13th International Conference on Membrane Computing - MTA Sztaki

Time-varying sequential P systems
Corollary 2. For all α ∈ {λ, w}, β ∈ {ac, ut}, and p ≥ 12,
L (mCF -αT V β (p)) = P sRE.
4 Conclusion
In this paper we have considered (sequential) P systems where the applications
of the rules assigned to each membrane are controlled by a regular language. We
have shown that with usual halting we can only get P sL (CF -MAT ). On the
other hand, with delayed halting, i.e., allowing the system to wait a bounded
number d of computation steps to become active again, even with delay two and
control languages of the form {w} ∗ , i.e., even time-varying P systems with only
one membrane and delay 2 characterize P sRE.
The same proof ideas as used in Theorem 3 can be used to show a similar
result for string languages, i.e., collecting terminal symbols sent out of the skin
membrane during a computation of a time-varying P systems into a string we can
obtain any recursively enumerable string language. Moreover, a lot of variants
deserve to be considered in the future, e.g.,
– other transition modes, especially the maximally parallel mode max, the
minimally parallel mode min, the min 1 -mode, etc.;
– other variants of halting, especially adult halting, halting with final state,
and partial halting;
– variants of combinations of types of rules assigned to the membranes and
types of control languages;
– dynamic P systems, i.e., control languages are assigned to labels of membranes
and not to membranes themselves;
– etc.
We shall return to these questions and related ones in an extended version
of this paper.
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