***** NOT A TEACHER *****
Hello, Ademoglu:
1. One authority * says that the perfect infinitive (to have + past participle) regularly [my emphasis] represents an action which occurred before [my emphasis] the time of the [other] verb.
a. Another authority ** gives this example: "You seem [now] to have annoyed Anne yesterday."
b. IF you accept this idea, then you can see why "She seems [now] to have quit her job by next Monday [the future]" is not correct.
i. But it is correct to say: "She seems [now] to have quit her job [maybe last week?]."
2. Remember that one authority said that the perfect infinitive "regularly" refers to something in the past. The other authority ** gives this perfectly correct exception: "We hope to have finished the job by next Saturday."
a. I believe that you could correctly say: "She hopes to have quit her job by next Monday" or "She hopes that she will have quit her job by next Monday."
3. I think (think!) that this exception to the rule MAY lie in the nature of the verb "hope." If you use "hope" with the perfect infinitive, then you must be referring to something in the future.
a. Some sentences that I have made up:
i. Those two nations hope (now) to have ended the war by next month. (= Those two nations hope that they will have ended the war by next month.)
ii. Raul and Monica hope (now) to have married by the end of this year. (= Raul and Monica hope that they will have married by the end of this year.)
James
* Walter Kay Smart, English Review Grammar (last copyright in 1968).
** Michael Swan, Practical English Usage (1995 edition).