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A Formal Framework for P Systems

A Formal Framework for P Systems,Rudolf Freund,Sergey Verlan

A Formal Framework for P Systems   (Citations: 6)
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    • ...Continuing the formal approach started in Freund and Verlan (2007), a variant of the minimally parallel transition mode was considered in Freund and Verlan (2008), where we considered a partitioning of the whole set of rules and allowed only multisets of rules to be applied in parallel which could not be extended by adding a rule from a partition from which no rule had already been taken into this multiset of rules...
    • ...In this section we consider membrane systems as a collection of interacting cells containing multisets of objects like in Bernardini et al. (2007) and Freund and Verlan (2007)...
    • ...The set of all multisets of rules applicable to C is denoted by Appl P; C ðÞ ; a procedural algorithm how to obtain Appl P; C ðÞ was described in Freund and Verlan (2007)...
    • ...Moreover, the basic k-restricted minimally and k-restricted maximally parallel transition mode may be restricted as exhibited for the other transition modes as shown in Freund and Verlan (2007), eventually with other variants of halting, e.g., see Freund (2009) as well as Freund and Kogler (2009)...

    Rudolf Freundet al. (Tissue) P systems working in the k -restricted minimally or maximally...

    • ...In [12], a formal framework for (tissue) P systems capturing the formal features of these transition modes was developed, based on a general model of membrane systems as a collection of interacting cells containing multisets of objects (compare with the models of networks of cells as discussed in [5] and networks of language processors as considered in [7])...
    • ...Continuing the formal approach started in [12], the k-bounded minimally parallel transition mode (see [13]) was introduced, where at most k rules can be taken from each of the sets covering the whole set of rules into a multiset of rules used in the minimally parallel transition mode...
    • ...The main parts of notions, definitions, and results presented in the following are taken from [12] and [13] as well as from [3] and [10]...
    • ...In this section we consider membrane systems as a collection of interacting cells containing multisets of objects like in [5] and [12]...
    • ...The set of all multisets of rules applicable to C is denoted by Appl (Π, C )( a procedural algorithm how to obtain Appl (Π, C) is described in [12])...
    • ...In [12], further restricting conditions on the four basic modes defined above, especially interesting for the minimally parallel transition mode, were considered...

    Rudolf Freund. Transition and Halting Modes in (Tissue) P Systems

    • ...In [9], a formal framework for (tissue) P systems capturing the formal features of these transition modes was developed, based on a general model of membrane systems as a collection of interacting cells containing multisets of objects (compare with the models of networks of cells as discussed in [1] and networks of language processors as considered in [4])...
    • ...In this section we consider membrane systems as a collection of interacting cells containing multisets of objects like in [1] and [9]...
    • ...The set of all multisets of rules applicable to C is denoted by Appl (Π, C )( a procedural algorithm how to obtain Appl (Π, C) is described in [9])...

    Rudolf Freundet al. (Tissue) P Systems with Hybrid Transition Modes

    • ... rules in parallel was introduced, the so-called minimal parallelism [5]: in each computation step, the chosen multiset of rules to be applied in parallel cannot be extended by any rule out of a set of rules from which no rule has been chosen so far for this multiset of rules in such a way that the resulting extended multiset still could be applied (this is not the only way to interpret the idea of minimal parallelism, e.g., see [6] for ...

    Rudolf Freundet al. Polarizationless P Systems with Active Membranes Working in the Minima...

    • ...In [9], a formal framework for (tissue) P systems capturing the formal features of these transition modes was developed, based on a general model of membrane systems as a collection of interacting cells containing multisets of objects (compare with the models of networks of cells as discussed in [1] and networks of language processors as considered in [4])...
    • ...In this section we consider membrane systems as a collection of interacting cells containing multisets of objects like in [1] and [9]...
    • ...The set of all multisets of rules applicable to C is denoted by Appl (;C ) (a procedural algorithm how to obtain Appl (;C ) is described in [9])...

    Rudolf Freundet al. Hybrid Transition Modes in (Tissue) P Systems

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