The Humphrey pump could operate with either a four-stroke or two-stroke cycle.
A two-stroke cycle was also possible, if adequate scavenging could be achieved.
With the addition of a supercharger or turbocharger, opposed-piston designs can make efficient two-stroke cycle Diesel engines.
They are two-stroke cycle and generally carbureted.
These typically run on a two-stroke cycle, but are radically different from glow two-stroke engines.
The thermodynamic analysis of the actual four-stroke or two-stroke cycles is not a simple task.
Now that you understand the two-stroke cycle you can see why.
Other engine types such as diesel, or two-stroke cycle can differ in the exact implementation, but the general theme still applies.
The simplest glow-engines operate on the two-stroke cycle.
Petrol engines may run on the four-stroke cycle or the two-stroke cycle.