Question

Give all possible values of \(x\) that can result from executing (define \(x\) 10) (parallel-execute (lambda () (set! \(x(* x x))\) ) (lambda () (set! \(x(* x x x))\) )) Which of these possibilities remain if we instead use serialized procedures: (define \(x\) 10) (define s (make-serializer)) (parallel-execute (s (lambda () (set! \(x(* x x))\) )) )) (s (lambda () (set! \(x(* x x x))\) )

Short answer

Parallel execution: possible results are 100, 1000, or 1000000. Serialized execution: the result is 1000000.

Step-by-step solution

Understanding Parallel Execution

Parallel execution allows multiple processes to run simultaneously. In this exercise, there are two operations executed in parallel: squaring the variable \(x\) and cubing the variable \(x\). Because these two operations are being executed at the same time, the order of their execution is non-deterministic, meaning either one could complete before the other.

Calculating Squaring Operation

The first operation is to square the variable \(x\): \(x = x^2\). Initially, \(x\) is set to 10, so if this operation executes first, we have \(x = 10^2 = 100\).

Calculating Cubing Operation

The second operation is to cube the variable \(x\): \(x = x^3\). Initially, \(x\) is 10, so if this operation executes first, we have \(x = 10^3 = 1000\).

Analyzing Parallel Outcomes

The parallel execution might result in different values of \(x\):1. If cubing happens first, \(x\) becomes 1000, then the squaring operation might read 1000 and square it, resulting in \(x = (1000)^2 = 1000000\).2. If squaring happens first, \(x\) becomes 100, then the cubing operation might read 100 and cube it, resulting in \(x = (100)^3 = 1000000\).3. If either operation solely completes without any interference from the other, \(x\) might be 100 or 1000, depending on whether squaring or cubing finishes first.

Understanding Serialized Execution

Serialized execution means the operations will run in a definite sequence. Here, a serializer `s` is used, ensuring that the two procedures execute one after the other, removing any non-determinism. The instructions call the squaring operation first, then the cubing operation.

Result of Serialized Execution

With serialization, the operations run in a strict sequence: 1. Squaring: \(x = 10^2 = 100\).2. Cubing: \(x = 100^3 = 1000000\).Thus, after serialized execution, \(x\) will consistently result in 1000000.

Key concepts

Serialization

Serialization is a mechanism to control the execution sequence of concurrent processes, ensuring they follow a specific order. Think of it as a method to line up tasks in a queue so that each task is executed one after the other, rather than at the same time.

This is essential when tasks can interfere with each other, such as updating the same variable in our example. By using serialization, like the 'make-serializer' in the exercise, we prevent the tasks of squaring and cubing the variable from running simultaneously, reducing unpredictability. It ensures the results are consistent and reliable, by forcing one task to complete before the next one begins. This method is crucial when you need to maintain a specific state or outcome.

• Controls sequence execution
• Prevents simultaneous task interference
• Ensures consistent results

Non-Determinism

Non-determinism in programming refers to outcomes that can vary unpredictably due to operations executed concurrently, especially without explicit control.

In the given exercise, multiple outcomes for the variable 'x' arise because the squaring and cubing operations are executed in parallel. The end value may differ because the order in which each operation occurs can change from one execution to another. This unpredictable behavior is called non-determinism. It leads to situations where you cannot be certain of what the final result will be without additional control, such as serialization.

• Unpredictable execution order
• Different outcomes possible
• Requires control for consistency

Operations Sequencing

Operations sequencing is the intentional arrangement in which tasks or instructions are executed to achieve a desired result.

In programming, the order of operations can significantly affect output, particularly when they modify a shared variable. In our exercise, this is evident when considering the sequence of squaring followed by cubing versus cubing followed by squaring. These different sequences can yield different results unless a mechanism like serialization is in place to enforce a specific order. Hence, understanding and controlling the sequence is vital to ensure a program behaves as intended.

• Directs task order
• Affects program outcome
• Critical in concurrent settings

Mutable State

Mutable state refers to the ability of a variable or data structure to be modified after it is created. In programming, variables like 'x' in our exercise can have their value changed by different operations.

This mutability is both powerful and precarious. It allows for dynamic data changes but also risks unintended side effects if multiple operations change the state simultaneously. In concurrent programming, handling mutable states delicately is crucial since overlapping updates can lead to incorrect or unexpected program behavior. Serialization helps manage these mutable states by ensuring changes occur in a controlled sequence, thereby maintaining integrity and predictability.

• Data can be changed
• Allows flexibility but can introduce hazards
• Requires careful handling in concurrent environments