Dynamic Programming as Graph Searching: An Algebraic Approach

Finding the solution of a dynamic programming problem m the form of polyadlc funcUonal equatmns is shown to be equivalent to searching a mmmaal cost path in an AND/OR graph with monotone cost functions The proof is given in an algebraic framework and is based on a commutaUvity result between solutton and mterpretauon of a symbohc system This approach Is simdar to the one used by some authors to prove the eqmvalence between the operaUonal and denotatmnal semantics of programming languages

[1]  Toshihide Ibaraki.  Classes of Discrete Optimization Problems and Their Decision Problems , 1974, J. Comput. Syst. Sci..

[2]  Donald E. Knuth,et al.  A Generalization of Dijkstra's Algorithm , 1977, Inf. Process. Lett..

[3]  Joseph A. Goguen,et al.  Initial Algebra Semantics and Continuous Algebras , 1977, J. ACM.

[4]  Nils J. Nilsson,et al.  A Formal Basis for the Heuristic Determination of Minimum Cost Paths , 1968, IEEE Trans. Syst. Sci. Cybern..

[5]  A. Tarski.  A LATTICE-THEORETICAL FIXPOINT THEOREM AND ITS APPLICATIONS , 1955 .

[6]  Donald B. Johnson,et al.  Algorithms for Shortest Paths , 1973 .

[7]  Journal of the Association for Computing Machinery , 1961, Nature.

[8]  Alfred V. Aho,et al.  Currents In The Theory Of Computing , 1973 .

[9]  M. Held,et al.  Finite-State Processes and Dynamic Programming , 1967 .

[10]  Kenneth C. Sevcik,et al.  The synthetic approach to decision table conversion , 1976, CACM.

[11]  Jeffrey D. Ullman,et al.  Formal languages and their relation to automata , 1969, Addison-Wesley series in computer science and information processing.

[12]  R. Bellman.  Dynamic programming. , 1957, Science.

[13]  W. W. Bledsoe,et al.  Review of "Problem-Solving Methods in Artificial Intelligence by Nils J. Nilsson", McGraw-Hill Pub. , 1971, SGAR.

[14]  U. Montanari,et al.  On the Foundations of Dynamic Programming , 1975 .

[15]  T. Ibaraki.  On the optimality of algorithms for finite state sequential decision processes , 1976 .

[16]  Alberto Martelli,et al.  Optimizing decision trees through heuristically guided search , 1978, CACM.

[17]  Maurice Nivat,et al.  Non Deterministic Recursive Program Schemes , 1977, FCT.

[18]  Andrzej Blikle,et al.  Equational Languages , 1972, Inf. Control..