How to enumerate trees from a context-free grammar
This provides a general method for numbering expressions in natural logical languages and could be extended to other combinatorial problems, though it appears incremental in nature.
The paper tackles the problem of enumerating trees from a context-free grammar by presenting a simple algorithm that uses a pairing function to create a bijection between derivations and natural numbers, enabling unique decoding of trees from counting. It also generalizes this approach to more complex derivations, such as analogs of Lempel-Ziv coding on trees.
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.