

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What is Distributed Computing?

Distributed computing is the process ofrunning a single computational task on morethan one distinct computers.

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Distributed Computing 6= Cluster Computing!

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Distributed computing can utilizecomputational resources that would beotherwise unused.

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Distributed computing can utilizecomputational resources that would beotherwise unused.

SETI@home (SETI at home) is a typicaldistributed computing project.

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Basic Characteristics of Distr. Comp.

Network Structure.

Hierarchical

Star

Ring

Multiaccess

Hybrid

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Network Structure.

Hierarchical

Star

Ring

Multiaccess

Hybrid

Programming Tools

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Network Structure.

Hierarchical

Star

Ring

Multiaccess

Hybrid

Programming Tools

File “Systems”

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Basic Characteristics of Distr. Comp. cont.

Coordination

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Basic Characteristics of Distr. Comp. cont.

Coordination

Distributed Architectures

client-server architecture

peer-to-peer architecture

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Network Structure

A hierarchical network can be easilyrepresented as a membrane structure.

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Network Structure


A star network structure is a restricted form ofa tree structure; ergo nodes can beconsidered as compartments that are placedinside a skin membrane.

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Network Structure



But in general a network structure is actuallya graph.

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Network Structure



But in general a network structure is actuallya graph.

Only P systems with a graph membranestructure are suitable to describe the networkstructure of any system.

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Graph-structured P Systems

The membrane structure is replaced by arelation in {1, . . . ,m} × {1, . . . ,m}, describingthe network structure of the system

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The new symbol “toj” should be used todirectly place an object from the hostcompartment to compartment j.

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The new symbol “toj” should be used todirectly place an object from the hostcompartment to compartment j.

The rule is applicable only if (i, j) ∈ gm or(j, i) ∈ gm, where gm is the relation describingthe network structure.

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P Systems and Distr. Progr.

P systems have at least the computationalpower of Turing machines.

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In addition, it is possible to encode anygeneral recursive function as P system.

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In addition, it is possible to encode anygeneral recursive function as P system.

Thus, we can implement “simple” functionalprogramming languages on P hardware.

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On P hardware

Designing a new kind of hardware is not anyeasy process.

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On P hardware


First, we need to design the hardware.

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On P hardware


First, we need to design the hardware.

Second, we need to implement it in silico or toimplement it in the form of a virtual machine.

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P processors

Each processor implements the functionalityof a compartment of a particular P system.

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P processors


Each P-processor must be able tocommunicate with other P-processors.

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P processors


Each P-processor must be able tocommunicate with other P-processors.

Thus, P-processors will form a network.

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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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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

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P Processor Intructions cont.

joinsys i Processor i joins the system

exec Start execution

noop A do-nothing instuction

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Open Problems

How do we specify the specify the possitionof a P-processor that joins a system?

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Open Problems


How do we enumerate the variousP-processors?

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Open Problems


How do we enumerate the variousP-processors?

How do we implement the maximalparallelism principle?

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That’s all!

Thank you very much for your attention!

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P Systems and Distributed Computing

Science

Transcript of P Systems and Distributed Computing