Gai's own graduate work picked up where Narasimhia's left off, and focused on the inscriptions from the eighth to the tenth centuries.
Gai subsequently received his Ph.D. from the University of Bombay, and his thesis, A Historical Grammar of Old Kannada: based entirely on the Kannada inscriptions of the 8th, 9th and 10th centuries A. D. was published in book form by the Deccan College Post-graduate and Research Institute, Poona, in 1946.
The book received a positive review by Thomas Burrow in Bulletin of the School of Oriental and African Studies, University of London, Vol.
Gai also authored over one hundred research papers on epigraphy, history, linguistics and archaeology.
XX and Epigraphia Indica vols XXXV to XXXVIII, published by the Archaeological Survey of India.