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In the context of studying for a class on distributed systems I stumbled upon the following definitions that I do not understand:

  • Let C(t) be a perfect clock.
  • A clock Ci(t) is called correct at time t if Ci(t) = C(t).
  • A clock Ci(t) is called accurate at time t if dCi(t)/dt = dC(t)/dt ≡ 1.

Question 1: I do get what the definition of correctness means, but how is accuracy different from it?

Question 2: What's the d all about? A not so mathematical explaination would be much appreciated.

Thank you very much in advance!

typeduke
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1 Answers1

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Without more symbols, but mathematical conceptually: Accuracy means your clock is changing at the same rate as the perfect clock. Correctness means the clocks register the same time. d is derivative - you can check a calculus book, or wikipedia. t means time, so change of the imperfect/perfect clock with respect to time.

jacoblambert
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    Thank you so much! Just to make sure I get it: A clock Ci(t) can be considered to be accurate even if it's time is totally different from C's (perfect clock) time. Accuracy is, instead, all about the requirement that Ci alters its time at the same rate/pace as C, right? Then, dCi(t)/dt = dC(t)/dt is true. Or did I mix it all up in my head now? :P – typeduke Jul 14 '15 at 13:56
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    And one more question: If C is indeed a perfect clock, shouldn't dC(t)/dt equal 1 by definition? – typeduke Jul 14 '15 at 14:01
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    you got it - in both your comments. in your second, it does, that's why the three equals marks: dCi(t)/dt = dC(t)/dt ≡ 1. – jacoblambert Jul 14 '15 at 14:03