For example, suppose M=3, T1 ... T6 have respective lengths 3, 2, 3, 4, 2, and 1, and T2 < T3, T1 < T4, T2 < T4, T3 < T5, and D=8. Then one valid schedule would be the following:
M1: Task T1 from 0 to 3, idle from 3 to 5, task T5 from 5 to 7, idle from 7 to 8 M2: Task T2 from 0 to 2, idle from 2 to 3, task T4 from 3 to 7, idle from 7 to 8 M3: Idle from 0 to 2, Task T3 from 2 to 5, task T6 from 5 to 6.If l(T), M, and D are all small integers, then the problem can be compiled into propositional satisfiability using propositional atoms of the form T_P_K meaning that task T begins on processor P at time K, where K=0 ... D-1. The number of propositional atoms is thus |T| * M * D. Describe the constraints you need for the general case. Illustrate each category of constraint with a sample constraint from the above example. As a function of M, |T|, and D, how many constraints are there (order of magnitude)?
p(X,Y) --- Predicate. X is a parent of Y.Express the following statements in L.
fa(X,Y) --- Predicate. X is a father of Y.
mo(X,Y) --- Predicate. X is a mother of Y.
fe(X) --- Predicate. X is female
a(X) --- Predicate. X is alive.
o(X) --- Predicate. X is an orphan.
s,a,b --- Constant. Sarah, Andy, Bob.