Conditions to hold true for deadlock to occur?

1. Mutual exclusion: At least one resource must be held in a non-sharable mode, meaning only one process can use it at a time.

2. Hold and wait: Processes must hold resources while waiting for additional resources that are currently being held by other processes.

3. No preemption: Resources cannot be forcibly taken away from a process. A process must voluntarily release a resource before another process can use it.

4. Circular wait: There must be a circular chain of two or more processes, each waiting for a resource held by the next process in the chain.

If all of these conditions are met, deadlock can occur.

Conditions for Deadlock:

1. Mutual Exclusion: Resources are non-sharable, meaning only one process can use them at a time.
2. Hold and Wait: Processes hold resources while waiting for additional resources.
3. No Preemption: Resources cannot be forcibly taken away from a process even if it is waiting for other resources.
4. Circular Wait: There is a circular path of waiting processes, each waiting for a resource held by the next process in the circle.

Formalized Representation:

A deadlock can be represented as a directed graph, where:

- Nodes: Processes
- Edges: Resources held by processes
- Deadlock: A cycle in the graph where all nodes are involved in a circular wait.