On rational definitions in complete algebras without rank. (English) Zbl 0498.68017


68Q65 Abstract data types; algebraic specification
68N01 General topics in the theory of software


Zbl 0278.68066
Full Text: DOI


[1] Bekić, H., Definable operations in general algebras, and the theory of automata and flowcharts, (Research Report (1969), IBM Laboratory: IBM Laboratory Vienna) · Zbl 0548.68004
[2] Büchi, J. R., Mathematische Theorie des Verhaltens endlicher Automaten, Z. Angew. Math. Mech., 42, T9-T16 (1962) · Zbl 0113.01401
[3] Cousineau, G., Les arbres á feuilles indicées: un cadre algébrique pour l’étude des structures de contrôle, (Thése d’Etat, VII (1977), Université Paris)
[4] Damm, W., The IO- and OI-hierarchies, Theoret. Comput. Sci., 20, 95-207 (1982) · Zbl 0478.68012
[5] Eilenberg, S.; Wright, J. B., Automata in general algebras, Information and Control, 11, 452-470 (1967) · Zbl 0175.27902
[6] Elgot, C. C., The common algebraic structure of exit-automata and machines, Computing, 6, 347-370 (1970) · Zbl 0264.94033
[7] Elgot, C. C., Monadic computation and iterative algebraic theories, (IBM Research Report RC 4563 (1973), Yorktown Heights) · Zbl 0123.33502
[8] Goguen, J. A.; Thatcher, J. W.; Wagner, E. G.; Wright, J. B., Initial algebra semantics, J. ACM, 24, 1, 68-95 (1977) · Zbl 0359.68018
[9] Mezei, J.; Wright, J. B., Algebraic automata and context-free sets, Information and Control, 11, 3-29 (1967) · Zbl 0155.34301
[10] Nivat, M., Languages algébriques sur le magma libre et sémantique des schémas de programme, (Nivat, M., Automata, Languages and Programming (1973), North-Holland: North-Holland Amsterdam), 293-308 · Zbl 0279.68010
[11] Nivat, M., On the interpretation of recursive program schemes, (Symposium Mathematica, 15 (1975), Academic Press: Academic Press New York) · Zbl 0384.68016
[12] Scott, D., Outline of a mathematical theory of computation, Proc. 4th Annual Princeton Conference on Information Sciences and Systems (1970) · Zbl 0419.68076
[13] Scott, D., The lattice of flow diagrams, (Engeler, E., Symposium on Semantics of Algorithmic Languages. Symposium on Semantics of Algorithmic Languages, Lecture Notes in Mathematics, 188 (1971), Springer: Springer Berlin), 311-366
[14] Thatcher, J. W.; Wright, J. B., Generalized finite automata theory with an application to a decision problem of second-order logic, Math. Systems Theory, 2, 57-81 (1968) · Zbl 0157.02201
[15] Wagner, E. G., An algebraic theory of recursive definitions and recursive languages, Proc. 3rd ACM Symposium on Theory of Computing, 12-23 (1971)
[16] Wagner, E. G., Languages for defining sets in arbitrary algebras, Proc. IEEE Conference SWAT, 12, 192-201 (1971)
[17] Wand, M., A concrete approach to abstract recursive definitions, (Nivat, M., Automata, Languages, and Programming (1973), North-Holland: North-Holland Amsterdam), 331-344
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