Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Set agreement and renaming are two tasks that allow processes to coordinate, even when agreement is impossible. In k -set agreement, n processes must decide on at most k of their input values. While n -set agreement is trivially wait-free solvable by each process deciding on its input, ( n - 1 ) -set agreement is not wait-free solvable. In M -renaming, processes must decide on distinct names in a range of size M . For any number n of processes, ( 2 n - 1 ) -renaming is wait-free solvable, but surprisingly, ( 2 n - 2 ) -renaming is wait-free solvable if and only if n is not a prime por; the only previous lor bound on the number of names necessary for renaming, when n is not a prime por, is n + 1 . In adaptive renaming, M decreases when the number p of participants in the execution decreases. It is known that ( 2 p - 1 ) -adaptive renaming is wait-free solvable, while ( 2 p - ? p n - 1 ? ) -adaptive renaming is not. presents counting-based proofs for the above mentioned impossibility results: n processes can wait-free solve neither ( n - 1 ) -set agreement nor ( 2 p - ? p n - 1 ? ) -adaptive renaming; if n is a prime por, n processes cannot wait-free solve ( 2 n - 2 ) -renaming. For an arbitrary number of processes,  give a lor bound for renaming, by reduction from renaming for a different number of processes, and relying on the distribution of prime numbers.Our proofs combine simple operational properties of a restricted set of executions with elementary counting arguments to show the existence of an execution violating the task's conditions. This makes the proofs easier to understand, verify, and,  hope, extend.  consider the wait-free solvability of tasks in shared memory systems.Only combinatorial and number-theoretic arguments are used. ( n - 1 ) -set agreement is not wait-free solvable.Adaptive ( 2 n - 2 ) -renaming and strong symmetry breaking are not wait-free solvable.Nonadaptive ( 2 n - 2 ) -renaming and ak symmetry breaking are not wait-free solvable, when n is the por of a prime number.
['Hagit Attiya', 'Ami Paz']
I am writing a research paper on a idea Counting-based impossibility proofs for set agreement and renaming
[{"from": "human", "value": "I am writing a research paper on a idea Counting-based impossibility proofs for set agreement and renaming"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Set agreement and renaming are two tasks that allow processes to coordinate, even when agreement is impossible. In k -set agreement, n processes must decide on at most k of their input values. While n -set agreement is trivially wait-free solvable by each process deciding on its input, ( n - 1 ) -set agreement is not wait-free solvable. In M -renaming, processes must decide on distinct names in a range of size M . For any number n of processes, ( 2 n - 1 ) -renaming is wait-free solvable, but surprisingly, ( 2 n - 2 ) -renaming is wait-free solvable if and only if n is not a prime por; the only previous lor bound on the number of names necessary for renaming, when n is not a prime por, is n + 1 . In adaptive renaming, M decreases when the number p of participants in the execution decreases. It is known that ( 2 p - 1 ) -adaptive renaming is wait-free solvable, while ( 2 p - ? p n - 1 ? ) -adaptive renaming is not. presents counting-based proofs for the above mentioned impossibility results: n processes can wait-free solve neither ( n - 1 ) -set agreement nor ( 2 p - ? p n - 1 ? ) -adaptive renaming; if n is a prime por, n processes cannot wait-free solve ( 2 n - 2 ) -renaming. For an arbitrary number of processes,  give a lor bound for renaming, by reduction from renaming for a different number of processes, and relying on the distribution of prime numbers.Our proofs combine simple operational properties of a restricted set of executions with elementary counting arguments to show the existence of an execution violating the task's conditions. This makes the proofs easier to understand, verify, and,  hope, extend.  consider the wait-free solvability of tasks in shared memory systems.Only combinatorial and number-theoretic arguments are used. ( n - 1 ) -set agreement is not wait-free solvable.Adaptive ( 2 n - 2 ) -renaming and strong symmetry breaking are not wait-free solvable.Nonadaptive ( 2 n - 2 ) -renaming and ak symmetry breaking are not wait-free solvable, when n is the por of a prime number."}]