Abstract
<title>Abstract</title> <p> Despite the special theoretical and practical significance of self-replication and the Turing machine (TM), being one of the most fundamental mathematical models on algorithmic processes, the reproduction/printing of a TM program by itself (starting from the blank tape) has not yet been realized in practice. Nevertheless, the reproduction of the program describing the driving algorithm is a key step in self-replication. To the author’s knowledge, the only exception is the <italic>preliminary self-printing</italic> (or quine) <italic>TM</italic> (program) worked out by us in a recent publication. Although, there exist other so-called self-describing TM-based algorithms, they do not print their complete program, only its (abbreviated) representation. In the paper, the preliminary self-printing TM is improved to the new <italic>simplified self-printing TM</italic> , in the sense that the length and the running time of the latter’s program are much lower than that of the former one. Mathematical derivation (containing heuristic considerations) is provided and suggests that the worked out construction should be close to optimal/minimal. By executing the provided (simplest) self-printing program (version), one can directly check its self-printing ability. In fact, the simplified TM program (similarly as the preliminary one) can print out not only itself but, optionally, any (other) program, and can be used to improve von Neumann’s fundamental self-replicating concept, in a certain sense. It is discussed how the simplified self-printing program can be utilized in artificial life research to model the genome of simplest possible organisms capable of self-reproduction, in a purely mathematical context. </p>