Download Computer architecture handbook on Verilog HDL by Hyde D.C. PDF

By Hyde D.C.

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Extra info for Computer architecture handbook on Verilog HDL

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We can do this by taking a finite set of contexts F ⊂ Σ ∗ ×Σ ∗ , which will include the special context (λ, λ) and constructing a lattice using only these contexts and all strings Σ ∗ . This give us a finite lattice B(L, F ), which will have at most 2|F | elements. We can think of F as being a set of features, where a string w has the feature (context) (l, r) iff lwr ∈ L. Definition 2. For a language L and a set of context F ⊆ Σ ∗ × Σ ∗ , the partial lattice B(L, F ) is the lattice of concepts S, C where C ⊆ F , and where C = S ∩ F , and S = C .

Let pref (t) and w be a tree t in prefix notation and a substring of pref (t), respectively. Then, w is the prefix notation of a subtree of t, if and only if ac(w) = 0, and ac(w1 ) ≥ 1 for each w1 , where w = w1 x, x = ε. Proof. In [10]. We show the dual principle for the postfix notation. Theorem 3. Let post(t) and w be a tree t in postfix notation and a substring of post(t), respectively. Then, w is the postfix notation of a subtree of t, if and only if ac(w) = 0, and ac(w1 ) ≤ −1 for each w1 , where w = xw1 , x = ε.

Given this partial order we can see easily that in fact this forms a complete lattice; which we write B(L), called the syntactic concept lattice. Here the topmost element is = C(Σ ∗ ) bottom is written ⊥ = C(Σ ∗ × Σ ∗ ), and the two meet and join operations are defined as Sx , Cx ∧ Sy , Cy is defined as Sx ∩Sy , (Sx ∩Sy ) and ∨ dually as (Cx ∩ Cy ) , Cx ∩ Cy . Figure 1 shows the syntactic concept lattice for the regular language L = {(ab)∗ }. L is infinite, but the lattice B(L) is finite and has only 7 concepts.

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