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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| Vydáno v: | Logical methods in computer science Ročník 18, Issue 4 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Logical Methods in Computer Science e.V
12.12.2022
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| Témata: | |
| ISSN: | 1860-5974, 1860-5974 |
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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. |
|---|---|
| AbstractList | 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. 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. |
| Author | Różycki, Jakub Hofman, Piotr |
| Author_xml | – sequence: 1 givenname: Piotr surname: Hofman fullname: Hofman, Piotr – sequence: 2 givenname: Jakub surname: Różycki fullname: Różycki, Jakub |
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unordered-data vectors and to ordered-data vectors, we perform a further
generalisation... Following a recently considered generalisation of linear equations to unordered-data vectors and to ordered-data vectors, we perform a further generalisation... |
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| Title | Linear equations for unordered data vectors in $[D]^k\to{}Z^d |
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