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Dynamic Programming Schemata

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Automata, Languages and Programming (ICALP 1974)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14))

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Abstract

In this paper we give a model of dynamic programming based on functional equations. A general method for solving these equations, based on the fixpoint theory for lattices, is given. Furthermore it is shown that a dynamic programming problem can be formulated in a suitable regular algebra and the system can be solved using Gaussian elimination.

A dynamic programming problem can be posed independently of the particular values of functions and constants. Therefore, we introduce three types of dynamic programming schemata. Equivalence of schemata is defined and investigated, and necessary and sufficient conditions are given for the case of positively monotone interpretations.

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References

  1. Martelli, A. and Montanari, U., On the Foundations of Dynamic Programming, in Topics in Combinatorial Optimization S. Rinaldi editor, CISM, Springer Verlag 1974, to appear.

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  2. Tarski, A., A Lattice-Theoretical Fixpoint Theorem and its Applica tions, Pacific J. of Math. 5, pp. 285–309.

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  3. Karp, R.M. and Held, M., Finite - State Processes and Dynamic Programming, SIAM J. Appl. Math. 15, 1967, pp.

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  4. Salomaa, A., Theory of Automata Pergamon Press, 1969.

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  5. Backhouse, R.C. and Carré, B.A., Regular Algebra Applied to Path--Finding Problems, to appear in J. Inst. Maths. Applics.

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  6. Dijkstra, E., A Note on Two Problems in Connection with Graphs, Numerische Math. 1, 1959, pp. 269–271.

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  7. Haines, L.H., On Free Monoids Partially Ordered by Embedding, J. Comb. Theory 6, 1969, pp. 94–98.

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Author information

Authors and Affiliations

  1. Istituto di Elaborazione della Informazione del CNR, Via S. Maria 46, 56100, Pisa, Italy

    A. Martelli & U. Montanari

Authors
  1. A. Martelli
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  2. U. Montanari
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Editor information

Editors and Affiliations

  1. Fachbereich Angewandte Mathematik und Informatik, Universität des Saarlandes, 66 Saarbrücken/BRD, Deutschland

    Jacques Loeckx

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© 1974 Springer-Verlag Berlin Heidelberg

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Martelli, A., Montanari, U. (1974). Dynamic Programming Schemata. In: Loeckx, J. (eds) Automata, Languages and Programming. ICALP 1974. Lecture Notes in Computer Science, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21545-6_5

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  • DOI: https://doi.org/10.1007/978-3-662-21545-6_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06841-9

  • Online ISBN: 978-3-662-21545-6

  • eBook Packages: Springer Book Archive

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