Servo-thread or base-thread

I am processing output of the step generator which used the base-thread for the step generation. Now if I am inverting the output of via a "not" component, shouldn't the "not" be hooked to the same base thread so the "not" doesn't introduce additional delay? The steps are being used to drive a stepper motor.

Yes, but you may not need to use a not. Most of Linuxcnc's hardware interface drivers have a built in means of inverting a signal. For example, with the parallel port driver using the pin "parport.0.pin-1-out-invert" instead of "parport.0.pin-1-out" would invert the signal sent to pin #1.

When I try to use "parport.0.pin-1-out-invert" in place of "parport.0.pin-1-out" I get an error : pin parport.0.pin-1-out-invert does not exist.

I'm sorry, I mislead you. Parport.0.pin-1-out-invert is not a pin, it is a parameter, that inverts the parallel port pin. So you would connect to the parallel port pin as normal using the normal names, and to invert the signal you would add the line "setp parport.0.pin-1-out-invert true" to your hal file.