Chapter

Automata, Universality, Computation

Volume 12 of the series Emergence, Complexity and Computation pp 117-126

Maurice Margenstern’s Contributions to the Field of Small Universal Turing Machines

  • Turlough NearyAffiliated withInstitute for Neuroinformatics, University of Zürich and ETH Zürich Email author 
  • , Damien WoodsAffiliated withCalifornia Institute of Technology

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Abstract

On the occasion of his 65th birthday we survey some of the work of Maurice Margenstern on small universal Turing machines. Margenstern has been one of the most prolific contributors to this field, having constructed numerous small universal programs for a number of Turing machine models. These positive results are complemented by Margenstern’s negative results, or lower bounds, on universal program size. Finally, he has even explored the space in-between the known program size upper and lower bounds by giving small programs that iterate the Collatz function, which suggests that proving negative results on programs of this size will be at least as hard as resolving the Collatz problem.