urestricted -> turing machine

context-sensitive -> linear bounded automaton (LBA)

context-free -> pushdown automaton (PDA)

regular -> finite state machine

Hi, I am kind of confused about relation between LBA and PDA.

Is the stack in pushdown automaton bounded (not using infinite space)?

If not, how can a LBA accept a language that PDA accepts? (How can one simulate a PDA with unbounded stack using a linear **bounded** automaton?)