How to enumerate trees from a context-free grammar

• URL: http://arxiv.org/abs/2305.00522v1
• Date: Sun, 30 Apr 2023 16:40:54 GMT
• Title: How to enumerate trees from a context-free grammar
• Authors: Steven T. Piantadosi
• Abstract summary: I present a simple algorithm for enumerating the trees generated by a Context Free Grammar (CFG) I also show how this algorithm may be generalized to more general forms of derivation, including analogs of Lempel-Ziv coding on trees.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: I present a simple algorithm for enumerating the trees generated by a Context Free Grammar (CFG). The algorithm uses a pairing function to form a bijection between CFG derivations and natural numbers, so that trees can be uniquely decoded from counting. This provides a general way to number expressions in natural logical languages, and potentially can be extended to other combinatorial problems. I also show how this algorithm may be generalized to more general forms of derivation, including analogs of Lempel-Ziv coding on trees.

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