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

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...

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Bibliographic Details
Published in:	Logical methods in computer science Vol. 18, Issue 4
Main Authors:	Hofman, Piotr, Różycki, Jakub
Format:	Journal Article
Language:	English
Published:	Logical Methods in Computer Science e.V 12.12.2022
Subjects:	68q85 computer science - computational complexity computer science - formal languages and automata theory computer science - symbolic computation f.3.1 f.4.2 g.2.2
ISSN:	1860-5974, 1860-5974
Online Access:	Get full text
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Summary:	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.
ISSN:	1860-5974 1860-5974
DOI:	10.46298/lmcs-18(4:11)2022