a topological characterization of weakness
We are interested in the relation between weak and strong temporal operators. We would like to find a characterization that shows what it means for an operator to be the weak or strong version of another operator, or more generally for a formula to be a weak or strong version of another formula. We show that the weak version of a formula is not the same as Alpern and Schneider's safety component . By working over an extended alphabet, we show that their topological characterization of safety can be adapted to obtain a topological characterization of weakness. We study the resulting topology and the relations between weak and strong formulas. Finally, we apply the method to show the internal consistency of a logic containing both weak and strong versions of regular expressions.
safety safety component liveness semantically weak and strong formulas temporal weakness and strength syntactically weak and strong formulas weak and strong components