Dynamics of Randomly Constructed Computational Systems

We studied Petri nets with five places constructed in a pseudo-random way: their underlying net is composed of join and fork. We report initial results linking the dynamical properties of these systems to the topology of their underlying net. The obtained results can be easily related to the computational power of some abstract models of computation

Dependencies and Simultaneity in Membrane Systems

Membrane system computations proceed in a synchronous fashion: at each step all the applicable rules are actually applied. Hence each step depends on the previous one. This coarse view can be refined by looking at the dependencies among rule occurrences, by recording, for an object, which was the a rule that produced it and subsequently (in a later step), which was the a rule that consumed it. In this paper we propose a way to look also at the other main ingredient in membrane system computations, namely the simultaneity in the rule applications. This is achieved using zero-safe nets that allows to synchronize transitions, i.e., rule occurrences. Zero-safe nets can be unfolded into occurrence nets in a classical way, and to this unfolding an event structure can be associated. The capability of capturing simultaneity of zero-safe nets is transferred on the level of event structure by adding a way to express which events occur simultaneously

Tissue P systems with cell division

In tissue P systems several cells (elementary membranes) communicate through symport/antiport rules, thus carrying out a computation. We add to such systems the basic feature of (cell–like) P systems with active membranes – the possibility to divide cells. As expected (as it is the case for P systems with active membranes), in this way we get the possibility to solve computationally hard problems in polynomial time; we illustrate this possibility with SAT problem.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58

Networks of Cells and Petri Nets

We introduce a new class of P systems, called networks of cells, with rules allowing several cells to simultaneously interact with each other in order to produce some new objects inside some other output cells. We define different types of behavior for networks of cells by considering alternative strategies for the application of the rules: sequential application, free parallelism, maximal parallelism, locally-maximal parallelism and minimal parallelism. We devise a way for translating network of cells into place- transition nets with localities (PTL-nets, for short) - a specific class of Petri nets. Then, for such a construction, we show a behavioral equivalence between network of cells and corresponding PTL-nets only in the case maximal parallelism, sequential execution, and free parallelism, whereas we observe that, in the case of locally-maximal parallelism and minimal parallelism, the corresponding PTL-nets are not always able to mimic the behavior of network of cells. Also, we address the reverse problem of finding a corresponding network of cells for a given PTL-net by obtaining similar results concerning the relation- ships between their semantics. Finally, we present network-of-cells-based models of two classical synchronization problems: producer/consumer and dining philosophers

Dependency Graph Technique Revisited

The dependency graph technique was initially thought as a method to find short paths in the computation tree of a membrane system using weak metrics. It could be used to obtain reasonably fast SAT-solvers, capable of competing with the ones available in the literature. Later on, they were used as a method to demonstrate the non-efficiency of some membrane systems, capturing the dynamics of the systems by a static directed graph structure. Recently, the dependency graphs have also been used to establish negative results in Membrane Computing. Specifically, in this work, demonstrating the inability of a kind of membrane system to solve some decision problems efficiently by means of a single system.Ministerio de Economía, Industria y Competitividad TIN2017-89842-

On Languages Accepted by P/T Systems Composed of joins

Recently, some studies linked the computational power of abstract computing systems based on multiset rewriting to models of Petri nets and the computation power of these nets to their topology. In turn, the computational power of these abstract computing devices can be understood by just looking at their topology, that is, information flow. Here we continue this line of research introducing J languages and proving that they can be accepted by place/transition systems whose underlying net is composed only of joins. Moreover, we investigate how J languages relate to other families of formal languages. In particular, we show that every J language can be accepted by a log n space-bounded non-deterministic Turing machine with a one-way read-only input. We also show that every J language has a semilinear Parikh map and that J languages and context-free languages (CFLs) are incomparable

How to Go Beyond Turing with P Automata: Time Travels, Regular Observer !-Languages, and Partial Adult Halting

In this paper we investigate several variants of P automata having in nite runs on nite inputs. By imposing speci c conditions on the in nite evolution of the systems, it is easy to nd ways for going beyond Turing if we are watching the behavior of the systems on in nite runs. As speci c variants we introduce a new halting variant for P automata which we call partial adult halting with the meaning that a speci c prede ned part of the P automaton does not change any more from some moment on during the in nite run. In a more general way, we can assign !-languages as observer languages to the in nite runs of a P automaton. Speci c variants of regular !-languages then, for example, characterize the red-green P automata

On acceptance conditions for membrane systems: characterisations of L and NL

In this paper we investigate the affect of various acceptance conditions on recogniser membrane systems without dissolution. We demonstrate that two particular acceptance conditions (one easier to program, the other easier to prove correctness) both characterise the same complexity class, NL. We also find that by restricting the acceptance conditions we obtain a characterisation of L. We obtain these results by investigating the connectivity properties of dependency graphs that model membrane system computations

Polarizationless P Systems with Active Membranes: Computational Complexity Aspects

P systems with active membranes, in their classical definition, make use of noncooperative rules only. However, it is well known that in living cells, proteins interact among them yielding new products. Inspired by this biological phenomenon, the previous framework is reformulated in this paper, allowing cooperation in object evolution rules, while removing electrical charges associated with membranes. More precisely, minimal cooperation in object evolution rules is incorporated in polarizationless P systems with active membranes. In this paper, the term “minimal” means that the left-hand side of such rules consists of at most two symbols, and its length is greater than or equal to the corresponding right-hand side. The computational efficiency of this kind of P systems is studied by providing a uniform polynomial-time solution to SAT problem in such manner that only division rules for elementary membranes are used and dissolution rules are forbidden. Bearing in mind that only tractable problems can be efficiently solved by families of polarizationless P systems with active membranes and without dissolution rules, passing from non-cooperation to minimal cooperation in object evolution rules amounts passing from non-efficiency to efficiency in this framework. This frontier of efficiency provides, as any other borderline does, a possible way to address the P versus NP problem.National Natural Science Foundation of China No. 61033003National Natural Science Foundation of China No. 6132010600

Basic completion strategies as another application of the Maude strategy language

The two levels of data and actions on those data provided by the separation between equations and rules in rewriting logic are completed by a third level of strategies to control the application of those actions. This level is implemented on top of Maude as a strategy language, which has been successfully used in a wide range of applications. First we summarize the Maude strategy language design and review some of its applications; then, we describe a new case study, namely the description of completion procedures as transition rules + control, as proposed by Lescanne.Comment: In Proceedings WRS 2011, arXiv:1204.531