Small universal register machines

Small universal spiking neural P systems

“…In [4], the register machines are used for computing functions, with the universality defined as follows. Let (ϕ 0 , ϕ 1 , .…”

“…Looking for small universal computing devices is a natural and well investigated topic in computer science, see, e.g., [4], [11], and the references therein. Recently, this issue started to be considered also in membrane computing; first contributions of this kind can be found in [13] (for tissue P systems with string objects processed by splicing operations) and [1] (for symport/antiport P systems).…”

“…The proof from [3] is based on simulating register machines with SN P systems, hence the same strategy as that followed in [1] in search of small universal P systems is useful also here: starting from a small universal register machine as those constructed in [4], we can get a small universal SN P system, with the important mentioning that in [4] one works with register machines computing functions. That is why we also start here with this case.…”

“…For this case, a universal register machine with 8 registers and 23 instructions (the halting one included) was constructed in [4]. (The "code" of the particular partial recursive function and the argument of the function are introduced in registers 1 and 2 of the universal machine and the value of the function for that argument, if defined, is found in register 0 when/if the machine halts.)…”

“…(The "code" of the particular partial recursive function and the argument of the function are introduced in registers 1 and 2 of the universal machine and the value of the function for that argument, if defined, is found in register 0 when/if the machine halts.) Following then the construction of an SN P system simulating a register machine from [3], with some improvements inspired from [2] and some additional "code optimization", as well as a suitable input module, we get an SN P system with 84 neurons simulating the register machine from [4].…”