Linear equations for unordered data vectors in $[D]^k\to{}Z^d$

Piotr Hofman; Jakub Różycki

doi:10.46298/lmcs-18(4:11)2022

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arXiv · 2109.03025

Linear equations for unordered data vectors in $[D]^k\to{}Z^d$

Piotr Hofman·Jakub Różycki

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Abstract

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 naturally appear in the analysis of vector addition systems (or Petri nets) extended so that each token carries a set of unordered data. We show that nonnegative-integer solvability of linear equations is in nondeterministic exponential time while integer solvability is in polynomial time.

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BibTeX RIS

Piotr Hofman, Jakub Różycki. 2021-08-09. Linear equations for unordered data vectors in $[D]^k\to{}Z^d$. https://doi.org/10.46298/lmcs-18(4%3A11)2022

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