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A Categorist's view of automata and systems

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Category Theory Applied to Computation and Control

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 25))

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References

  1. S. Alagić, Natural state transformations, Department of Computer and Information Science Technical Report 73B-2, Univ. of Mass., 1973.

    Google Scholar 

  2. — Algebraic aspects of ALGOL 68, Computer and Information Science Technical Report 73B-5, Univ. of Mass., 1973.

    Google Scholar 

  3. — Categorical theory of tree transformations, this volume.

    Google Scholar 

  4. H. Appelgate, Acyclic models and resolvent functors, dissertation, Columbia University, 1965.

    Google Scholar 

  5. B. D. O. Anderson, M. A. Arbib and E. G. Manes, Finitary and infinitary conditions in categorical realization theory, to appear.

    Google Scholar 

  6. M. A. Arbib, Theories of Abstract Automata, Prentice-Hall, 1969.

    Google Scholar 

  7. M. A. Arbib and E. G. Manes, Machines in a category: an expository introduction, Siam Review, to appear.

    Google Scholar 

  8. — Adjoint machines, state-behavior machines, and duality, J. Pure Appl. Alg., to appear.

    Google Scholar 

  9. — Fuzzy morphisms in automata theory, this volume.

    Google Scholar 

  10. — Time-varying systems, this volume.

    Google Scholar 

  11. — The Categorical Imperative: Arrows, Structures, and Functors, Academic Press, 1974.

    Google Scholar 

  12. E. S. Bainbridge, A unified minimal realization theory, with duality for machines in a hyperdoctrine, dissertation, Univ. of Mich., 1972.

    Google Scholar 

  13. — Addressed machines and duality, this volume.

    Google Scholar 

  14. M. Barr, Coequalizers and free triples, Math. Zeit. 116, 1970, 307–322.

    Article  MathSciNet  MATH  Google Scholar 

  15. J. Beck, Triples, algebras and cohomology, dissertation, Columbia University, 1967; available from University Microfilms, Ann Arbor, Michigan.

    Google Scholar 

  16. D. Benson, An abstract machine theory for formal language parsers, this volume.

    Google Scholar 

  17. R. W. Brockett and A. S. Willsky, Finite-state homomorphic sequential machines, IEEE Trans. Aut. Cont. AC-17, 1973, 483–490.

    MathSciNet  Google Scholar 

  18. — Some structural properties of automata defined on groups, this volume.

    Google Scholar 

  19. L. Budach, Automata in additive categories with applications to stochastic linear automata, this volume.

    Google Scholar 

  20. E. Burroni, Algèbres relatives à une loi distributive, Comp. R. Acad. Sc. Paris, t. 276 (5 fév. 1973), Ser. A, 443–446.

    Google Scholar 

  21. R. W. Burstall and J. W. Thatcher, Algebraic theory of recursive program schemes, this volume.

    Google Scholar 

  22. N. Chomsky, On certain formal properties of grammars, Inf. Cont. 2, 1959, 136–167.

    Google Scholar 

  23. P. M. Cohn, Universal Algebra, Harper and Row, 1965.

    Google Scholar 

  24. E. J. Dubuc, Kan Extensions in Enriched Category Theory, Lecture Notes in Mathematics 145, Springer-Verlag, 1970.

    Google Scholar 

  25. B. Eckmann ed., Seminar on Triples and Categorical Homology Theory, Lecture Notes in Mathematics 80, Springer-Verlag, 1969.

    Google Scholar 

  26. H. Ehrig; K. D. Kiermeier; H.-J. Kreowski and W. Kühnel, Systematisierung der Automatentheorie, Seminarbericht, Technische Universität Berlin, Fachbereich Kybernetik, 1973.

    Google Scholar 

  27. H. Ehrig and H.-J. Kreowski, Power and initial automata in pseudoclosed categories, this volume.

    Google Scholar 

  28. E. Engeler ed., Symposium on Semantics of Algorithmic Languages, Lecture Notes in Mathematics 188, Springer-Verlag, 1971.

    Google Scholar 

  29. S. Ginsburg, An Introduction to Mathematical Machine Theory, Addison-Wesley, 1962.

    Google Scholar 

  30. J. A. Goguen, L-fuzzy sets, J. Math. Anal. Appl. 18, 1967, 145–174.

    Article  MathSciNet  MATH  Google Scholar 

  31. — On homomorphisms, simulations, correctness, subroutines, and termination for programs and program schemes, Proceedings of the 13th IEEE Conference on Switching and Automata Theory, 1972, 52–60.

