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Automata Theory and its Applications (Paperback, Softcover reprint of the original 1st ed. 2001)
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Automata Theory and its Applications (Paperback, Softcover reprint of the original 1st ed. 2001)
Series: Progress in Computer Science and Applied Logic, 21
Expected to ship within 10 - 15 working days
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The theory of finite automata on finite stings, infinite strings,
and trees has had a dis tinguished history. First, automata were
introduced to represent idealized switching circuits augmented by
unit delays. This was the period of Shannon, McCullouch and Pitts,
and Howard Aiken, ending about 1950. Then in the 1950s there was
the work of Kleene on representable events, of Myhill and Nerode on
finite coset congruence relations on strings, of Rabin and Scott on
power set automata. In the 1960s, there was the work of Btichi on
automata on infinite strings and the second order theory of one
successor, then Rabin's 1968 result on automata on infinite trees
and the second order theory of two successors. The latter was a
mystery until the introduction of forgetful determinacy games by
Gurevich and Harrington in 1982. Each of these developments has
successful and prospective applications in computer science. They
should all be part of every computer scientist's toolbox. Suppose
that we take a computer scientist's point of view. One can think of
finite automata as the mathematical representation of programs that
run us ing fixed finite resources. Then Btichi's SIS can be thought
of as a theory of programs which run forever (like operating
systems or banking systems) and are deterministic. Finally, Rabin's
S2S is a theory of programs which run forever and are
nondeterministic. Indeed many questions of verification can be
decided in the decidable theories of these automata.
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