On the power of membrane division in P systems

Gheorghe Pǎun, Yasuhiro Suzuki, Hiroshi Tanaka, Takashi Yokomori

    Research output: Contribution to journalArticle

    36 Citations (Scopus)

    Abstract

    First, we consider P systems with active membranes, hence with the possibility that the membranes can be divided, with non-cooperating evolution rules (the objects always evolve separately). These systems are known to be able to solve NP-complete problems in linear time. Here we give a normal form theorem for such systems: their computational universality is preserved even if only the elementary membranes are divided. The possibility of solving SAT in linear time is preserved only when non-elementary membranes may also be divided under the influence of objects in their region. Second, we consider a slight generalization, namely, we allow that a membrane can produce by division both a copy of itself and a copy of a membrane with a different label; again, only elementary membranes may be divided. In this case, we prove that the hierarchy on the maximal number of membranes present in the system collapses: three membranes at a time are sufficient in order to characterize the recursively enumerable sets of vectors of natural numbers. This result is optimal, two membranes are shown not to be sufficient. Third, we consider P systems with cooperating rules (several objects may evolve together). Making use of this powerful feature, we show that many NP-complete problems can be solved in linear time in a quite uniform way (by systems which are very similar to each other), using only elementary membranes division (and not further ingredients, such as electrical charges). The degree of cooperation is minimal: two objects at a time.

    Original languageEnglish
    Pages (from-to)61-85
    Number of pages25
    JournalTheoretical Computer Science
    Volume324
    Issue number1
    DOIs
    Publication statusPublished - 2004 Sep 16

    Fingerprint

    P Systems
    Division
    Membrane
    Membranes
    Linear Time
    Computational complexity
    NP-complete problem
    Recursively Enumerable Set
    Sufficient
    Set of vectors
    Natural number
    Normal Form
    Universality
    Labels
    Charge

    Keywords

    • Membrane computing
    • Recursively enumerable language
    • SAT problem
    • Universality

    ASJC Scopus subject areas

    • Computational Theory and Mathematics

    Cite this

    On the power of membrane division in P systems. / Pǎun, Gheorghe; Suzuki, Yasuhiro; Tanaka, Hiroshi; Yokomori, Takashi.

    In: Theoretical Computer Science, Vol. 324, No. 1, 16.09.2004, p. 61-85.

    Research output: Contribution to journalArticle

    Pǎun, Gheorghe ; Suzuki, Yasuhiro ; Tanaka, Hiroshi ; Yokomori, Takashi. / On the power of membrane division in P systems. In: Theoretical Computer Science. 2004 ; Vol. 324, No. 1. pp. 61-85.
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