2011/10/10 by Turlough Neary, Neary, Turlough, Damien Woods +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #Cellular Automata and Applications #Computability, Logic, AI Algorithms #Computational Complexity (cs.CC) #DNA and Biological Computing #FOS: Computer and information sciences
paper · pdf · doi:10.48550/arxiv.1110.2230
openalex publication_date 2011/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We survey some work concerned with small universal Turing machines, cellular automata, tag systems, and other simple models of computation. For example it has been an open question for some time as to whether the smallest known universal Turing machines of Minsky, Rogozhin, Baiocchi and Kudlek are efficient (polynomial time) simulators of Turing machines. These are some of the most intuitively simple computational devices and previously the best known simulations were exponentially slow. We discuss recent work that shows that these machines are indeed efficient simulators. In addition, another related result shows that Rule 110, a well-known elementary cellular automaton, is efficiently universal. We also discuss some old and new universal program size results, including the smallest known universal Turing machines. We finish the survey with results on generalised and restricted Turing machine models including machines with a periodic background on the tape (instead of a blank symbol), multiple tapes, multiple dimensions, and machines that never write to their tape. We then discuss some ideas for future work.