Membrane systems with proteins embedded in membranes

Membrane computing is a biologically inspired computational paradigm. Motivated by brane calculi we investigate membrane systems which differ from conventional membrane systems by the following features: (1) biomolecules (proteins) can move through the regions of the systems, and can attach onto (and de-attach from) membranes, and (2) membranes can evolve depending on the attached molecules. The evolution of membranes is performed by using rules that are motivated by the operation of pinocytosis (the pino rule) and the operation of cellular dripping (the drip rule) that take place in living cells. We show that such membrane systems are computationally universal. We also show that if only the second feature is used then one can generate at least the family of Parikh images of the languages generated by programmed grammars without appearance checking (which contains non-semilinear sets of vectors). If, moreover, the use of pino/drip rules is non-cooperative (i.e., not dependent on the proteins attached to membranes), then one generates a family of sets of vectors that is strictly included in the family of semilinear sets of vectors. We also consider a number of decision problems concerning reachability of configurations and boundness

Membrane Systems with Marked Membranes

AbstractMembrane computing is a biologically inspired computational paradigm. Motivated by brane calculi we investigate membrane systems which differ from conventional membrane systems by the following features: (1) biomolecules (proteins) can move through the regions of the systems, and can attach onto (and de-attach from) membranes, and (2) membranes can evolve depending on the attached molecules. The evolution of membranes is performed by using rules that are motivated by the operation of pinocytosis (the pino rule) and the operation of cellular dripping (the drip rule) that take place in living cells. We show that such membrane systems are computationally universal. We also show that if only the second feature is used then one can generate at least the family of Parikh images of the languages generated by programmed grammars without appearance checking (which contains non-semilinear sets of vectors). If, moreover, the use of pino/drip rules is non-cooperative (i.e., not dependent on the proteins attached to membranes), then one generates a family of sets of vectors that is strictly included in the family of semilinear sets of vectors. We also consider a number of decision problems concerning reachability of configurations and boundness

Playing with Derivation Modes and Halting Conditions

In the area of P systems, besides the standard maximally parallel derivation mode, many other derivation modes have been investigated, too. In this paper, many variants of hierarchical P systems and tissue P systems using different derivation modes are considered and the effects of using di erent derivation modes, especially the maximally parallel derivation modes and the maximally parallel set derivation modes, on the generative and accepting power are illustrated. Moreover, an overview on some control mechanisms used for (tissue) P systems is given. Furthermore, besides the standard total halting mode, we also consider different halting conditions such as unconditional halting and partial halting and explain how the use of different halting modes may considerably change the computing power of P systems and tissue P systems

One-Membrane P Systems with Activation and Blocking of Rules

We introduce new possibilities to control the application of rules based on the preceding applications, which can be de ned in a general way for (hierarchical) P systems and the main known derivation modes. Computational completeness can be obtained even for one-membrane P systems with non-cooperative rules and using both activation and blocking of rules, especially for the set modes of derivation. When we allow the application of rules to in uence the application of rules in previous derivation steps, applying a non-conservative semantics for what we consider to be a derivation step, we can even \go beyond Turing"

P Systems: from Anti-Matter to Anti-Rules

The concept of a matter object being annihilated when meeting its corresponding anti-matter object is taken over for rule labels as objects and anti-rule labels as the corresponding annihilation counterpart in P systems. In the presence of a corresponding anti-rule object, annihilation of a rule object happens before the rule that the rule object represents, can be applied. Applying a rule consumes the corresponding rule object, but may also produce new rule objects as well as anti-rule objects, too. Computational completeness in this setting then can be obtained in a one-membrane P system with non-cooperative rules and rule / anti-rule annihilation rules when using one of the standard maximally parallel derivation modes as well as any of the maximally parallel set derivation modes (i.e., non-extendable (multi)sets of rules, (multi)sets with maximal number of rules, (multi)sets of rules a ecting the maximal number of objects). When using the sequential derivation mode, at least the computational power of partially blind register machines is obtained

(Tissue) P Systems with Anti-Membranes

The concept of a matter object being annihilated when meeting its corresponding anti-matter object is taken over for membranes as objects and anti-membranes as the corresponding annihilation counterpart in P systems. Natural numbers can be represented by the corresponding number of membranes with a speci c label. Computational completeness in this setting then can be obtained with using only elementary membrane division rules, without using objects. A similar result can be obtained for tissue P systems with cell division rules and cell / anti-cell annihilation rules. In both cases, as derivation modes we may take the standard maximally parallel derivation modes as well as any of the maximally parallel set derivation modes (non-extendable (multi)sets of rules, (multi)sets with maximal number of rules, (multi)sets of rules a ecting the maximal number of objects)

P Systems with Randomized Right-hand Sides of Rules

P systems are a model of hierarchically compartmentalized multiset rewriting. We introduce a novel kind of P systems in which rules are dynamically constructed in each step by non-deterministic pairing of left-hand and right-hand sides. We de ne three variants of right-hand side randomization and compare each of them with the power of conventional P systems. It turns out that all three variants enable non-cooperative P systems to generate exponential (and thus non-semi-linear) number languages. We also give a binary normal form for one of the variants of P systems with randomized rule right-hand sides. Finally, we also discuss extensions of the three variants to tissue P systems, i.e., P systems on an arbitrary graph structure

Membrane Systems with External Control

We consider the idea of controlling the evolution of a membrane system. In particular, we investigate a model of membrane systems using promoted rules, where a string of promoters (called the control string) “travels” through the regions, activating the rules of the system. This control string is present in the skin region at the beginning of the computation – one can interpret that it has been inserted in the system before starting the computation – and it is “consumed”, symbol by symbol, while traveling through the system. In this way, the inserted string drives the computation of the membrane system by controlling the activation of evolution rules. When the control string is entirely consumed and no rule can be applied anymore, then the system halts – this corresponds to a successful computation. The number of objects present in the output region is the result of such a computation. In this way, using a set of control strings (a control program), one generates a set of numbers. We also consider a more restrictive definition of a successful computation, and then study the corresponding model. In this paper we investigate the influence of the structure of control programs on the generative power. We demonstrate that different structures yield generative powers ranging from finite to recursively enumerable number sets. In determining the way that the control string moves through the regions, we consider two possible “strategies of traveling”, and prove that they are similar as far as the generative power is concerned

Variants of P Systems with Toxic Objects

Toxic objects have been introduced to avoid trap rules, especially in (purely) catalytic P systems. No toxic object is allowed to stay idle during a valid derivation in a P system with toxic objects. In this paper we consider special variants of toxic P systems where the set of toxic objects is prede ned { either by requiring all objects to be toxic or all catalysts to be toxic or all objects except the catalysts to be toxic. With all objects staying inside and being toxic, purely catalytic P systems cannot go beyond the nite sets, neither as generating nor as accepting systems. With allowing the output to be sent to the environment, exactly the regular sets can be generated. With non-cooperative systems with all objects being toxic we can generate exactly the Parikh sets of languages generated by extended Lindenmayer systems. Catalytic P systems with all catalysts being toxic can generate at least PsMAT

(Tissue) P Systems Using Non-cooperative Rules Without Halting Conditions

We consider (tissue) P systems using non-cooperative rules, but considering computations without halting conditions. As results of a computation we take the contents of a specified output membrane/cell in each derivation step, no matter whether this computation will ever halt or not, eventually taking only results completely consisting of terminal objects only. The computational power of (tissue) P systems using non-cooperative rules turns out to be equivalent to that of (E)0L systems