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Book Review
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Book Information
Author(s):
J. Richard B\"uchi
Title:
Finite automata, their algebras and grammars:
Towards a theory of formal expressions
Additional book information:
Dirk Siefkes, editor, Springer-Verlag, New York, 1988, 316 pp., US$69.50. ISBN 3-540-96905-5
References:
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- A. Aho, R. Sethi, and J. Ullman, Compilers\RM : Principles, techniques and tools, Addison-Wesley, Reading, MA, 1986.
- [2]
- D. Mix Barrington and D. Th\'erien, Finite monoids and the fine structure of $NC^1$, J. Assoc. Comput. Mach. \textbf{35} (1988), 941--952.
- [3]
- J. R. B\"uchi, Weak second-order arithmetic and finite automata, Z. Math. Logik Grundlag. Math. \textbf{6} (1960), 66--92.
- [4]
- J. R. B\"uchi, Regular canonical systems and finite automata, Arch. Math. Logik Grundlag. \textbf{6} (1964), 91--111.
- [5]
- N. Chomsky, Three models for the description of language, IRE Trans. Inform. Theory \textbf{2} (1956), 113--124.
- [6]
- N. Chomsky, On certain formal properties of grammars, Inform. and Control \textbf{2} (1959), 137--167.
- [7]
- S. Eilenberg, Automata, languages and machines, vol.~B, Academic Press, New York, 1976.
- [8]
- B. W. Kernighan and R. Pike, The UNIX programming environment, Prentice-Hall, Englewood Cliffs, NJ, 1984.
- [9]
- S. C. Kleene, \emph{Representations of events in nerve nets and finite automata}, Princeton Univ. Press, Princeton, NJ, 1956.
- [10]
- K. Krohn and J. Rhodes, The algebraic theory of machines\RM I. Prime decomposition theorem for finite semigroups and machines, Trans. Amer. Math. Soc. \textbf{116} (1965), 450--464.
- [11]
- J. E. Pin, Varieties of formal languages, Plenum, London, 1986.
- [12]
- A. Pnueli, The temporal logic of programs, Proc. 18th Sympos. Found. Comput. Sci. IEEE Press, New York 1977, pp.~46--57.
- [13]
- E. Post, Recursively enumerable sets of positive integers and their decision problems, Bull. Amer. Math. Soc. \textbf{50} (1944), 284--316.
- [14]
- E. Post, Recursive unsolvability of a problem of Thue, J. Symbolic Logic \textbf{12} (1974), 1--11.
- [15]
- M. O. Rabin, Decidability of second-order theories and automata on infinite trees, Trans. Amer. Math. Soc. \textbf{141} (1969), 1--35.
- [16]
- S. Safra and M. Vardi, \emph{On $\omega $-automata and temporal logic}, ACM Press, New York, 1989 pp.~127--137.
- [17]
- M. P. Sch\"utzenberger, On the definition of a family of automata, Inform. and Control \textbf{4} (1961), 245--270.
- [18]
- J. Thatcher and J. Wright, Generalized finite automata theory with an application to a decision problem of second-order logic, Math. Systems Theory \textbf{2} (1968), 57--81.
- [19]
- A. Thue, Die L\"osung eines spezialfalles eines generallen logischen problems, Vidensdapssedkapet Skrifter Christiania, I. Math.-Nat. Klasse No. 8 (1910).
- [20]
- A. Thue, \"Uber die gegenseitige Lage gleicher Teile gewisser Zeichenreihen, Vidensdapssedkapet Skrister Christiania, I. Math.-Nat. Klasse No. 9 (1912).
- [21]
- A. Thue, Probleme \"uber Ver\"anderungen von Zeichenreihen nach gegebenen Regeln, Vidensdapssedkapet Skrifter Christiania, I. Math.-Nat. Klasse No. 10 (1914).
- [22]
- A. Turing, On computable numbers, with an application to the entscheidungsproblem, Proc. London Math. Soc. (2) \textbf{42} (1936), 230--265.
- [23]
- R. Wexelblat, ed., History of programming languages, Academic Press, New York, 1981.
Additional Information:
Reviewer(s):
Howard
Straubing
Review Information:
Journal:
Bull. Amer. Math. Soc.
26
(1992),
340-344.
DOI:
10.1090/S0273-0979-1992-00264-1
PII:
S 0273-0979(1992)00264-1
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