His contributions include the design of the Floyd–Warshall algorithm (independently of Stephen Warshall), which efficiently finds all shortest paths in a graph and his work on parsing; Floyd's cycle-finding algorithm for detecting cycles in a sequence was attributed to him as well.

Born in New York City, Floyd finished high school at age 14.

Becoming a computer operator in the early 1960s, he began publishing many papers, including on compilers (particularly parsing).

He was a pioneer of operator-precedence grammars, and is credited with initiating the field of programming language semantics in Floyd (1967).

He was a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi,[3] which specified, maintains, and supports the programming languages ALGOL 60 and ALGOL 68.

[6] His hobbies included hiking, and he was an avid backgammon player: We once were stuck at the Chicago O'Hare airport for hours, waiting for our flight to leave, owing to a snow storm.

As we sat at our gate, Bob asked me, in a casual manner, "do you know how to play backgammon?"

He proceeded instead to give me a free lesson in the art and science of playing backgammon.