Computational Universality and Efficiency in Morphogenetic Systems - Sosík, Petr; Drastík, Jan (Machines, Computations, and Universality, 2022)
The topic of computational universality and efficiency of various types of abstract machines is still subject of intensive research. Besides many crucial open theoretical problems, there are also numerous potential applications, e.g., in construction of small physical computing machines (nano-automata), harnessing algorithmic processes in biology or biochemistry, efficient solving of computationally hard problems and many more. The study of computability and complexity of new abstract models can help to understand the borderline between non-universality and universality, or between tractable and intractable problems. Here we study computational universality (in Turing sense) and computational complexity in the framework of morphogenetic (M) systems—computational models combining properties of membrane systems and algorithmic self-assembly of pre-defined atomic polytopes. Even very simple morphogenetic systems can exhibit complex self-organizing behaviour and phenomena such as controlled growth, self-reproduction, homeostasis and self-healing. We present two small universal M systems, one of which is additionally self-healing. Then we show how the borderline P versus NP can be characterized by some properties of morphogenetic systems.