Year: 2023
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Piantadosi, Steven T.
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4367694375