Linear equations for unordered data vectors in $[D]^k\to{}Z^d$
Computational Complexity
2023-06-22 v5 Formal Languages and Automata Theory
Symbolic Computation
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.
Keywords
Cite
@article{arxiv.2109.03025,
title = {Linear equations for unordered data vectors in $[D]^k\to{}Z^d$},
author = {Piotr Hofman and Jakub Różycki},
journal= {arXiv preprint arXiv:2109.03025},
year = {2023}
}