Lower bounds on the size of deterministic parsers

Abstract

Worst-case lower bounds on the size of deterministic parsers as a function of the size of the grammar are studied. It is shown first that there is no recursive function bounding the succinctness gained using parsable content-free grammars instead of parsers. Also is shown that there exists an infinite family of LL(2) grammars such that the size of every left or right parser for these grammars must be ⩾2^cm for some c > 0, where m is the size of the grammar. Similarly, it is shown that there exists an infinite family of LR(0) grammars such that the size of every right parser for these grammars must be $\text{⩾2}{}^{\mathrm{c}}\text{m}$. Hence for all k ⩾ 0, the class of the LR(k) grammars cannot be parsed using right parsers whose size is polynomially bounded in the size of the grammar, and for all k ⩾ 2, the class of the LL(k) grammars cannot be parsed using left parsers whose size is polynomially bounded in the size of the grammar.