Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A clause is not-all-equal satisfied if it has at least one literal assigned with true and one literal assigned with false. Max NAE-SAT is given by a boolean variable set U and a clause set C, asks to find an assignment of U, such that the number of not-all-equal satisfied clauses in C is maximized. Max NAE-SAT turns into Max NAE-k-SAT if each clause contains exactly k literals. Local search has long been used in various SAT solvers. Hover, little has been done on local search to approximate Max NAE-k-SAT. Moreover, it is still open for what a quantitative bound could Max NAE-k-SAT be approximated to, at best. ,  propose a local search algorithm which can approximate Max NAE-k-SAT to 2 k - 1 2 k - 1 - 1 for each fixed k ź 2 . Then  show that Max NAE-k-SAT cannot be approximated within 2 k - 1 2 k - 1 - 1 in polynomial time, if P ź NP . The algorithm for Max NAE-k-SAT can be extended to approximate Max NAE-SAT where each clause contains at least k literals to 2 k - 1 2 k - 1 - 1 . Using the algorithm for Max NAE-SAT where each clause contains at least k literals,  present a new algorithm to approximate Max-SAT where each clause contains at least k literals to 2 k 2 k - 1 .
['Aiyong Xian', 'Kaiyuan Zhu', 'Daming Zhu', 'Lianrong Pu', 'Hong Liu']
I am writing a research paper on a idea Approximating Max NAE-k-SAT by anonymous local search
[{"from": "human", "value": "I am writing a research paper on a idea Approximating Max NAE-k-SAT by anonymous local search"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A clause is not-all-equal satisfied if it has at least one literal assigned with true and one literal assigned with false. Max NAE-SAT is given by a boolean variable set U and a clause set C, asks to find an assignment of U, such that the number of not-all-equal satisfied clauses in C is maximized. Max NAE-SAT turns into Max NAE-k-SAT if each clause contains exactly k literals. Local search has long been used in various SAT solvers. Hover, little has been done on local search to approximate Max NAE-k-SAT. Moreover, it is still open for what a quantitative bound could Max NAE-k-SAT be approximated to, at best. ,  propose a local search algorithm which can approximate Max NAE-k-SAT to 2 k - 1 2 k - 1 - 1 for each fixed k \u017a 2 . Then  show that Max NAE-k-SAT cannot be approximated within 2 k - 1 2 k - 1 - 1 in polynomial time, if P \u017a NP . The algorithm for Max NAE-k-SAT can be extended to approximate Max NAE-SAT where each clause contains at least k literals to 2 k - 1 2 k - 1 - 1 . Using the algorithm for Max NAE-SAT where each clause contains at least k literals,  present a new algorithm to approximate Max-SAT where each clause contains at least k literals to 2 k 2 k - 1 ."}]