First, there is no fixed such that the invertible-map equivalence ≡ k , P IM coincides with isomorphism on all finite graphs. Second, no extension of fixed-point logic by linear-algebraic operators over fields can capture polynomial time.
Sep 15, 2021 · This note draws conclusions that arise by combining two recent papers, by Anuj Dawar, Erich Grädel, and Wied Pakusa, published at ICALP 2019 and by Moritz ...
The intuition is that two graphs G ≡IM k,Q H cannot be distinguished by iterative refinements of equivalences on k-tuples defined via linear operators on ...
Feb 7, 2024 · We show a first limitation of this approach by studying linear-algebraic logic, which is strictly more expressive than first-order counting ...
Limitations of the invertible-map equivalences - RWTH AACHEN ...
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Limitations of the invertible-map equivalences. Dawar, Anuj; Grädel, Erich (Corresponding author); Lichter, Moritz. Eynsham, Oxford : Oxford Univ.
This note draws conclusions that arise by combining two recent papers, by Anuj Dawar, Erich Grädel and Wied Pakusa, published at ICALP 2019, and by Moritz ...
Logics induce equivalence relations on finite structures. • A ≡Ck B if A and B satisfy the same Ck-sentences. • Logical equivalences are characterised by ...
This note draws conclusions that arise by combining two recent papers, by Anuj Dawar, Erich Gr\"adel, and Wied Pakusa, published at ICALP 2019 and by Moritz ...
Limitations of the Invertible-Map Equivalences · UnRAVeL Research Training Group [080060] · Department of Mathematics [110000] · Mathematical Fundamentals of ...
We show a first limitation of this approach by studying linear-algebraic logic, which is strictly more expressive than first-order counting logic and whose k- ...