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**11 - 12**of**12**### Modularity, Reuse and Hierarchy: Measuring Complexity by Measuring Structure and Organization

"... To develop better complexity measures, a reasonable approach is to base them on those principles of design that designers use. Modularity, reuse and hierarchy (MR&H) have been identified by engineers as useful principles for designing complex systems, and these characteristics can be seen in Nature. ..."

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To develop better complexity measures, a reasonable approach is to base them on those principles of design that designers use. Modularity, reuse and hierarchy (MR&H) have been identified by engineers as useful principles for designing complex systems, and these characteristics can be seen in Nature. Here we develop metrics for each of MR&H, and then use them to develop several metrics of structure and organization. Further, we propose to evaluate complexity measures both empirically and on a set of abstract object-construction examples. After applying these tests to a handful of previously defined complexity measures, as well as ones we define here, we find that only two of our measures pass both sets of tests. Key words: design, evolutionary algorithm, evolutionary design, complexity, structure, organization 1

### Streams and Strings in Formal Proofs

"... Streams are acyclic directed subgraphs of the logical flow graph of a proof and represent bundles of paths with the same origin and the same end. Streams can be described with a natural algebraic formalism which allows to explain in algebraic terms the evolution of proofs during cutelimination. ..."

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Streams are acyclic directed subgraphs of the logical flow graph of a proof and represent bundles of paths with the same origin and the same end. Streams can be described with a natural algebraic formalism which allows to explain in algebraic terms the evolution of proofs during cutelimination. In our approach, "logic" is often forgotten and combinatorial properties of graphs are taken into account to explain logical phenomena.