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Arbres infinis et systèmes d’équations. (French) Zbl 0406.68017


MSC:

68Q60 Specification and verification (program logics, model checking, etc.)
18B20 Categories of machines, automata
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References:

[1] 1. ADJ ( J. GOGUEN, J. THATCHER, E. WAGNER et J. WRIGHT), Initial Algebra Semantics and Continuous Algebras, J. Assoc. Comput. Math., vol. 24, 1977, p. 68-95. Zbl0359.68018 MR520711 · Zbl 0359.68018 · doi:10.1145/321992.321997
[2] 2. A. ARNOLD et M. NIVAT, The Metric Space of Infinite Trees, Algebraic and Topological Properties, Rapport Laboria n^\circ 323, septembre 1978.
[3] 3. S. BLOOM et C. ELGOT, The Existence and Construction of Free Iterative Theories, J. Comput. System Sc., vol. 12, 1976, p. 305-318. Zbl0333.68017 MR505399 · Zbl 0333.68017 · doi:10.1016/S0022-0000(76)80003-7
[4] 4. N. BOURBAKI, Topologie générale, 4e édition, Hermann, Paris.
[5] 5. G. COUSINEAU, Algebraic Definition of Control Structures, Theor. Comput. Sc. (à paraître). Zbl0456.68015 · Zbl 0456.68015 · doi:10.1016/0304-3975(80)90028-6
[6] 6. B. COURCELLE, A Representation of Trees by Languages, II, Theor. Comput. Sc., vol. 7, 1978, p. 25-55. Zbl0428.68088 MR495226 · Zbl 0428.68088 · doi:10.1016/0304-3975(78)90039-7
[7] 7. B. COURCELLE, On Recursive Equations Having a Unique Solution, Communication au 19e Symp. on Foundations of Computer Science, Ann Arbor, 1978. MR539842 · Zbl 0377.68040
[8] 8. B. COURCELLE, G. KAHN et J. VUILLEMIN, Algorithmes à’équivalence et de réduction à des expressions minimales dans une classe d’équations récursives simples, Proc. 2nd I.C.A.L.P., Saarbrücken, 1974 Lecture Notes in Computer Science, vol. 14, Springer-Verlag, p. 200-213. Zbl0285.68022 MR428778 · Zbl 0285.68022
[9] 9. B. COURCELLE et M. NIVAT, Algebraic Families of Interpretations, 17th Symp. on Foundations of Computer Science, Houston, 1978 p. 137-146 et Rapport Laboria n^\circ 189. MR451817 · Zbl 0384.68016
[10] 10. B. COURCELLE et M. NIVAT, The Algebraic Semanticsof Recursive Program Schemes, Communication au Colloque Mathematical Foundation of Computer Science, 1978, in Lecture Notes in Computer Science, J. WINKOWSKI, éd., vol. 64, Springer-Verlag, p. 16-30. Zbl0384.68016 MR519827 · Zbl 0384.68016
[11] 11. C. ELGOT, S. BLOOM et R. TINDELL, On the Algebraic Theory of Rooted Trees, J. Comput. System Sc., vol. 16, 1978, p. 362-399. Zbl0389.68007 MR496954 · Zbl 0389.68007 · doi:10.1016/0022-0000(78)90024-7
[12] 12. G. HUET, Résolution d’équations dans les langages d’ordre 1, 2, ..., \omega , Thèse d’État, Université Paris-VII, 1976.
[13] 13. M. NIVAT, Mots infinis engendrés par une grammaire algébrique, R.A.I.R.O., Informatique théorique, vol. 11, 1977, p. 311-327. Zbl0371.68025 MR468353 · Zbl 0371.68025
[14] 14. B. ROSEN, Program Equivalence and Context-Free Grammars, J. Comput. System Sc., vol. 11, 1965, p. 358-374. Zbl0315.68063 MR423889 · Zbl 0315.68063 · doi:10.1016/S0022-0000(75)80057-2
[15] 15. J. TIURYN, Fixed-Points and Algebras with Infinitely Long Expressions I dans Mathematical Foundations of Computer Science, 1977, Lecture Notes in Comput, Sc, vol. 53, Springer-Verlag, 1977, p. 513-522. Zbl0397.68086 MR483663 · Zbl 0397.68086
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