Acceptance condition in Omega Automata

Question

For the Problem 6a in Feb 2022 exam, the solution(solution link) gives only two acceptance condition , while I am getting 3(as shown in the picture), how to eliminate the acceptance conditions?
 

  

Answer 1

This is explained on page 94 in the temporal logic chapter: we can neglect the fairness constraint for positive occurrences of weak operators and we can neglect the fairness constraint for negative occurrences of strong operators.

Comments

Thank you for the response, I tried looking at and understanding the slide page, but did not understand how to identify negative occurrence  or positive occurrence of an operator, can you please explain the same if possible ?

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A positive occurrence is one that occurs behind an even number of negations, while a negative occurrence is one that occurs behind an odd number of negations (if we just consider negation, conjunction, and disjunction). Moreover, one has to be careful with the before operators since they also change the sign of occurrences of one of their arguments.