Tag Systems and the Complexity of Simple Programs

Conference paper

DOI: 10.1007/978-3-662-47221-7_2

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9099)
Cite this paper as:
Neary T., Woods D. (2015) Tag Systems and the Complexity of Simple Programs. In: Kari J. (eds) Cellular Automata and Discrete Complex Systems. AUTOMATA 2015. Lecture Notes in Computer Science, vol 9099. Springer, Berlin, Heidelberg

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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Copyright information

© IFIP International Federation for Information Processing 2015

Authors and Affiliations

  1. 1.Institute of NeuroinformaticsUniversity of Zürich and ETH ZürichZürichSwitzerland
  2. 2.Division of Engineering and Applied ScienceCalifornia Institute of TechnologyPasadenaUSA

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