Splicing systems for universal turing machines

Abstract

In this paper, we look at extended splicing systems (i.e., H systems) in order to find how small such a system can be in order to generate a recursively enumerable language. It turns out that starting from a Turing machine M with alphabet A and finite set of states Q which generates a given recursively enumerable language L, we need around 2× |I|+2 rules in order to define an extended H system H which generates L, where I is the set of instructions of Turing machine M. Next, coding the states of Q and the non-terminal symbols of L, we obtain an extended H system H1 which generates L using |A|+2 symbols. At last, by encoding the alphabet, we obtain a splicing system U which generates a universal recursively enumerable set using only two letters. © Springer-Verlag Berlin Heidelberg 2005.