Formula for the Candidate Set in Greedy Search

A text generation model using a greedy decoding approach has produced the sequence 'The dog chased'. At the current step, it calculates the probabilities for the next token as follows: 'the' (0.7), 'a' (0.2), 'its' (0.08), and 'his' (0.02). Based on this information, what constitutes the set of candidate sequences that will be considered for the next step of the generation process?

When generating text by iteratively appending the single most probable token at each step, the collection of partial sequences under consideration for the next step always includes multiple high-probability options.

Candidate Sequence in a Word-by-Word Generation