The document proposes a new type of P system called Interaction P Systems that are meant to model interaction and concurrency in a more primitive way than sequential computing models like Turing machines. Interaction P Systems would use interaction grammars and multiset rewriting rules to process continuous streams of data from their environment. They are intended to operate indefinitely without termination, producing partial results over time. The document suggests these systems may be more computationally powerful and better able to model living organisms compared to conventional P systems. It provides an initial definition and outlines future work needed to fully specify the model and explore its applications.

1. Interaction P Systems
S. Doumanis and A Syropoulos
Xanthi, Greece
E-mail: gmcg@araneous.com
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2. Is this the end or not?
Is the Turing machine the ultimate conceptual
computing device?
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3. Is this the end or not?
Is the Turing machine the ultimate conceptual
computing device?
Unless you are a Pythagorean, there is no reason to
accept the universality of the Church-Turing Thesis.
– p. 2/10

4. Is this the end or not?
Is the Turing machine the ultimate conceptual
computing device?
Unless you are a Pythagorean, there is no reason to
accept the universality of the Church-Turing Thesis.
Interaction and Concurrency are more primitive than
sequential reading and writing a storage medium.
– p. 2/10

5. Is this the end or not?
Is the Turing machine the ultimate conceptual
computing device?
Unless you are a Pythagorean, there is no reason to
accept the universality of the Church-Turing Thesis.
Interaction and Concurrency are more primitive than
sequential reading and writing a storage medium.
Interactive systems are more expressive than arbitrary
sequential processes and purely functional systems.
– p. 2/10

6. Some thoughts on termination
Typical conceptual computing devices deliver a result
only when they terminate.
– p. 3/10

7. Some thoughts on termination
Typical conceptual computing devices deliver a result
only when they terminate.
Organisms that cease to operate do not make up a
success story.
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8. Some thoughts on termination
Typical conceptual computing devices deliver a result
only when they terminate.
Organisms that cease to operate do not make up a
success story.
Modern computer based equipment that stops
operating is considered total failure.
– p. 3/10

9. Some thoughts on termination
Typical conceptual computing devices deliver a result
only when they terminate.
Organisms that cease to operate do not make up a
success story.
Modern computer based equipment that stops
operating is considered total failure.
Only continuous operation of operating systems makes
them reliable.
– p. 3/10

10. Why a new variant of P systems?
P systems suffer from Turingism!
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11. Why a new variant of P systems?
P systems suffer from Turingism!
There is no agreement on the notion of success!
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12. Why a new variant of P systems?
P systems suffer from Turingism!
There is no agreement on the notion of success!
Typical systems do not really interact with their
environment!
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13. Why a new variant of P systems?
P systems suffer from Turingism!
There is no agreement on the notion of success!
Typical systems do not really interact with their
environment!
Multiple systems do not interact with other systems by
using the environment.
– p. 4/10

14. Why a new variant of P systems?
P systems suffer from Turingism!
There is no agreement on the notion of success!
Typical systems do not really interact with their
environment!
Multiple systems do not interact with other systems by
using the environment.
There is no notion of history (i.e., P systems do not
remember).
– p. 4/10

15. A New Idea
No universal clock.
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16. A New Idea
No universal clock.
P systems should live for ever!
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17. A New Idea
No universal clock.
P systems should live for ever!
Computation should be continuous, while results
should be partially “delivered” (think of a turnstile that
counts people continuously).
– p. 5/10

18. A New Idea
No universal clock.
P systems should live for ever!
Computation should be continuous, while results
should be partially “delivered” (think of a turnstile that
counts people continuously).
There should be a continuous flow of information, data,
etc.
– p. 5/10

19. A New Idea
No universal clock.
P systems should live for ever!
Computation should be continuous, while results
should be partially “delivered” (think of a turnstile that
counts people continuously).
There should be a continuous flow of information, data,
etc.
Special compartments might serve as
history-recording compartments.
– p. 5/10

20. Interaction multiset rewriting rules
Interaction grammars have been introduced by Wegner
to specify streams (i.e., interactive time-sensitive
analog of strings).
– p. 6/10

21. Interaction multiset rewriting rules
Interaction grammars have been introduced by Wegner
to specify streams (i.e., interactive time-sensitive
analog of strings).
Interaction multiset rewriting rules are the interactive
analog of multiset rewriting rules.
– p. 6/10

22. Interaction multiset rewriting rules
Interaction grammars have been introduced by Wegner
to specify streams (i.e., interactive time-sensitive
analog of strings).
Interaction multiset rewriting rules are the interactive
analog of multiset rewriting rules.
Rules have the form α → β, where β may be formed
using the “listening” operator “.” and the
“nondeterministic choice” operator “+”.
– p. 6/10

23. Interaction multiset rewriting rules
Interaction grammars have been introduced by Wegner
to specify streams (i.e., interactive time-sensitive
analog of strings).
Interaction multiset rewriting rules are the interactive
analog of multiset rewriting rules.
Rules have the form α → β, where β may be formed
using the “listening” operator “.” and the
“nondeterministic choice” operator “+”.
The “.” operator waits for input, while the “+” operator
select nondeterministically an event from a list of input
events.
– p. 6/10

24. Interaction P System
May have initial data, but, in principle, process streams
coming from the environment.
– p. 7/10

25. Interaction P System
May have initial data, but, in principle, process streams
coming from the environment.
Have a number of history compartments where data
may be stored.
– p. 7/10

26. Interaction P System
May have initial data, but, in principle, process streams
coming from the environment.
Have a number of history compartments where data
may be stored.
At each moment t the output compartment contains a
partial result.
– p. 7/10

27. Interaction P System
May have initial data, but, in principle, process streams
coming from the environment.
Have a number of history compartments where data
may be stored.
At each moment t the output compartment contains a
partial result.
The system “litters” the environment with “useless”
data.
– p. 7/10

28. On their computational power
Remember: Interaction is more fundamental than
reading and writing to storage!
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29. On their computational power
Remember: Interaction is more fundamental than
reading and writing to storage!
Ergo: Interaction P system ought to be more
expressive than “conventional” P systems.
– p. 8/10

30. On their computational power
Remember: Interaction is more fundamental than
reading and writing to storage!
Ergo: Interaction P system ought to be more
expressive than “conventional” P systems.
Side effect: They better model living organisms. . .
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31. To Do List
To completely formally specify interaction P systems.
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32. To Do List
To completely formally specify interaction P systems.
To see for what problems they are good for.
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33. To Do List
To completely formally specify interaction P systems.
To see for what problems they are good for.
To use them for the simulation of living organisms.
– p. 9/10

34. To Do List
To completely formally specify interaction P systems.
To see for what problems they are good for.
To use them for the simulation of living organisms.
Any suggestions?
– p. 9/10

35. That’s all!
Thank you for your attention!
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