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 \({\cal H}\) 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 \({\cal L}\), we obtain an extended H system \({\cal H}_1\) which generates L using |A| + 2 symbols. At last, by encoding the alphabet, we obtain a splicing system \({\cal U}\) which generates a universal recursively enumerable set using only two letters.
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Harju, T., Margenstern, M. (2005). Splicing Systems for Universal Turing Machines. In: Ferretti, C., Mauri, G., Zandron, C. (eds) DNA Computing. DNA 2004. Lecture Notes in Computer Science, vol 3384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11493785_13
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DOI: https://doi.org/10.1007/11493785_13
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