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I'm confused by this: "The only restriction placed on grammars for such languages is that no production maps a string to a shorter string." I don't understand how does the conclusion "Thus no derivation of a string in a context-sensitive language can contain a sentential form longer than the string
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The
Operation section says, "A linear bounded automaton is a nondeterministic Turing machine". But the History section says, "In 1960, John Myhill introduced an automaton model today known as deterministic linear bounded automaton." This suggests there are both deterministic and nondeterministic
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I was hoping to see a formal tuple definition of an LBA (analogous to the one provided for a Turing machine). It is mentioned that it's a restricted variant of a Turing machine, but it's not at all clear to me whether this restriction changes the formal definition of an LBA or not.
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Yes, your example grammar is a valid context-sensitive grammar. - In your example, none of the sentential forms is shorter than any of its predecessors in your derivation chain. So where is your problem in this example? -
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SS | x is a valid LBA grammar, but this clearly maps S to SS, then to SSS, then to SSSS and so on.
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Is the requirement that the string maps to shorter or equal or longer or equal string?
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