Time-free Solution to Independent Set Problem using P Systems with Active Membranes

Membrane computing is a branch of natural computing aiming to abstract computing models from the structure and functioning of living cells. The computation models obtained in the field of membrane computing are usually called P systems. P systems have been used to solve computationally hard problems efficiently on the assumption that the execution of each rule is completed in exactly one time-unit (a global clock is assumed for timing and synchronizing the execution of rules). However, in biological reality, different biological processes take different times to be completed, which can also be influenced by many environmental factors. In this work, with this biological reality, we give a time-free solution to independent set problem using P systems with active membranes, which solve the problem independent of the execution time of the involved rules.

A Note on the Reality of Incomputable Real Numbers and Its Systemic Significance

We discuss mathematical and physical arguments contrasting continuous and discrete, limitless discretization as arbitrary granularity. In this regard, we focus on Incomputable (lacking an algorithm that computes in finite time) Real Numbers (IRNs). We consider how, for measurements, the usual approach to dealing with IRNs is to approximate to avoid the need for more detailed, unrealistic surveys. In this regard, we contrast effective computation and emergent computation. Furthermore, we consider the alternative option of taking into account the properties of the decimal part of IRNs, such as the occurrence, distribution, combinations, quasi-periodicities, and other contextual properties, e.g., topological. For instance, in correspondence with chaotic behaviors, quasi-periodic solutions, quasi-systems, uniqueness, and singularities, non-computability represents and corresponds to theoretically incomplete properties of the processes of complexity, such as emergence and quantum-like properties. We elaborate upon cases of equivalences and symmetries, characterizing complexity and infiniteness as corresponding to the usage of multiple non-equivalent models that are constructively and theoretically incomplete due to the non-exhaustive nature of the multiplicity of complexity. Finally, we detail alternative computational approaches, such as hypercomputation, natural computing, quantum computing, and analog and hybrid computing. The reality of IRNs is considered to represent the theoretical incompleteness of complex phenomena taking place through collapse from equivalences and symmetries. A world of precise finite values, even if approximated, is assumed to have dynamics that are zippable in analytical formulae and to be computable and symbolically representable in the way it functions. A world of arbitrary precise infinite values with dynamics that are non-zippable in analytical formulae, non-computable, and, for instance, sub-symbolically representable, is assumed to be almost compatible with the coherence of emergence. The real world is assumed to be a continuous combination of the two—functioning and emergent—where the second dominates and is the norm, and the first is the locus of primarily epistemic extracts. Research on IRNs should focus on properties representing and corresponding to those that are detectable in real, even if extreme, phenomena, such as emergence and quantum phenomena.

Solomon Marcus Contributions to Theoretical Computer Science and Applications

Solomon Marcus (1925–2016) was one of the founders of the Romanian theoretical computer science. His pioneering contributions to automata and formal language theories, mathematical linguistics and natural computing have been widely recognised internationally. In this paper we briefly present his publications in theoretical computer science and related areas, which consist in almost ninety papers. Finally we present a selection of ten Marcus books in these areas.

Improved Biogeography-Based Optimization Algorithm by Hierarchical Tissue-Like P System with Triggering Ablation Rules

BBO is one of the new metaheuristic optimization algorithms, which is based on the science of biogeography. It can be used to solve optimization problems through the migration and drift of species between habitats. Many improved BBO algorithms have been proposed, but there were still many shortcomings in global optimization, convergence speed, and algorithm complexity. In response to the above problems, this paper proposes an improved BBO algorithm (DCGBBO) by hierarchical tissue-like P system with triggering ablation rules. Membrane computing is a branch of natural computing that aims to abstract computational models (P system) from the structure and function of biological cells and from the collaboration of cell groups such as organs and tissues. In this paper, firstly, a dynamic crossover migration operator is generated to improve the global search ability and also increase the species diversity. Secondly, a dynamic Gaussian mutation operator is introduced to speed up convergence and improve local search capabilities. To guarantee the correctness and feasibility of the mutation, a unified maximum mutation rate is designed. Finally, a hierarchical tissue-like P system with triggering ablation rules is combined with the DCGBBO algorithm, making use of evolution rules and communication rules to achieve migration and mutation of solutions and reduce computational complexity. In the experiments, eight classic benchmark functions and CEC 2017 benchmark functions are applied to demonstrate the effect of our algorithm. We apply the proposed algorithm to segment four colour pictures, and the results proved to be better compared to other algorithms.

A Survey of Nature-Inspired Computing

Nature-inspired computing is a type of human-designed computing motivated by nature, which is based on the employ of paradigms, mechanisms, and principles underlying natural systems. In this article, a versatile and vigorous bio-inspired branch of natural computing, named membrane computing is discussed. This computing paradigm is aroused by the internal membrane function and the structure of biological cells. We first introduce some basic concepts and formalisms of membrane computing, and then some basic types or variants of P systems (also named membrane systems ) are presented. The state-of-the-art computability theory and a pioneering computational complexity theory are presented with P system frameworks and numerous solutions to hard computational problems (especially NP -complete problems) via P systems with membrane division are reported. Finally, a number of applications and open problems of P systems are briefly described.