A Second Step Towards Complexity-Theoretic Analogs of Rice's Theorem

Lane A. Hemaspaandra; Joerg Rothe

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arXiv · cs/9907038

A Second Step Towards Complexity-Theoretic Analogs of Rice's Theorem

Lane A. Hemaspaandra·Joerg Rothe

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Abstract

Rice's Theorem states that every nontrivial language property of the recursively enumerable sets is undecidable. Borchert and Stephan initiated the search for complexity-theoretic analogs of Rice's Theorem. In particular, they proved that every nontrivial counting property of circuits is UP-hard, and that a number of closely related problems are SPP-hard. The present paper studies whether their UP-hardness result itself can be improved to SPP-hardness. We show that their UP-hardness result cannot be strengthened to SPP-hardness unless unlikely complexity class containments hold. Nonetheless, we prove that every P-constructibly bi-infinite counting property of circuits is SPP-hard. We also raise their general lower bound from unambiguous nondeterminism to constant-ambiguity nondeterminism.

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Lane A. Hemaspaandra, Joerg Rothe. 1999-07-25. A Second Step Towards Complexity-Theoretic Analogs of Rice's Theorem. https://arxiv.org/abs/cs/9907038

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