Weak Cost Register Automata are Still Powerful

Shaull Almagor, Michaël Cadilhac, Filip Mazowiecki, Guillermo A. Pérez

Research output: Contribution to journalArticlepeer-review


We consider one of the weakest variants of cost register automata over a tropical semiring, namely copyless cost register automata over N with updates using min and increments. We show that this model can simulate, in some sense, the runs of counter machines with zero-tests. We deduce that a number of problems pertaining to that model are undecidable, namely equivalence, upperboundedness, and semilinearity. In particular, the undecidability of equivalence disproves a conjecture of Alur et al. from 2012. To emphasize how weak these machines are, we also show that they can be expressed as a restricted form of linearly-ambiguous weighted automata.

Original languageEnglish
Pages (from-to)689-709
Number of pages21
JournalInternational Journal of Foundations of Computer Science
Issue number6
StatePublished - 1 Sep 2020


  • Cost register automata
  • equivalence
  • semilinearity

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)


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