Counter Machines and Distributed Automata

A Story About Exchanging Space and Time
  • Olivier Carton
  • Bruno Guillon
  • Fabian ReiterEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10875)


We prove the equivalence of two classes of counter machines and one class of distributed automata. Our counter machines operate on finite words, which they read from left to right while incrementing or decrementing a fixed number of counters. The two classes differ in the extra features they offer: one allows to copy counter values, whereas the other allows to compute copyless sums of counters. Our distributed automata, on the other hand, operate on directed path graphs that represent words. All nodes of a path synchronously execute the same finite-state machine, whose state diagram must be acyclic except for self-loops, and each node receives as input the state of its direct predecessor. These devices form a subclass of linear-time one-way cellular automata.



We are grateful to the anonymous reviewers for their constructive comments. We also thank Martin Kutrib and Pierre Guillon for interesting discussions, especially concerning the connection of our results with the field of cellular automata. This work was partially supported by the ERC project EQualIS (FP7-308087) and the DeLTA project (ANR-16-CE40-0007).


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Copyright information

© IFIP International Federation for Information Processing 2018

Authors and Affiliations

  1. 1.IRIF, Université Paris DiderotParisFrance
  2. 2.Department of Computer ScienceUniversity of MilanMilanItaly
  3. 3.LSV, Université Paris-SaclayParisFrance

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