If parallel algorithms achieve speedup only at the cost of exponentially many processors relative to input size, there is little hope of building a concrete computing device to implement them
How much data or how many items a program needs to process; for example, the number of items in a list you're sorting.
Parallel algorithms(as used in computer science)
Step-by-step instructions for solving a problem where many tasks happen at the same time instead of one after another, like having multiple workers tackle different parts of a job simultaneously.
Processors(as used in computer science)
The computing chips or units that actually do the calculations and execute instructions in a computer.
Speedup(as used in computer science)
How much faster a computation gets done when you use multiple processors working together compared to using just one.
3 Parallel, probabilistic, and quantum complexity Even taking into account our current inability to resolve Open Questions 1–3, the hierarchy of complexity classes depicted in Figure 2 ranging from \(\textbf{P}\) to \(\textbf{EXP}\) represent the most robust benchmarks of computational difficulty now available. Beyond this hierarchy a wide array of additional classes are also studied which are believed to demarcate additional structure either inside \(\textbf{P}\) or between \(\textbf{P}\) and \