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"Hard" real-time refers to a system that must complete its operation within a specified timeframe -- typically in tiny time units, e.g., microseconds. Hard real-time systems are typically used when interfacing with physical systems -- like a robotic system, anti-lock brakes, or a pacemaker. "Live" real-time refers to systems that interact with humans and must deliver results within a timeframe that doesn't cause the user to get frustrated with the delay.
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