For instance, designed a cellular automaton algorithm to generate the prime numbers based on an earlier solution to the firing squad synchronization problem.

The firing squad synchronization problem has been generalized to many other types of cellular automaton, including higher dimensional arrays of cells .

He is also the namesake of the Moore neighborhood for cellular automata, used by Conway's Game of Life, and was the first to publish on the firing squad synchronization problem in cellular automata.

For instance, he showed how to generate the sequence of prime numbers using a one-dimensional cellular automaton, based on earlier solutions to the firing squad synchronization problem, and his work in this area set the foundation for much later work on parallel algorithms.

During his visit to MIT in 1961, Goto devised the first time-optimal solution to the firing squad synchronization problem, a problem of designing a cellular automaton in which all cells simultaneously fire, starting from an initial configuration with only one active cell.

The firing squad synchronization problem is a problem in computer science and cellular automata in which the goal is to design a cellular automaton that, starting with a single active cell, eventually reaches a state in which all cells are simultaneously active.

He is also known for posing the firing squad synchronization problem of designing an automaton that, starting from a single non-quiescent cell, evolves to a configuration in which all cells reach the same non-quiescent state at the same time; this problem was again solved by Moore.