Numerical P Systems With Boolean Condition And Their Universalities

Bio-inspired computing is the cross fusion of computer science and biological science.It has the advantages of high parallelism,high efficiency and strong fault tolerance.Membrane computing is an important branch of bio-inspired computing,which aims to abstract computational models from the structure and function of biological cells and the collaboration of cell swarm in organs and tissues.At present,membrane computing has become into a hot field in bio-inspired computing.Numerical P systems are a kind of variant of membrane computing models.which are a class of distributed and parallel computing systems abstracted from the structure of biological cells and the economics ideas.In recent years,by introducing some control mechanisms,several variants of numerical P system have been proposed,for example,enzymatic numerical P systems,numerical P systems with threshold and numerical P systems with production threshold.In order to control the execution of program more effectively,this paper introduces a more general Boolean control mechanism into the numerical P system,and proposes a new variant of numerical P system,called numerical P system with Boolean condition(for short,BNP systems).Compared to the existing variants,BNP systems provide more flexible and powerful program control ability.The innovations in this paper are summarized as follows:(1)A new variant of the numerical P system,the numerical P system with Boolean conditions,is proposed.(2)We prove that BNP systems as number generating devices,respectively,under one-parallel working mode and sequential working mode,are Turing universal.(3)We prove that BNP systems as number accepting devices,respectively,under all-parallel working mode,one-parallel working mode and sequential working mode,are Turing universal.(4)We prove that BNP systems,respectively,under all-parallel working mode,one-parallel working mode and sequential working mode,can be used as Turing universal function computing devices.(5)This paper studies the generation ability of BNP system as a language generator,respectively,under one-parallel working mode and sequential working mode,and compares the generated language with the infinite language,finite language,regular language and non-context-free language in Chomsky language.