Top-down synthesis of divide-and-conquer algorithms
Artificial Intelligence
Universal Realization, Persistent Interconnection and Implementation of Abstract Modules
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Algorithm synthesis through problem reformulation
Algorithm synthesis through problem reformulation
Representation of Models for Expert Problem Solving in Physics
IEEE Transactions on Knowledge and Data Engineering
Interactions of Abstractions in Programming
SARA '02 Proceedings of the 4th International Symposium on Abstraction, Reformulation, and Approximation
Perception-Based Granularity Levels in Concept Representation
ISMIS '00 Proceedings of the 12th International Symposium on Foundations of Intelligent Systems
Abstraction and complexity measures
SARA'07 Proceedings of the 7th International conference on Abstraction, reformulation, and approximation
Algorithm synthesis through problem reformulation
AAAI'87 Proceedings of the sixth National conference on Artificial intelligence - Volume 2
Algorithm synthesis through problem reformulation
AAAI'87 Proceedings of the sixth National conference on Artificial intelligence - Volume 2
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A good problem representation incorporates important problem constraints while hiding superfluous detail. This paper presents methods for abstracting a problem representation by making implicit problem properties into explicit properties of the representation. The mathematics of the abstraction search space are given in terms of model theory and universal algebra. The Behavioral Abstraction method uses predefined representation maps to lift a problem representation to an abstract theory. The Behavioral Congruence method generates abstract theories and representation maps which incorporate problem constraints expressed as Behavioral Equivalences. Two meta-level methods for generating Behavioral Equivalence theorems are given. The STRATA automatic programming system described in this paper is currently being implemented.