3 results
Piotr Hofman ; Jakub Różycki.
Following a recently considered generalisation of linear equations to unordered-data vectors and to ordered-data vectors, we perform a further generalisation to data vectors that are functions from k-element subsets of the unordered-data set to vectors of integer numbers. These generalised equations […]
Published on December 12, 2022
Piotr Hofman ; Slawomir Lasota ; Richard Mayr ; Patrick Totzke.
One-counter nets (OCN) are finite automata equipped with a counter that can store non-negative integer values, and that cannot be tested for zero. Equivalently, these are exactly 1-dimensional vector addition systems with states. We show that both strong and weak simulation preorder on OCN are […]
Published on March 14, 2016
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 […]
Published on March 5, 2019