Arithmetic abilities of SNP systems with astrocytes producing calcium

Abstract

Are the membrane systems able of performing arithmetic operations? In the last dozen years, there were published several implementations of the arithmetic operations based on membrane systems by using all available topologies (cell-like, tissue-like, or neural-like). In particular, the spiking neural P systems perform arithmetic operations by using the numbers represented in binary base. In this paper, we consider numbers represented in unary base (to each number n corresponds an object with multiplicity n), and we propose two encodings for the main arithmetic operations (addition, subtraction, multiplication and division) between numbers given in unary base: (i) for each pair of input values generate an instance of a spiking neural P system with astrocytes producing calcium with rules based on these values; (ii) generate a spiking neural P system with astrocytes producing calcium that does not depend on these values. While the second approach is commonly used in membrane computing to construct only a system for each operation, the first approach is interesting because each system is uniquely constructed based on a pair of input values , and so it performs faster the desired arithmetic operation. The main advantage (with respect to other attempts) of using any of these two approaches to perform arithmetic operations consists in the reduced size of created systems (number of locations and used rules). Additionally, we extend a semantic interpreter (in Haskell) for spiking neural P systems to test all the encodings of the arithmetic operations presented in this paper.