Catalytic and communicating Petri nets are Turing complete

In most studies about the expressiveness of Petri nets, the focus has been put either on adding suitable arcs or on assuring that a complete snapshot of the system can be obtained. While the former still complies with the intuition on Petri nets, the second is somehow an orthogonal approach, as Petri nets are distributed in nature. Here, inspired by membrane computing, we study some classes of Petri nets where the distribution is partially kept and which are still Turing complete

Computational Completeness of P Systems Using Maximal Variants of the Set Derivation Mode

We consider P systems only allowing rules to be used in at most one copy in each derivation step, especially the variant of the maximally parallel derivation mode where each rule may only be used at most once. Moreover, we also consider the derivation mode where from those sets of rules only those are taken which have the maximal number of rules. We check the computational completeness proofs of several variants of P systems and show that some of them even literally still hold true for the for these two new set derivation modes. Moreover, we establish two new results for P systems using target selection for the rules to be chosen together with these two new set derivation modes

Proceedings of the Workshop on Membrane Computing, WMC 2016.

yesThis Workshop on Membrane Computing, at the Conference of Unconventional Computation and Natural Computation (UCNC), 12th July 2016, Manchester, UK, is the second event of this type after the Workshop at UCNC 2015 in Auckland, New Zealand*. Following the tradition of the 2015 Workshop the Proceedings are published as technical report. The Workshop consisted of one invited talk and six contributed presentations (three full papers and three extended abstracts) covering a broad spectrum of topics in Membrane Computing, from computational and complexity theory to formal verification, simulation and applications in robotics. All these papers – see below, but the last extended abstract, are included in this volume. The invited talk given by Rudolf Freund, “P SystemsWorking in Set Modes”, presented a general overview on basic topics in the theory of Membrane Computing as well as new developments and future research directions in this area. Radu Nicolescu in “Distributed and Parallel Dynamic Programming Algorithms Modelled on cP Systems” presented an interesting dynamic programming algorithm in a distributed and parallel setting based on P systems enriched with adequate data structure and programming concepts representation. Omar Belingheri, Antonio E. Porreca and Claudio Zandron showed in “P Systems with Hybrid Sets” that P systems with negative multiplicities of objects are less powerful than Turing machines. Artiom Alhazov, Rudolf Freund and Sergiu Ivanov presented in “Extended Spiking Neural P Systems with States” new results regading the newly introduced topic of spiking neural P systems where states are considered. “Selection Criteria for Statistical Model Checker”, by Mehmet E. Bakir and Mike Stannett, presented some early experiments in selecting adequate statistical model checkers for biological systems modelled with P systems. In “Towards Agent-Based Simulation of Kernel P Systems using FLAME and FLAME GPU”, Raluca Lefticaru, Luis F. Macías-Ramos, Ionuţ M. Niculescu, Laurenţiu Mierlă presented some of the advatages of implementing kernel P systems simulations in FLAME. Andrei G. Florea and Cătălin Buiu, in “An Efficient Implementation and Integration of a P Colony Simulator for Swarm Robotics Applications" presented an interesting and efficient implementation based on P colonies for swarms of Kilobot robots. *http://ucnc15.wordpress.fos.auckland.ac.nz/workshop-on-membrane-computingwmc- at-the-conference-on-unconventional-computation-natural-computation

An Improved Apriori Algorithm Based on an Evolution-Communication Tissue-Like P System with Promoters and Inhibitors

Apriori algorithm, as a typical frequent itemsets mining method, can help researchers and practitioners discover implicit associations from large amounts of data. In this work, a fast Apriori algorithm, called ECTPPI-Apriori, for processing large datasets, is proposed, which is based on an evolution-communication tissue-like P system with promoters and inhibitors. The structure of the ECTPPI-Apriori algorithm is tissue-like and the evolution rules of the algorithm are object rewriting rules. The time complexity of ECTPPI-Apriori is substantially improved from that of the conventional Apriori algorithms. The results give some hints to improve conventional algorithms by using membrane computing models

The Computational Complexity of Tissue P Systems with Evolutional Symport/Antiport Rules

Tissue P systems with evolutional communication (symport/antiport) rules are computational models inspired by biochemical systems consisting of multiple individuals living and cooperating in a certain environment, where objects can be modified when moving from one region to another region. In this work, cell separation, inspired from membrane fission process, is introduced in the framework of tissue P systems with evolutional communication rules.The computational complexity of this kind of P systems is investigated. It is proved that only problems in class P can be efficiently solved by tissue P systems with cell separation with evolutional communication rules of length at most (��, 1), for each natural number �� ≥ 1. In the case where that length is upper bounded by (3, 2), a polynomial time solution to the SAT problem is provided, hence, assuming that P ̸= NP a new boundary between tractability and NP-hardness on the basis of the length of evolutional communication rules is provided. Finally, a new simulator for tissue P systems with evolutional communication rules is designed and is used to check the correctness of the solution to the SAT problem

