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Complexity of Equivalence Relations and Preorders from Computability Theory
Journal of Symbolic Logic. 2014. Vol. 3. No. 79. P. 859–881.
Ianovski E., Miller R., Ng K. M., Nies A.
We study the relative complexity of equivalence relations and preorders from computability theory and complexity theory. Given binary relations R, S, a componentwise reducibility is defined by
R ≤ S ⇔ ∃f ∀x, y [x R y ↔ f (x) S f (y)].
Here, f is taken from a suitable class of effective functions. For us the relations will be on natural numbers, and f must be computable. We show that there is a -complete equivalence relation, but no -complete for k ≥ 2. We show that preorders arising naturally in the above-mentioned areas are -complete. This includes polynomial time m-reducibility on exponential time sets, which is , almost inclusion on r.e. sets, which is , and Turing reducibility on r.e. sets, which is .
Language:
English
Hualin M., Jie Z., Jerome Y. et al., Journal of Internet Technology 2026 Vol. 27 No. 3 P. 367–382
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Springer, 2026.
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Netherlands: ScienceDirect, 2025.
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IEEE, 2024.
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Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
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Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
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