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<p>In this paper, we consider simple P systems, i.e., membrane systems with only one membrane region, together with various derivation modes as they have been defined and thoroughly investigated during the last 25&#xa0;years, for instance, the variants of parallel derivation modes using non-extendable multisets of rules as the maximally parallel derivation mode, but also some more complicated variants, for example, simple P systems with prescribed teams of sets of rules as introduced recently. In this context, we recall many known results, especially for purely catalytic and catalytic P systems. In most cases, computational completeness of these simple P systems has been established, in other cases, especially when using only non-cooperative rules, only regular sets can be obtained, and in some cases, we get the same computational power as <i>ET</i>0<i>L</i> systems used for multisets.</p>

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An overview on simple P systems with specific variants of derivation modes

  • 期刊论文

  • 发表日期：

    2025年7月26日

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  • Artiom Alhazov,
  • Rudolf Freund,
  • Sergiu Ivanov,
  • Sergey Verlan

摘要

In this paper, we consider simple P systems, i.e., membrane systems with only one membrane region, together with various derivation modes as they have been defined and thoroughly investigated during the last 25 years, for instance, the variants of parallel derivation modes using non-extendable multisets of rules as the maximally parallel derivation mode, but also some more complicated variants, for example, simple P systems with prescribed teams of sets of rules as introduced recently. In this context, we recall many known results, especially for purely catalytic and catalytic P systems. In most cases, computational completeness of these simple P systems has been established, in other cases, especially when using only non-cooperative rules, only regular sets can be obtained, and in some cases, we get the same computational power as ET0L systems used for multisets.