A snap-stabilizing algorithm, regardless of the initial configuration of the system, guarantees that it always behaves according to its specification. We consider here the locally shared memory model. In this model, we propose the first snap-stabilizing Propagation of Information with Feedback (PIF) algorithm for rooted networks of arbitrary connected topology which is proven assuming the distributed unfair daemon. Then, we use the proposed PIF algorithm as a key module in designing snap-stabilizing solutions for some fundamental problems in distributed systems, such as Leader Election, Reset, Snapshot, and Termination Detection. Finally, we show that in the locally shared memory model, snap-stabilization is as expressive as self-stabilization by designing a universal transformer to provide a snap-stabilizing version of any algorithm that can be self-stabilized with the transformer of Katz and Perry (Distributed Computing, 1993). Since by definition a snap-stabilizing algorithm is also self-stabilizing, self-and snap-stabilization have the same expressiveness in the locally shared memory model.