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I need some help with a question. I'm currently studying for an exam and I could therefore use some help with this following question:

Order the following formalisms (but one) 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. Point out the formalism that does not fit into the ordering.

  • Context Free Grammars ( CFG )
  • Deterministic Finite Automata (DFA)
  • Deterministic Pushdown Automata (DPDA)
  • LR(0) grammars
  • LR(1) grammars
  • Nondeterministic Finite Automata ( NFA)
  • Nondeterministic Finite Automata with epsilon-transitions ( NFA - epsilon)
  • Nondeterministic Turing Machines ( NTM )
  • Pushdown Automata ( PDA )
  • Regular Expressions ( reg. exp )
  • Turing Machines ( TM )
  • Turing Machines with two heads ( TM 2h )

The trick here is to find the one that does not fit into the ordering and why. I'm just not able to find that one.

Nevermore
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Lurr
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1 Answers1

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I think that LR(0) is incomparable to the regular languages, see the answers to question Are regular expressions $LR(k)$? . Thus it does not fit in a linear hierarchy with all the rest. It could be the bottom element, but for REG there are several characterizations; thus more than one class would not fit in the hierarchy. Therefore they probably mean LR(0).

Community
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Peter Leupold
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