I find the word "reducible" used in complexity theory not very intuitive, and too general taken on a face value.
What does it exactly mean by problem A reducible to B?
Does it mean that A can be reworded into B? i.e. Finding Vertex Set is actually the same as finding an independent set?
Does it mean that an algorithm that solves problem B will solve A? i.e. An algorithm that finds longest path will in fact also find the shortest path?
Does it mean that A can be proved to be in the same complexity class as B? i.e. A is NP-Hard, B is NPC, then if A is reducible to B, A is in fact NPC?
In other words, A is reducible to B, what can we say about A or B?
As you can see my understanding is quite flaw at the moment, can someone please clarify the application of the word for me maybe even rephrase it into something more intuitive?