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On the succinctness properties of unordered context-free grammars

M. Drew. Moshier, William C. Rounds

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Abstract

We prove in this paper that unordered, or ID/LP grammars, are exponentially more succinct than context-free grammars, by exhibiting a sequence (Ln) of finite languages such that the size of any CFG for Ln must grow exponentially in n, but which can be described by polynomial-size ID/LP grammars. The results have implications for the description of free word order languages.

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What this paper is about

We prove in this paper that unordered, or ID/LP grammars, are exponentially more succinct than context-free grammars, by exhibiting a sequence (Ln) of finite languages such that the size of any CFG for Ln must grow exponentially in n, but which can be described by polynomial-size ID/LP grammars. The results have implications for the description of free word order languages.

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Available abstract

We prove in this paper that unordered, or ID/LP grammars, are exponentially more succinct than context-free grammars, by exhibiting a sequence (Ln) of finite languages such that the size of any CFG for Ln must grow exponentially in n, but which can be described by polynomial-size ID/LP grammars. The results have implications for the description of free word order languages.

Key concepts: Succinctness, Tree-adjoining grammar, Context-free grammar, Rule-based machine translation, L-attributed grammar, Computer science, Context-sensitive grammar, Embedded pushdown automaton

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