Dynamic programming schemata

  • A. Martelli
  • U. Montanari
Monday Afternoon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 14)


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.


Dynamic Programming Transition Schema Regular Language Transition Graph Expression Schema 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • A. Martelli
    • 1
  • U. Montanari
    • 1
  1. 1.Istituto di Elaborazione della Informazione del CNRPisaItaly

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