Most if not all (some early electronic controls used relay logic) run off Industrial PLCs(programmable logic controllers).
Roller coasters have more more in common with your standard automated assembly line in a factory than anything else when it comes to control systems. Many manufacturers use Allen Bradley/Rockwell Automation as their preferred brand of gear.
You'll find most coaster manufactures use a preferred sub contractor for their controls. For instance Intamin use Inautec. RMC often use Irvine Ondrey, S&S actually do their own. Disney also build all their own control systems for their rides regardless of who supplies them.
They em are all programmed in simple but highly dependable Ladder Logic with each manufacturer of equipment, AB, Siemens, Mitsubishi, etc, having their own proprietary software to do so.
Previously coasters would use multiple PLCs wired together for error checking and redundancy however recently most people have changed over to using a single Safety Rated PLC as these have become more economical and flexible.
A dark ark ride will typically operate the same for vehicle control (basically anything that can kill you) and a seperate system will control the show elements. This may include more PLCs but also likely audio, video, lighting controllers as well which usually come out of the theatrical/entertainment industry.