Zhaobo Liu · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.27962 · cited by 0 works (OpenAlex) · open-access PDF
Estudiamos la complejidad de la realización positiva mínima para los sistemas de tiempo discreto. demostramos que, dada una matriz de transferencia estrictamente adecuada con coeficientes racionales y un vínculo de orden codificado en unario, decidir si existe una realización positiva dentro de ese vínculo es completo para la teoría existencial de los reales.
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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