13th International Conference on Membrane Computing - MTA Sztaki

Fast hardware implementations of P systems
The corresponding system (2) of linear equations has the following solution
q 0 = x3 + 2x 2 + x
1 − x 2 − x 3
x + 1
q 1 =
1 − x 2 − x 3
q 2 =
x2 + x
1 − x 2 − x 3
q 3 = x2 + x + 1
1 − x 2 − x 3
q 4 =
x2 + x
1 − x 2 − x 3
We can expand q 0 to obtain q 0 (n) (= [x n ]q 0 )
q 0 = x + 2x 2 + 2x 3 + 3x 4 + 4x 5 + 5x 6 + 7x 7 + 9x 8 + . . .
The coefficients of the above series give the number of words of the corresponding
length. For example, there are 9 words of length 8 in L I .
It is not difficult to verify that the coefficients [x n ]q k , 0 ≤ k ≤ 4, of the
corresponding power series are particular cases of the Padovan sequence q k (n) =
q k (n − 2) + q k (n − 3), n > 3, with the following starting values:
k q k (0) q k (1) q k (2)
0 1 1 2
1 1 1 1
2 0 1 1
3 1 1 2
4 0 1 1
3 Formal Part of Simulator’s Design
We will follow the approach given in [3], however we will not enter into deep
details concerning the notation and the definition of derivation modes given
there. Consider a (static) P system Π of any type evolving in any derivation
mode. The key point of the semantics of P systems is that according to the type
of the system and the derivation mode δ for any configuration of the system
C a set of multisets (over R) of applicable rules, denoted by Appl(Π, C, δ),
is computed. After that, one of the elements R from this set is chosen, nondeterministically,
for the further evolution of the system.
The main idea for the construction of a fast simulator is to avoid the computation
of the set Appl(Π, C, δ) and to compute the multiset of rules to be
applied R directly. In this article we are interested by algorithms that permit
to perform this computation on FPGA in constant time. We remark that, in a
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