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Tag Systems and the Complexity of Simple Programs

Abstract : In this mini-survey we discuss time complexity and program size results for universal Turing machines, tag systems, cellular automata, and other simple models of computation. We discuss results that show that many of the simplest known models of computation including the smallest known universal Turing machines and the elementary cellular automaton Rule 110 are efficient simulators of Turing machines. We also recall a recent result where the halting problem for tag systems with only 2 symbols (the minimum possible) is proved undecidable. This result has already yielded applications including a significant improvement on previous undecidability bounds for the Post correspondence problem and the matrix mortality problem.
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Submitted on : Friday, January 20, 2017 - 4:09:33 PM
Last modification on : Thursday, May 27, 2021 - 1:54:06 PM
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Turlough Neary, Damien Woods. Tag Systems and the Complexity of Simple Programs. 21st Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2015, Turku, Finland. pp.11-16, ⟨10.1007/978-3-662-47221-7_2⟩. ⟨hal-01442479⟩



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