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arXiv · 1804.06336

Weak Cost Register Automata are Still Powerful

Shaull Almagor·Michaël Cadilhac·Filip Mazowiecki·Guillermo A. Pérez
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Abstract

We consider one of the weakest variants of cost register automata over a tropical semiring, namely copyless cost register automata over $\mathbb{N}$ 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, in particular equivalence, disproving 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.

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Shaull Almagor, Michaël Cadilhac, Filip Mazowiecki, Guillermo A. Pérez. 2018-04-17. Weak Cost Register Automata are Still Powerful. https://arxiv.org/abs/1804.06336

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