What is an asynchronous programming in terms of c#?

Task objects, one for each input number, and use Task.Run to run the ComputeFibonacci method on a separate thread for each input number. The results are stored in an output array, and Task.WhenAll is used to wait for all tasks to complete before returning the results.
Note that in order for this approach to be effective, the ComputeFibonacci method should be implemented in a way that allows it to be run concurrently on multiple threads without interference or contention. This may require some additional synchronization or locking mechanisms to ensure thread safety, depending on the implementation.

Can you explain me how does state machine work?

Sure! A state machine is a computational model used to describe and analyze systems that change their behavior in response to input. It consists of a set of states and transitions between these states, which are triggered by input events.
In the context of software development, a state machine is often used to model the behavior of complex systems, such as user interfaces or business workflows. It is a way to represent the different states and transitions that a system can go through in response to user input or other events.
A state machine typically consists of three main components:

1. 
   States: These represent the different modes or conditions that the system can be in. Each state has a unique identifier and a set of properties that describe its behavior.
   
2. 
   Transitions: These represent the ways in which the system can move from one state to another in response to input events. Each transition has a trigger, which is an event that causes the transition to occur, and a set of actions, which are executed when the transition takes place.
   
3. 
   Inputs: These are the events or signals that can trigger a state transition. Inputs can be generated by the user, by other systems or processes, or by the system itself.
   

When an input event occurs, the state machine evaluates the current state and the available transitions to determine the appropriate action to take. It then executes the actions associated with the selected transition and moves the system to the next state.
State machines can be implemented using different programming techniques and tools, such as switch statements, if-else conditions, or specific libraries or frameworks designed for state machine modeling and execution. They are particularly useful in complex systems that require flexible and dynamic behavior, as they provide a clear and structured way to model and analyze the system's behavior.

So, in c# state machine handles all asynchronous programming?

In C#, a state machine can be used to handle asynchronous programming using the "async/await" syntax. The "async/await" keywords allow you to write asynchronous code that looks like synchronous code, making it easier to read and write.
When you use the "async" keyword on a method, it tells the compiler that the method contains asynchronous operations. Inside the method, you can use the "await" keyword to indicate which operations should be awaited before continuing execution of the method.
The "await" keyword causes the method to suspend execution until the awaited operation completes. While the operation is running, the state machine behind the scenes switches to a different state and executes other code.
When the awaited operation completes, the state machine resumes execution of the method from the point where it was suspended. The method then returns the result of the awaited operation.
The state machine handles the complex details of suspending and resuming execution, allowing you to write code that is both asynchronous and easy to read.
However, it's worth noting that not all asynchronous programming in C# requires the use of a state machine. For example, you can use the "Task" class to run a method asynchronously without using the "async/await" keywords. Additionally, there are other techniques for handling asynchronous programming in C#, such as using callbacks or events.

So, you are saying it is possible to create asynchronous program without async/await and state machine?

Yes, it is possible to create asynchronous programs in C# without using the "async/await" syntax and the state machine. Asynchronous programming can be achieved in several ways, such as using callbacks, events, or the Task Parallel Library (TPL).
One way to use callbacks for asynchronous programming is to define a delegate method that is called when an operation completes. The method can then be registered as a callback function for the operation. When the operation completes, the callback function is called with the results of the operation.
Another way to perform asynchronous programming in C# is to use the TPL, which provides a set of classes and methods for running tasks asynchronously. For example, you can use the "Task.Run" method to run a method on a background thread and return a Task object that represents the result of the operation.

Is async/await just a syntactic sugar?

Async/await is more than just syntactic sugar, although it does make writing and reading asynchronous code much easier.
At a high level, async/await allows you to write asynchronous code that looks and behaves like synchronous code. This means you can write asynchronous code that is much easier to understand and reason about, since it does not require complicated nested callbacks or other async programming patterns.
However, async/await is also backed by a powerful infrastructure that manages the underlying state machine and ensures that asynchronous operations are properly scheduled and executed. This infrastructure includes components like the Task Parallel Library (TPL), the .NET ThreadPool, and the Windows IO completion port system, all of which work together to provide efficient and scalable support for asynchronous programming.
So while async/await may look like just syntactic sugar on the surface, it is actually a powerful and well-designed framework that enables efficient and scalable asynchronous programming in C#.