State Based Control of Timed Discrete Event Systems using Binary ...

Chapter 5. BDD based implementation 43A set can also be represented by a predicate. For example the set A := {a, b, c} can berepresented by:P A := (v = a) ∨ (v = b) ∨ (v = c)where v is a BDD variable.The state set Q p × Q s can be described by the tuple (q p , q s ) where q p ∈ Q p and q s ∈ Q s .This set can be represented by the predicate S:S(v p , v s ) := (0 ≤ v p ≤ n p − 1) ∧ (0 ≤ v s ≤ n s − 1)where {0, ..., n p − 1} are the states of G p and {0, ..., n s − 1} are the states of G s .The set of states (q p , q s ) where (q p , q s ) F can be described byS F (v p , v s ) := S ∧ ¬(∃(v p , v s )(S ∧ T s, f ))whereT s, f =∨σ∈Σ forT s, σand (∃(v p , v s ))(S ∧ T s, f ) 1 will be the set of states (q p , q s ) where ∃σ ∈ Σ for , δ s (q s , σ)!.Actually the existential quantifier quantifies out the variable v s ′ which is present in T s, f[9] [19]. Now we will present the realization of each step of algorithm in Theorem 4.1.1.Step 1: P good1 := 1.1 This can be done using the Buddy package function bdd exist(Appendix A)