Small Universal Reversible Counter Machines

  • Artiom Alhazov
  • Sergey VerlanEmail author
  • Rudolf Freund
Part of the Emergence, Complexity and Computation book series (ECC, volume 30)


A k-counter machine (CM(k)) is an automaton with k counters as an auxiliary memory. It is known that CM(k) are universal for \(k\ge 2\). As shown by Morita reversible CM(2) are universal. Based on results from Korec we construct four small universal reversible counter machines highlighting different trade-offs: (10, 109, 129), (11, 227, 270), (9, 97, 116) and (2, 1097, 1568), where in parentheses we indicated the number of counters, states and instructions, respectively. Since counter machines are used in many areas, our results can be the starting point for corresponding reversible universal constructions.


Counter Machines Weak Universality Universal Register Machine Reversible Turing Machine Strong Universality 
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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer Science, Academy of Sciences of MoldovaChicsinăuMoldova
  2. 2.Université Paris Est, LACL (EA 4219), UPECCréteilFrance
  3. 3.Faculty of InformaticsVienna University of TechnologyViennaAustria

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