Small Universal Reversible Counter Machines

Artiom Alhazov (1) , Sergey Verlan (2) , Rudolf Freund (3)

1 Institute of Mathematics [Moldova]
2 LACL - Laboratoire d'Algorithmique Complexité et Logique
3 Institut für Computersprachen

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>=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.

Domaines: Théorie et langage formel [cs.FL]

Artiom Alhazov, Sergey Verlan, Rudolf Freund. Small Universal Reversible Counter Machines. Adamatzky, Andrew. Reversibility and Universality: Essays Presented to Kenichi Morita on the Occasion of his 70th Birthday, Springer International Publishing, pp.433--446, 2018, 978-3-319-73216-9. ⟨10.1007/978-3-319-73216-9_20⟩. ⟨hal-01757525⟩