Algorithm Time Complexity
An algorithm is said to take linear time, or O(n) time, if its time complexity is O(n). Informally, this means that the running time increases at most linearly with the size of the input.
Relationship between PA, NP, and P
Is PA a subset of NP? P is subset of NP (any problem that can be solved by a deterministic machine in polynomial time can also be solved by a non-deterministic machine in polynomial time).
Chess Complexity
Is chess np or p? It’s a common misconception that chess is NP-hard. Generalized chess may be NP-hard. Chess has an 8×8 board, generalized chess has an nxn board with many pieces.
Chess Solvability
Is chess solved? No, chess is not a solved game. There are around 10^50 possible games, and more like 10^120 reasonable games (Shannon Number).
Impact of P vs. NP on Cryptography
How does P NP affect cryptography? A proof of P = NP would imply that almost no secure cryptographic primitives can exist according to the accepted definitions of security.
TSP Complexity
Is tsp np-complete? Traveling Salesman Optimization(TSP-OPT) is a NP-hard problem and Traveling Salesman Search(TSP) is NP-complete. However, TSP-OPT can be reduced to TSP.
Relationship between NP-Hard and NP-Complete
Are NP-hard problems NP-complete? A Problem X is NP-Hard if there is an NP-Complete problem Y, such that Y is reducible to X in polynomial time. NP-Hard problems are as hard as NP-Complete problems.
Difference between NP-Hard and NP-Complete
NP-hard: To solve this problem, it does not have to be in NP.
NP-Complete: To solve this problem, it must be both NP and NP-hard problems.