The notated key was usually found after a few processing steps and from then on remained stable- but was still sensitive to modulation. The model has been tested for a range of tonal music including the fugue subjects of J. The model makes a parallel search for the key in the scalar and chordal domains, taking into account primacy and memory constraints.

Each tone is input as a pitch class and a duration. Using the multi-attribute domain CSP computational model, the conditions for backtrack-free search are stated and proven.Ī model of key finding is presented for single-voiced pieces of tonal music. Experimental results show that the attribute-space representation in conjunction with the space-shrinking heuristics reduces backtracking in randomly generated problems, in comparison with binary-search methods.

ACDS agents concurrently shrink the space by applying local knowledge, properties of the domain, and heuristics, until a solution is found. Agents communicate using design protocols and employ a distributed attribute-space representation that bounds the space of all possible designs. The ACDS algorithms are guaranteed to terminate with a solution if one exists. This model is used to identify properties and heuristics for managing the complexity of a large class of design problems. ACDS is based on a multi-attribute domain constraint-satisfaction problem (CSP) computational model of the distributed part-selection problem.

This dissertation describes the Automated Configuration-Design Service (ACDS), a set of algorithms and system for solving distributed part-selection problems using a network of design agents that represent part catalogs and design constraints. Wide-area networks, such as the Internet, facilitate communication among designers making possible the use of algorithms to resolve constraint violations, and provide a way to make the contents of distributed part catalogs available to designers. Solving these problems requires communication among designers and algorithms to resolve constraint violations. In addition, the catalogs that contain the parts necessary to solve such problems often do not reside in a single location. Large-scale part-selection problems that consist of thousands of required functions and millions of parts are too complex for a single designer or small group of designers to manage. Functionality defines what the design is supposed to do, specifications define optimality goals, and constraints define the feasibility relationships that must be satisfied for the design to operate correctly. In part-selection problems, parts are selected from catalogs and connected to meet the following problem requirements: functionality, specifications, and constraints.

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