Node-splitting increases the size of the grammar and reduces the amount of training data available for each grammar rule. This leads to overfitting, so it is important to arrive at a correct level of granularity for a particular training set. The split and merge algorithm starts with a simple X-bar grammar and alternately splits and merges non-terminals to find the set of annotates nodes that maximizes the likelihood of training set treebank. 

Columbia University

We can split NP non-terminals into two versions: one for subjects, and one for objects. Having two nodes ($NP_{subject}$ and $NP_{object}$) would allow us to correctly model their different distributional properties since we could have different probabilities for the rules $NP_{subject} \to PRP$ and $NP_{object} \to PRP$. The intuition of splits can be implemented by doing parent annotation, in which we annotate each node with its parent in the parse tree. A PCFG can also be improved by splitting pre-terminal POS nodes. Adding specific tags for parts of speech can be useful in improving PCFG modeling. 


Improving PCFGs by splitting NP non-terminals


An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

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