The tensor spectral threshold decision problem is ∃R-hard via an explicit polynomial-time reduction from bounded quartic equality feasibility.
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Tensor degeneracy is ∃ℝ-complete via exact algebraic reductions from quadratic feasibility, while hyperdeterminant vanishing's deterministic hardness reduces to a structured PIT instance.
In concurrent graph games with distributed private randomness, memoryless strategies decide threshold reachability (NP-hard) and almost-sure reachability is NP-complete; IRATL extends ATL for probability thresholds without shared randomness.
citing papers explorer
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Tensor Spectral Threshold is $\exists\mathbb{R}$-Hard
The tensor spectral threshold decision problem is ∃R-hard via an explicit polynomial-time reduction from bounded quartic equality feasibility.
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$\exists\mathbb{R}$-Completeness of Tensor Degeneracy and a Derandomization Barrier for Hyperdeterminants
Tensor degeneracy is ∃ℝ-complete via exact algebraic reductions from quadratic feasibility, while hyperdeterminant vanishing's deterministic hardness reduces to a structured PIT instance.
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Randomise Alone, Reach as a Team
In concurrent graph games with distributed private randomness, memoryless strategies decide threshold reachability (NP-hard) and almost-sure reachability is NP-complete; IRATL extends ATL for probability thresholds without shared randomness.