# Formal Languages - Expressive power of Formalisms

I need help with the following question:

Order the following formalisms according to their expressive power: placing A before B means that any language definable by A is definable by B. Also state which, if any, of them are equivalent.

• Turing Machines (TM)
• Regular expressions (reg.exp.)
• Turing Machines with multiple tapes (TM+)
• Pushdown Automata (PDA)
• Nondeterministic Finite Automata with ǫ-transitions (NFAǫ)
• Nondeterministic Finite Automata (NFA)
• LR(1) grammars
• Nondeterministic Turing Machines (NTM)
• Deterministic Pushdown Automata (DPDA)
• Deterministic Finite Automata (DFA)
• Context-free Grammars (CFG)


Is this the correct answer ? I have a exam next week and need to know If my answer is correct.

NFAe=NFA=DFA=Reg.exp, LR(1)-Grammar=DPDA, CFG=PDA, TM=NTM=TM+


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NFAe=NFA=DFA=Reg.exp, LR(1)-Grammar=DPDA, CFG=PDA, TM=NTM=TM+

Seems OK to me.

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