Generation Problems

Given a fixed computable binary operation , we study the complexity of the following generation problem: The input consists of strings ½ Ò . The question is whether is in the closure of ½ Ò under operation . For several subclasses of operations we prove tight upper and lower bounds for the generation problems. For example, we prove exponential-time upper and lower bounds for generation problems of length-monotonic polynomial-time computable operations. Other bounds involve classes like ÆÈ and ÈËÈ . Here the class of bivariate polynomials with positive coefficients turns out to be the most interesting class of operations. We show that many of the corresponding generation problems belong to ÆÈ. However, we do not know this for all of them, e.g., for ܾ · ¾Ý this is an open question. We prove ÆÈ-completeness for polynomials Ü Ý where ½. Also, we show ÆÈ-hardness for polynomials like ܾ · ¾Ý. As a by-product we obtain ÆÈ-completeness of the extended sum-of-...

• Type: Conference
• Year: 2004
• Where: MFCS
• Authors: Elmar Böhler, Christian Glaßer, Bernhard Schwarz, Klaus W. Wagner
• Keywords: Computable Binary Operation, Generation Problems, Lower Bounds, MFCS 2004