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Alternative representations of P systems solutions to the graph colouring problem

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Abstract

This paper first presents a simulation of the simple kernel P systems solution to the graph 3-colouring problem presented in a previous paper by Gheorghe et al., implemented in a programming style named Concurrent ML, which is based on the concept of synchronous communication between logical processing elements. This paper then presents and informally analyses an alternative compact single-cell solution to the same problem using P systems with compound objects (cP systems), which has the benefit of naturally adapting to the use of any number of colours greater than zero—only the specified colour symbols need to be changed. Successful and failing examples of the latter solution are also presented.

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Notes

  1. https://github.com/Hopac/Hopac.

  2. The final program can be found at https://github.com/jcoo092/acmc2018.

  3. Note that, while Concurrent ML uses synchronous communication by default, it is relatively simple to implement asynchronous communication also using it [17].

  4. Note that this is different to the random graphs that are also commonly denoted by this notation.

  5. The latest version of MeCoSim available from http://www.p-lingua.org/mecosim/ as at 10 January 2019 was used.

  6. One could see ad hoc as being akin to running a program compiled to native instructions, while using a general simulation is similar in principle to running a program in an interpreter. The latter is typically simpler to work with and more portable, but comes with overheads that slow down execution.

  7. In fact, any finite set of arbitrary symbols could be used, but we use the natural numbers here for ease of reading.

  8. We note that, should it be desired, it would be possible to have the system make a random selection between possible starting nodes, simply by starting the system with more than one \(s\) functor. The correctness and termination of the system will be unaffected, however.

  9. We consider these rules to be fairly easy to understand nevertheless —they are simply longer and involve a greater number of symbols than those of other systems.

References

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Acknowledgements

We would like to thank Luis Valencia-Cabrera of Universidad de Sevilla (the University of Seville), Spain, for providing valuable assistance with regards to the use of MeCoSim. We also would like to thank the anonymous reviewers for their detailed and considered reviews, which proved very helpful to us in improving the paper.

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  1. School of Computer Science, University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand

    James Cooper & Radu Nicolescu

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  1. James Cooper
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Correspondence to James Cooper.

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Cooper, J., Nicolescu, R. Alternative representations of P systems solutions to the graph colouring problem. J Membr Comput 1, 112–126 (2019). https://doi.org/10.1007/s41965-019-00013-2

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