    Google Scholar 

  32. — Minimal realization of machines in closed categories, Bull. Amer. Math. Soc. 78, 1972, 777–783.

    Article  MathSciNet  MATH  Google Scholar 

  33. — Axioms, extensions and applications for fuzzy sets: languages and the representation of concepts, to appear.

    Google Scholar 

  34. — Some comments on applying mathematical system theory, to appear.

    Google Scholar 

  35. J. A. Goguen; J. W. Thatcher; E. G. Wagner and J. B. Wright, A junction between computer science and category theory, I: basic concepts and examples (part 1), IBM Research Report RC 4526, T. J. Watson Research Center, 1973.

    Google Scholar 

  36. G. Grätzer, Universal Algebra, Van Nostrand, 1967.

    Google Scholar 

  37. R. E. Kalman; P. L. Falb and M. A. Arbib, Topics in Mathematical System Theory, McGraw-Hill, 1969.

    Google Scholar 

  38. A. Kock, Monads on symmetric monoidal closed categories, Arch. Math. XXI, 1970, 1–10.

    Article  MathSciNet  Google Scholar 

  39. J. Lambek, Deductive systems and categories, Math. Sys. Th. 2, 1968, 287–318.

    Article  MathSciNet  MATH  Google Scholar 

  40. F. W. Lawvere, Functorial semantics of algebraic theories, dissertation, Columbia University, 1963.

    Google Scholar 

  41. F. E. J. Linton, Triples for closed categories, Seminar in Category Theory, notes by D. Taylor, NSF summer institute at Bowdoin College, 1969.

    Google Scholar 

  42. S. Mac Lane, Categories for the Working Mathematician, Springer-Verlag, 1972.

    Google Scholar 

  43. E. G. Manes, Algebraic Theories, Springer-Verlag, to appear.

    Google Scholar 

  44. J. Meseguer and I. Sols, Automata in semimodule categories, this volume.

    Google Scholar 

  45. L. Padulo and M. A. Arbib, System Theory: a Unified Approach to Discrete and Continuous Systems, W. B. Saunders, 1974.

    Google Scholar 

  46. A. Paz, Introduction to Probabilistic Automata, Academic Press, 1971.

    Google Scholar 

  47. R. S. Pierce, Introduction to the Theory of Abstract Algebras, Holt, Rinehart and Winston, 1968.

    Google Scholar 

  48. J. Rissanen and B. F. Wyman, Duality of input/output maps, this volume.

    Google Scholar 

  49. D. Scott, The lattice of flow diagrams, Symposium on Semantics of Algorithmic Languages, Lecture Notes in Mathematics 188, Springer-Verlag, 1971.

    Google Scholar 

  50. J. W. Thatcher, Generalized2 sequential machine maps, J. Comp. Syst. Sci. 4, 1970, 339–367.

    MathSciNet  MATH  Google Scholar 

  51. M. Wand, An unusual application of program-proving, Proceedings of the Fifth ACM Symposium on the Theory of Computing, 1973, 59–66.

    Google Scholar 

  52. — An algebraic formulation of the Chomsky hierarchy, this volume.

    Google Scholar 

  53. — On the recursive specification of data types, this volume.

    Google Scholar 

  54. — On the behavioral description of data structures, to appear.

    Google Scholar 

  55. B. F. Wyman, Linear systems over rings of operators, this volume.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computer and Information Science, University of Massachusetts, 01002, Amherst, MA, USA

    M. A. Arbib

  2. Mathematics, University of Massachusetts, 01002, Amherst, MA, USA

    E. G. Manes

Authors
  1. M. A. Arbib
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  2. E. G. Manes
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Editor information

Ernest Gene Manes

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© 1975 Springer-Verlag Berlin Heidelberg

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Arbib, M.A., Manes, E.G. (1975). A Categorist's view of automata and systems. In: Manes, E.G. (eds) Category Theory Applied to Computation and Control. Lecture Notes in Computer Science, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07142-3_61

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  • DOI: https://doi.org/10.1007/3-540-07142-3_61

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07142-6

  • Online ISBN: 978-3-540-37426-8

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