Kenneth Fordyce
ABSTRACT
A critical computational requirement for many of the decision technologies in the fields of operations research (PERT/CPM, Markov chains, decision trees, Bayesian analysis, MRP, simulation, …), artificial intelligence (evidential reasoning, truth maintenance systems, propositional logic, rule based inference, frames and semantic nets, …), and decision support systems (worksheet or financial planning models, data / entity models, …) is the development and manipulation of a function network or directed graph describing the relationship between "variables", "objects", or "actors" involved in the application of the decision technology to a specific problem. The manipulation of such networks or graphs using Boolean matrices and vector of integer vectors is well known in portions of the APL community (see bibliography), but intertwined with specific applications and spread out across a variety sources (some of which are difficult to obtain). This paper succinctly and simply describes the basics of manipulating a function network with Boolean matrices and integer vectors including focusing networks, finding circular conditions (A depends on B, B depends on C, C depends on A, therefore A depends on A, …), and grouping functions based on relative independence to identify parallel computational opportunities and substantially reduces the non-procedural aspect of the problem.
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Index Terms
- Using boolean of integer arrays to analyze networks
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