Dragoş Sburlan

Time–independent p systems

We introduce a class of P systems called timed P systems where to each rule is associated an integer that represents the time needed by the rule (reaction) to be entirely executed. The idea comes from cell biology where chemical reactions take certain times to be executed. In this work we are interested in a special class of P systems, called time-free, working always in the same way (i.e., always producing the same result) independently from the values associated to the execution time of their rules. Later we introduce a generalization of time-free P systems, namely clock-free P systems, where a time of execution is associated directly to each single application of the rules (in this case, different applications, even of the same rule, may take a different time to be executed). Several results are presented together with open problems and research proposals.

Simulating Boolean Circuits with P Systems

We propose a model for simulating Boolean circuits with P systems. The simulation is done in two steps, by first simulating the gates of such a circuit, and next by showing how these can be combined to obtain actual circuits. The type of P systems used is with symbol objects, context-free rewriting rules and some other features like mobile catalysts, weak priorities and promoters.

Membrane Systems with Marked 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.

Static Sorting P Systems

This chapter deals with the application of P systems to sorting problems. Traditional studies of sorting assume constant time for comparing two numbers and compute the time complexity with respect to the number of components of a vector to be sorted. Here, we assume the number of components to be a fixed number k, and study various algorithms based on different models of P systems and their time complexities with respect to the maximal number or to the sum of the numbers. Massively parallel computations that can be realized within the framework of P systems may lead to major improvements in solving the classical integer sorting problems. Despite this important characteristic, we will see that, depending on the model used, the massive parallelism feature cannot be always used, and so some results will have complexities “comparable” with the classical integer sorting algorithms. Still, computing a word (ordered) from a multiset (unordered) can be a goal not only for computer science, but also, e.g., for biosynthesis (separating mixed objects according to some characteristics). Here, we will move from ranking algorithms that, starting with numbers represented as multisets, produce symbols in an order, to effective sorting algorithms.

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.

Multiset random context grammars, checkers, and transducers

We introduce a general model of random context multiset grammars as well as the concept of multiset random context checkers and transducers. Our main results show how recursively enumerable sets of finite multisets can be generated using these models of computing; corresponding results for antiport P systems are established, too.

P systems with chained rules

In this paper we introduce a new model of P systems that uses vectors of rules to describe a causal dependence relation between the executions of the rules. We also study their computational power by considering several restrictions on the types of the rules.

Computing using signals: from cells to P systems

In cell biology a fundamental topic is the study of how biological signals are managed by cells. Signals can arise from inside the cell or from the external environment and the correct answer to certain signals is essential for bacteria to survive in a certain environment. Starting from these biological motivations we consider a model of P systems where the computation is controlled by signals which move across the regions. In particular, we consider signals-based P systems where the symbol-objects cannot be moved and the evolution rules can be activated/inactivated using a finite number of signals (signal-promoters) moved across the membranes; differently from standard P systems using promoters, in our case signal-promoters cannot be created during the computation. After discussing the biological motivations we show how this model becomes universal when it uses one catalyst and a bounded number of signal-promoters. Also results concerning signals-based P systems using non cooperative rules together with several open problems are presented.

Ultimately confluent rewriting systems. parallel multiset–rewriting with permitting or forbidding contexts

The aim of this paper is to study the power of parallel multiset-rewriting systems with permitting or forbidding context (or P systems with non-cooperative rules with promoters or inhibitors). The main results obtained are those if we use promoters or inhibitors of weight two, then the systems are computational universal. Moreover, both constructions satisfy a special property we define: they are ultimately confluent. This means that if the system allows at least one halting computation, then their final configurations are reachable from any reachable configuration. The other property both constructions satisfy is that a system allowing at least one halting computation will halt with probability 1.

Non-cooperative p systems with priorities characterize PsET0L

The paper answers an open problem from [4], proving that transition P systems with non-cooperative rules using priorities generate exactly the Parikh images of ET0L languages.