| Abstract: | A new model for the well-known problem, the satisfiablility problem of boolean formula (SAT), is introduced. Based on this model, some variants of SAT and their properties are presented. Denote by NP the class of all languages which can be decided by a non-deterministic polynomial Turing machine and by P the class of all languages which can be decided by a deterministic polynomial-time Turing machine. This model also allows us to give another candidate for the natural problems in ((NP-NPC)-P), denoted as NPI, under the assumption P≠NP, where NPC represents NP-complete. It is proven that this candidate is not in NPC under P≠NP. While, it is indeed in NPI under some stronger but reasonable assumption, specifically, under the Exponential-Time Hypothesis (ETH). Thus we can partially solve this long standing important open problem. |
