Zhaobo Liu · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.27962 · cited by 0 works (OpenAlex) · open-access PDF
우리는 합리적인 요소와 합리적인 순서로 인한 엄격한 적절한 전송 매트릭스와 유니어로 인코딩된 순서 묶음으로 인해, 그 묶음 내에 긍정적 인 실현이 존재하는지 결정하는 것이 실재적 이론에 완전하다고 증명한다.우리는 또한 긍정적 인 실현을 허용하는 안정적인 단일 입력 단일 출력 전송 기능에 대한 어려움을 증명한다.
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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