Greedy Grammar Induction Algorithm Achieves Weak Equivalence on Benchmark Languages
Researchers propose a non-lexicalized grammar-induction procedure that uses indirect negative evidence to learn formal grammars from finite examples. The method separates recognition of observed data from rejection of unsupported generated strings, using a rule-coverage bound to constrain the search space. The approach demonstrates weak equivalence to target grammars across 31 benchmark runs including context-free and context-sensitive language families.
The paper introduces a greedy search algorithm for grammar induction that addresses the challenge of learning formal grammars from limited positive examples. The key innovation is the rule-coverage bound ℓ*(G), which limits the length of preterminal strings examined for each rule, creating a finite comparison universe where unsupported generated strings serve as implicit negative evidence. The authors prove a conditional weak-recovery theorem showing that under explicit reachability conditions and sufficient data saturation, the algorithm recovers grammars weakly equivalent to unknown targets. Complexity analysis shows polynomial exploration of rule-set extensions for each fixed incrementality radius. Empirical validation spans diverse language families: Dyck languages, palindromes, a^n b^n, English-like recursive structures, and inherently ambiguous languages, with grammar-level analysis confirming weak equivalence in all 31 benchmark runs.
Limitations & open questions
The paper does not discuss computational complexity bounds in absolute terms (e.g., runtime or memory requirements for specific benchmark instances), comparison with other grammar induction methods on the same benchmarks, or practical applicability to natural language learning beyond the English-like recursive fragments tested.
What different sources said
- arXiv cs.CLCenter
Greedy Grammar Induction with Indirect Negative Evidence
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