09.09.2014 Views

13th International Conference on Membrane Computing - MTA Sztaki

13th International Conference on Membrane Computing - MTA Sztaki

13th International Conference on Membrane Computing - MTA Sztaki

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

Fast hardware implementati<strong>on</strong>s of P systems<br />

6 C<strong>on</strong>clusi<strong>on</strong>s<br />

In this article we presented a new design for a fast hardware implementati<strong>on</strong><br />

of a simulator for P systems. The obtained circuit permits to simulate a n<strong>on</strong>deterministic<br />

computati<strong>on</strong>al step of the system in a c<strong>on</strong>stant time (5 clock cycles).<br />

Hence, the obtained simulator achieves a high performance that is close to<br />

the maximal possible value (<strong>on</strong>e cycle per step). The key point of our approach<br />

is the representati<strong>on</strong> of the sequences of all possible rule applicati<strong>on</strong>s as words<br />

of some regular or n<strong>on</strong>-ambiguous c<strong>on</strong>text-free language. In this case using the<br />

generating series for the corresp<strong>on</strong>ding language it is possible to generate functi<strong>on</strong>s<br />

that precompute all possible rule applicati<strong>on</strong>s. It is worth to note that the<br />

speed of the computati<strong>on</strong> does not depend <strong>on</strong> the number of rules. However,<br />

there is a dependency between this number and the space <strong>on</strong> the chip. With the<br />

used board it is possible to simulate P systems having up to 100 rules.<br />

We exemplified our approach by an FPGA implementati<strong>on</strong> of different P<br />

systems working in maximal set mode with rules dependency graph in a form of<br />

a chain. We obtained a speed of about 2 × 10 7 computati<strong>on</strong>al steps per sec<strong>on</strong>d.<br />

Our different tests showed that the computati<strong>on</strong> is n<strong>on</strong>-deterministic and that<br />

the values of the parameters have expected mean values.<br />

As a future research we plan to develop a software that will allow us to generate<br />

the hardware design in an automatical way based <strong>on</strong> the regular language<br />

describing the rules joint applicability.<br />

The design described in this article is quite generic and does not use many<br />

features of FPGA. Therefore, it could be interesting to use the presented method<br />

for the speed-up of the existing software simulators of P systems.<br />

Acknowledgements<br />

This work has been partially supported by the Ministerio de Ciencia e Innovación<br />

of the Spanish Government under project TEC2011-27936 (HIPERSYS),<br />

by the European Regi<strong>on</strong>al Development Found (ERDF) and by the Ministry of<br />

Educati<strong>on</strong> of Spain (FPU grant AP2009-3625).<br />

References<br />

1. G. Ciobanu, G. Wenyuan: P systems running <strong>on</strong> a cluster of computers. In C.<br />

Martin-Vide, Gh. Paun, G. Rozenberg, A. Salomaa, eds., Workshop <strong>on</strong> <strong>Membrane</strong><br />

<strong>Computing</strong> 2003, LNCS 2933, Springer, 2004. 123–139.<br />

2. N. Chomsky, M.-P. Schützenberger, The Algebraic Theory of C<strong>on</strong>text-Free Languages,<br />

in P. Braffort and D. Hirschberg (eds.), Computer Programming and Formal<br />

Systems, North Holland, 118–161, 1963.<br />

3. R. Freund, S. Verlan: A formal framework for static (tissue) P systems. In Proc.<br />

of WMC 2008 (G. Eleftherakis et al., eds.), Thessal<strong>on</strong>iki, Greece, Springer, 2007,<br />

LNCS 4860, 271–284.<br />

4. D. E. Knuth, The Art of Computer Programming, Volume 2: Seminumerical Algorithms.<br />

Third Editi<strong>on</strong>, Addis<strong>on</strong>-Wesley, 1997.<br />

451

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!