Zhaobo Liu · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.27962 · cited by 0 works (OpenAlex) · open-access PDF
我们研究了对离散时间系统的最小正面的实现的复杂性,我们证明了,鉴于具有合理系数的严格正确的转移矩阵和编码为统一的顺序约束,决定是否在该约束内存在正面的实现,对于现实的存在理论来说是完整的。
Machine translation (Meta M2M100); the English original follows.
We study the complexity of minimal positive realization for discrete-time systems. We prove that, given a strictly proper transfer matrix with rational coefficients and an order bound encoded in unary, deciding whether a positive realization exists within that bound is complete for the existential theory of the reals. We further prove hardness for stable single-input single-output transfer functions that admit positive realizations, even when the bound equals the McMillan degree.
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Topics: Realization (probability), Mathematics, Upper and lower bounds, Existential quantification, Transfer (computing), Discrete mathematics
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