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General Alphabets: The Theory of Push-down Automata and Context-free Languages

In: Finite Automata, Their Algebras and Grammars

Author

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  • J. Richard Büchi

    (Purdue University, Computer Science Department)

  • Dirk Siefkes

    (Technische Universität Berlin, Fachbereich Informatik)

Abstract

In Chapter 6 we outlined the theory of term acceptor as based on the right-Polish notation. It is obvious how matters would have to be modified were we to use left-Polish notation. Although these elegant notations are now often used in mathematics (especially in general algebra and topology), they are not the classic terms. These make use of mated signs, such as the parent (and the thesis). Now imagine what an analyst, schoolboy, or machine user would do to you, were you to spell x y + 2 x 22x • y • +y 2 + = in place of (x + y)2 = x 2 + 2 • x• y + y 2. I would not like you either. The classic notation clearly possesses intrinsic merits that go far beyond more familiarity. This comes from its natural growth under the guidance of understanding parents such as Leibniz. True, it does not accommodate ternary operations (i.e., quaternary relations). But these do not naturally occur often, and can be replaced by binary operations (i.e., ternary relations). This is Peirce’s principle of thirdness.

Suggested Citation

  • J. Richard Büchi & Dirk Siefkes, 1989. "General Alphabets: The Theory of Push-down Automata and Context-free Languages," Springer Books, in: Dirk Siefkes (ed.), Finite Automata, Their Algebras and Grammars, chapter 0, pages 271-292, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-8853-1_7
    DOI: 10.1007/978-1-4613-8853-1_7
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