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Consider a system having p processes, where each process needs a maximum of m instances of resource type R1. Given that there are r instances

Consider a system having p processes, where each process needs a maximum of m instances of resource type R1. Given that there are r instances of resource type R1 in total, what is the minimum value of r as a function of p and m to ensure that the system is deadlock free?

(An explanation in addition to the formula would be very helpful, thanks)

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