Methodologies & formalisms for modeling macroscopic biological problems

This work presents a new computational approach, based on the formalism of P systems, for modelling and running simulations of animal population dynamics phenomena. The three formalisms proposed are: MPP systems (Minimal Probabilistic P systems), APP systems (Attributed Probabilistic P systems) and MAPP systems (Multilevel Attributed Probabilistic P systems). All of them are formally defined by providing their syntax notations and formal semantics as inference rules. Case study are provided with examples for all three formalism

Towards a P Systems Normal Form Preserving Step-by-step Behavior

Starting from a compositional operational semantics of transition P Systems we have previously defined, we face the problem of developing an axiomatization that is sound and complete with respect to some behavioural equivalence. To achieve this goal, we propose to transform the systems into a unique normal form which preserves the semantics. As a first step, we introduce axioms which allow the transformation of mem- brane structures with no dissolving rules into flat membranes. We discuss the problems which arise when dissolving rules are allowed and we suggest possible solutions. We leave as future work the further step that leads to the wanted normal form

Multilevel Attributed Probabilistic P System Implementazione e Definizione

1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Published Material . . . . . . . . . . . . . . . . . . . . . . . . 5 2 State of the art 7 3 Background 13 3.1 Denition of multiset and related operations . . . . . . . . . . 13 3.2 Notions of P Systems . . . . . . . . . . . . . . . . . . . . . . . 14 3.2.1 Formal denition of a P Systems . . . . . . . . . . . . 15 3.2.2 Some relevant extensions . . . . . . . . . . . . . . . . . 16 3.2.3 Minimal Probabilistic P systems . . . . . . . . . . . . 18 3.2.4 Attributed Probabilistic P Systems . . . . . . . . . . . 22 4 Multilevel Attributed Probabilistic P Systems 25 4.1 MAPPS formal and informal denition . . . . . . . . . . . . . 26 4.1.1 informal denition . . . . . . . . . . . . . . . . . . . . 26 4.1.2 Formal denition . . . . . . . . . . . . . . . . . . . . . 28 4.2 Semantics, formal denition . . . . . . . . . . . . . . . . . . . 31 4.2.1 notes about termination . . . . . . . . . . . . . . . . . 36 4.3 MAPPS a simple example . . . . . . . . . . . . . . . . . . . . 37 4.4 MAPPS another example: Predator / Prey . . . . . . . . . . 39 4.4.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.4.2 Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.4.3 Functions . . . . . . . . . . . . . . . . . . . . . . . . . 45 5 APP - General purpose implementation 47 5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.1.1 Programming language used in the project . . . . . . . 47 5.2 Commentary to code . . . . . . . . . . . . . . . . . . . . . . . 48 5.2.1 software engine . . . . . . . . . . . . . . . . . . . . . . 48 5.2.2 input les . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.2.3 apply method . . . . . . . . . . . . . . . . . . . . . . . 52 7 5.2.4 Rating method . . . . . . . . . . . . . . . . . . . . . . 53 5.2.5 How we implements the probability - Matrices of choice 54 5.2.6 State updating . . . . . . . . . . . . . . . . . . . . . . 56 6 MAPP - General purpose implementation 59 6.1 Software engine extension . . . . . . . . . . . . . . . . . . . . 59 6.1.1 class Membrane . . . . . . . . . . . . . . . . . . . . . 59 6.1.2 input les . . . . . . . . . . . . . . . . . . . . . . . . . 62 6.1.3 class Membrane implementation . . . . . . . . . . . . 62 6.1.4 Membrane Attributes . . . . . . . . . . . . . . . . . . 63 6.1.5 Updating functions . . . . . . . . . . . . . . . . . . . . 64 6.1.6 Membrane example . . . . . . . . . . . . . . . . . . . . 65 7 A case of study: Serengeti Lions. 67 7.1 Serengeti Lions - informal description . . . . . . . . . . . . . . 69 7.2 Serengeti Lions - Formal denition . . . . . . . . . . . . . . . 71 8 Experimental results 83 8.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 8.2 data and results . . . . . . . . . . . . . . . . . . . . . . . . . . 83 8.2.1 rst results . . . . . . . . . . . . . . . . . . . . . . . . 83 8.3 A step forward . . . . . . . . . . . . . . . . . . . . . . . . . . 89 9 Final Conclusions 93 Bibliography 9

Switchable Genetic Oscillator Operating in Quasi-Stable Mode

Ring topologies of repressing genes have qualitatively different long-term dynamics if the number of genes is odd (they oscillate) or even (they exhibit bistability). However, these attractors may not fully explain the observed behavior in transient and stochastic environments such as the cell. We show here that even repressilators possess quasi-stable, travelling-wave periodic solutions that are reachable, long-lived and robust to parameter changes. These solutions underlie the sustained oscillations observed in even rings in the stochastic regime, even if these circuits are expected to behave as switches. The existence of such solutions can also be exploited for control purposes: operation of the system around the quasi-stable orbit allows us to turn on and off the oscillations reliably and on demand. We illustrate these ideas with a simple protocol based on optical interference that can induce oscillations robustly both in the stochastic and deterministic regimes.Comment: 24 pages, 5 main figure