Step 1: Identify the core question: The inquiry concerns the specific title held by the supreme rulers of the Vijayanagara Empire.
Step 2: Analyze each option:
(1) Rayas: This was indeed the title adopted by the Vijayanagara kings. 'Raya' is a direct Kannada/Telugu equivalent of the Sanskrit term 'Raja' (king). A prominent example is Krishnadeva Raya.
(2) Nayakas: These individuals were significant military commanders and regional administrators who served under the Rayas. They were subordinates, not the supreme rulers.
(3) Kudirais: This is the Tamil word for horses. While 'Kudirai chettis' (horse merchants) played a role in the empire's economy, 'Kudirai' itself was not a royal title.
(4) Samrajyapatis: Although this term denotes an emperor, 'Raya' was the distinct and commonly used title for the monarchs of Vijayanagara.
Step 3: Conclude: The supreme rulers of the Vijayanagara Empire were known as Rayas.