# Actor-Like cP Systems

## Abstract

We propose a new version of our cP systems, extended to match the Actor model, thereby solving an earlier open problem. In the new version, top-cells have control upon the input message flow, to decide which message types are acceptable and at what time. We assess its capabilities by proposing a revised version of our previous best models for the Byzantine agreement problem – a famous problem in distributed algorithms, with non-trivial data structures and algorithms. The new actor-based solution uses a substantially shorter fixed sized alphabet and ruleset, independent of the problem size. Moreover, in contrast to our previous models, additional helper/firewall cells are not anymore needed to ensure protection against Sybil attacks. Also, as any standard distributed algorithm, the novel actor-based cP model uses exactly one top-level cell for each process in Byzantine agreement, thus solving another open problem.

## Keywords

Distributed algorithms Synchronous model Actor model Membrane computing P systems cP systems Prolog terms and unification Inter-cell parallelism Intra-cell parallelism Byzantine agreement EIG trees## Notes

### Acknowledgments

We are deeply indebted to the co-authors of our former studies on the Byzantine agreement, for their earlier contributions.

## References

- 1.Abd-El-Malek, M., Ganger, G.R., Goodson, G.R., Reiter, M.K., Wylie, J.J.: Fault-scalable Byzantine fault-tolerant services. In: Herbert, A., Birman, K.P. (eds.) SOSP, pp. 59–74. ACM (2005)Google Scholar
- 2.Cachin, C., Kursawe, K., Shoup, V.: Random oracles in Constantinople: practical asynchronous Byzantine agreement using cryptography. J. Cryptol.
**18**(3), 219–246 (2005)MathSciNetCrossRefGoogle Scholar - 3.Castro, M., Liskov, B.: Practical Byzantine fault tolerance and proactive recovery. ACM Trans. Comput. Syst.
**20**(4), 398–461 (2002)CrossRefGoogle Scholar - 4.Cooper, J., Nicolescu, R.: The travelling salesman problem in cP systems. In: Zhang, G., Wang, J., Pan, L., Qiang, Zeng, Y. (eds.) Asian Conference on Membrane Computing, pp. 9–21 (2017)Google Scholar
- 5.Dinneen, M.J., Kim, Y.-B., Nicolescu, R.: A faster P solution for the Byzantine agreement problem. In: Gheorghe, M., Hinze, T., Păun, G., Rozenberg, G., Salomaa, A. (eds.) CMC 2010. LNCS, vol. 6501, pp. 175–197. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-18123-8_15CrossRefGoogle Scholar
- 6.Dinneen, M.J., Kim, Y.B., Nicolescu, R.: A faster P solution for the Byzantine agreement problem. Report CDMTCS-388, Centre for Discrete Mathematics and Theoretical Computer Science, The University of Auckland, Auckland, New Zealand, July 2010. http://www.cs.auckland.ac.nz/CDMTCS/researchreports/388-DKN.pdf
- 7.Gilad, Y., Hemo, R., Micali, S., Vlachos, G., Zeldovich, N.: Algorand: Scaling Byzantine agreements for cryptocurrencies. In: Proceedings of the 26th Symposium on Operating Systems Principles, pp. 51–68. ACM, New York (2017)Google Scholar
- 8.Hewitt, C.: What is computation? Actor model versus Turing’s model. In: A Computable Universe: Understanding and Exploring Nature as Computation, pp. 159–185. World Scientific (2013)Google Scholar
- 9.Hewitt, C., Bishop, P., Steiger, R.: A universal modular actor formalism for artificial intelligence. In: Proceedings of the 3rd International Joint Conference on Artificial Intelligence, IJCAI 1973, pp. 235–245. Morgan Kaufmann Publishers Inc., San Francisco (1973). http://dl.acm.org/citation.cfm?id=1624775.1624804
- 10.Lamport, L., Shostak, R.E., Pease, M.C.: The Byzantine generals problem. ACM Trans. Program. Lang. Syst.
**4**(3), 382–401 (1982)CrossRefGoogle Scholar - 11.Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann Publishers Inc., San Francisco (1996)zbMATHGoogle Scholar
- 12.Martin, J.P., Alvisi, L.: Fast Byzantine consensus. IEEE Trans. Dependable Sec. Comput.
**3**(3), 202–215 (2006)CrossRefGoogle Scholar - 13.Nicolescu, R.: Parallel and distributed algorithms in P systems. In: Gheorghe, M., Păun, G., Rozenberg, G., Salomaa, A., Verlan, S. (eds.) CMC 2011. LNCS, vol. 7184, pp. 35–50. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28024-5_4CrossRefGoogle Scholar
- 14.Nicolescu, R.: Revising the membrane computing model for Byzantine agreement. In: Leporati, A., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) CMC 2016. LNCS, vol. 10105, pp. 317–339. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-54072-6_20CrossRefzbMATHGoogle Scholar
- 15.Nicolescu, R., Wu, H.: Complex objects for complex applications. Roman. J. Inf. Sci. Technol.
**17**(1), 46–62 (2014)Google Scholar - 16.Pease, M.C., Shostak, R.E., Lamport, L.: Reaching agreement in the presence of faults. J. ACM
**27**(2), 228–234 (1980)MathSciNetCrossRefGoogle Scholar