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TRIE Memory, CACM, Vol. 3, No. 9 (1960), pp. 490-499. [7] Knott, G. : Expandable Open Addressing Hash Table Storage and Retrieval, Proc. ACMSIGFIDET Workshop on Data Description, Access and Control (1971), pp. 186206. : Dynamic Hashing, BIT, Vol. 18 (1978), pp. 184-201. : Virtual Hashing: a Dynamically Changing Hashing, Proc. VLDB (1978), pp. 517-523. [10] Merret, T. : Relational Information Systems, Reston Pub. , 1984. [11] Orenstein, J. : Multidimensional Tries Used for Associative Searching, Inf.

The function nextlocation returns the address of the next location of a code which has already been output, that is, the last address of code + 1. Procedure pop(TRUE, op) pops up a set of addresses from the TRUE stack and assigns it to a variable op. Procedure patch(op, true, loc) assigns the value of loc to the true field of every address of the set op. 2 59 Parenthesis Check We will here consider the problem of checking whether or not a given string of parentheses is balanced. Our attribute grammar description is given in Fig.

12) proves that the lemma also holds for A = C{T). D Using this lemma, we can prove the following theorem. 1. Let leaves(T) denote the set of node identifiers of all the leaves in a colored binary trie Γ. Then it holds that Cavg(T, A) = E a € / e o t ) e s (T(l/2)'^«». (16) Proof. We will prove this theorem by mathematical induction on the number of leaves of T. If T has only one leaf, it has only its root node, and hence, p{A{a)) is zero for any attribute A. Therefore, the right hand side of Eq.

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