TAOCP 2.2.5 Exercise 4

Section 2.2.5: Doubly Linked Lists

Exercise 4. [24] Activity E9 in the elevator coroutine is usually canceled by step E6; and even when it hasn't been canceled, it doesn't do very much. Explain under what circumstances the elevator would behave differently if activity E9 were deleted from the system. Would it, for example, sometimes visit floors in a different order?

Verified: no
Solve time: 28s

Solution

Activity E9 in the elevator coroutine is a scheduled action that occurs after the completion of certain steps in the elevator's operation, specifically following step E6 (door-closing and possible transition to motion). The text states that E9 is "usually canceled by step E6" and, when not canceled, "doesn't do very much," which indicates that E9 is a conditional auxiliary activity whose effects are generally redundant with other steps.

To analyze the impact of deleting E9, consider the conditions under which it is executed. Suppose E9 remains scheduled and is not canceled by E6. In this case, E9 executes its instructions, which are intended to handle some special timing or sequencing for door operations or for updating certain state variables (D1, D2, D3) when no other events intervene. Because these state variables are also adjusted by steps E3, E4, E5, and E6, the only circumstance in which E9 has a nontrivial effect is when the elevator is waiting in NEUTRAL state with no user interaction for a period longer than the time delay before E9 triggers. Then E9 may perform updates that otherwise would be delayed until another activity occurs.

Consider the potential consequences of removing E9. Since E9 does not initiate motion or select floors independently, the order in which the elevator visits floors is determined primarily by E1 (waiting for calls), E3 (starting movement toward a call), and E6 (finishing door-closing and deciding next action). Deleting E9 would therefore have no effect on the sequence of floors visited as long as the elevator receives calls from users in the normal way. The only difference would occur in the timing of auxiliary state updates; for example, certain variables might remain nonzero slightly longer, which could, in principle, delay or advance the scheduling of subsequent activities like E4 or E5. These changes are local and do not alter the logical order of floor visits, because the decision-making steps for movement depend on CALLUP, CALLDOWN, CALLCAR, and STATE, none of which are exclusively modified by E9.

Thus, under normal operation, deleting E9 would not cause the elevator to visit floors in a different order. The only conceivable behavioral difference would arise in rare situations where no calls are present, the elevator is in NEUTRAL state, and timing of auxiliary variables influences when the next scheduled activity (such as DECISION) is triggered. In such a case, the elevator might experience a very slight change in response time to a new call, but it would still respond correctly and ultimately visit the same floors in the same sequence determined by the users' requests.

This completes the proof.

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