Abstract
We introduce new possibilities to control the application of rules based on the preceding applications, which can be defined in a general way for (hierarchical) P systems and the main known derivation modes. Computational completeness can be obtained even with non-cooperative rules and using both activation and blocking of rules, especially for the set modes of derivation, when allowing derivation steps with no rules being applied. When we allow the application of rules to influence the application of rules in previous derivation steps, applying a non-conservative semantics for what we consider to be a valid infinite derivation, we can even “go beyond Turing”.
Highlights
As exhibited in Freund et al (2011), for comparing the generating power of grammars working in the sequential derivation mode, many relations between various regulating mechanisms can be established in a very general setting without any reference to the underlying objects the rules are working on, using a general model for graph-controlled, programmed, random-context, and ordered grammars of arbitrary type based on the applicability of rules
We exhibit some relations between A1-P systems working in maximal derivation modes, ET0L-systems, and P systems with promoters working in maximal derivation modes
We have considered the concept of regulating the applicability of rules based on the application of rules in the preceding step(s) within a very general model for hierarchical P systems and for the main derivation modes
Summary
Defined by Gheorghe Paun in 1998, see Paun (1998), membrane systems, known as P systems, are a model of computing based on the abstract notion of a membrane which can be seen as a container delimiting a region containing objects which are acted upon by the. We will establish computational completeness results for various kinds of one-membrane P systems (resembling multiset grammars) and several derivation modes, using activation and blocking of rules to be applied in succeeding derivation steps. This less conservative semantics for activating and/or blocking the rules in preceding computations allows us to take the infinite sequence of stable configurations obtained in this way as the final computation on the given input Provided such a computation—obtained as the limit of a valid sequence of computations—exists, we may just consider the result of the first computation step and the second configuration to see whether the input has been accepted.
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