This chapter generalizes the finite automaton, the pushdown automaton, and the context-free grammar. Section 8.1 generalizes the finite automaton to the Turing machine. The tape of the Turing machine is potentially infinite to the right. The tape head shifts in either direction on the tape, and during these shifts, the head not only reads but also writes symbols. The Turing machine represents a central model used in computational theory, including all the crucial topics discussed in Chapter 10. Section 8.2 generalizes the pushdown automaton to the two pushdown automaton. As its name indicates, the two-pushdown automaton possesses two, rather than one, pushdowns. Section 8.3 generalizes the context-free grammar to the unrestricted grammar. The left-hand side of every production in the unrestricted grammar is a word, consisting of several symbols. Section 8.4 demonstrates that these three generalized models characterize the family of recursively enumerable languages, which properly contains the family of context-free languages.
KeywordsTuring Machine Input Word Rule Word Universal Turing Machine Pushdown Automaton
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