Looking for an Analogue of Rice's Theorem in Circuit Complexity Theory

Rice’s Theorem says that every nontrivial semantic property of programs is undecidable. In this spirit we show the following: Every nontrivial absolute (gap, relative) counting property of circuits is UP-hard with respect to polynomial-time Turing reductions. For generators [31] we show a perfect analogue of Rice’s Theorem. Mathematics Subject Classification: 03D15, 68Q15.

• Type: Conference
• Year: 1997
• Where: KGC
• Authors: Bernd Borchert, Frank Stephan
• Keywords: Automated Reasoning, KGC 1997, Mathematics Subject Classification, Nontrivial Semantic Property, Polynomial-time Turing Reductions