Before revision:  In this paper, motivated by the difficulty in designing parallel batch-dynamic algorithms by hand, we propose a framework for algorithmically dynamizing static round-synchronous algorithms  to obtain parallel batch-dynamic algorithms with good bounds on their work and span.
After revision:  In this work, we design the first work-efficient parallel batch-dynamic algorithms by hand, we propose a framework for algorithmically dynamizing static round-synchronous algorithms to obtain parallel batch-dynamic algorithms with good bounds on their work and span.