Abstract
Let G i = ( V N , V T , P , X i ) be a linear context-free grammar with the nonterminals V N , the terminals V T , the start symbol X i , and a special production system P ⊆ V N × ( V N V N ∪ V T ). The stack size S i ( τ ) of a derivation tree τ generated by G i is the maximum number of nodes in the stack during postorder traversing of τ . We give an explicit formula for the average stack size {if354-1} of a derivation tree with n leaves that are labeled by terminals and show that {if354-2} has an asymptotic behavior of the form {if354-3}, where the functions F 1 ( i )} ( n ) and F 2 ( i )} ( n ) are quotients of trigonometric polynomials.
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