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Shortest paths in one-counter systems

Dmitry Chistikov ; Wojciech Czerwiński ; Piotr Hofman ; Michał Pilipczuk ; Michael Wehar.

We show that any one-counter automaton with $n$ states, if its language is non-empty, accepts some word of length at most $O(n^2)$. This closes the gap between the previously known upper bound of $O(n^3)$ and lower bound of $\Omega(n^2)$. More generally, we prove a tight upper bound on the length of&nbsp;[&hellip;]

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The Big-O Problem

Dmitry Chistikov ; Stefan Kiefer ; Andrzej S. Murawski ; David Purser.

Given two weighted automata, we consider the problem of whether one is big-O of the other, i.e., if the weight of every finite word in the first is not greater than some constant multiple of the weight in the second. We show that the problem is undecidable, even for the instantiation of weighted&nbsp;[&hellip;]

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