I was learning LALR parsers from the dragon book (Compilers: Principles, Techniques, and Tools by Alfred V. Aho, Monica S. Lam, Ravi Sethi, and Jeffrey D. Ullman) and I came across the example on page 267. I'll try my best to describe my question without needing the actual book for reference.
The book states that:
I4 and I7 form such a pair, with core $\{C -> d.\}$ . Similarly, I3 and I6 form another pair, with core $\{C -> c.C, C -> .cC, C -> .d\}$ . There is one more pair, I8 and I9 with common core $\{C -> cC.\}$ .
Here, I3 and I6 have the same set of cores $\{C -> c.C, C -> .cC, C -> .d\}$ . My question is, should I combine I3 and I6 if I3 had the set of cores $\{C -> c.C, C -> .cC\}$ and I6 had the set of cores $\{C -> c.C, C -> .cC, C -> .d\}$ ? That is, should the set of cores for the itemsets should be exactly the same for combining them or can one be a proper subset of the other?
Thanks in advance!