The multidimensional forest languages

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1985
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O'Neil, Thomas
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Computer Science

Computer Science—the theory, representation, processing, communication and use of information—is fundamentally transforming every aspect of human endeavor. The Department of Computer Science at Iowa State University advances computational and information sciences through; 1. educational and research programs within and beyond the university; 2. active engagement to help define national and international research, and 3. educational agendas, and sustained commitment to graduating leaders for academia, industry and government.

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The Computer Science Department was officially established in 1969, with Robert Stewart serving as the founding Department Chair. Faculty were composed of joint appointments with Mathematics, Statistics, and Electrical Engineering. In 1969, the building which now houses the Computer Science department, then simply called the Computer Science building, was completed. Later it was named Atanasoff Hall. Throughout the 1980s to present, the department expanded and developed its teaching and research agendas to cover many areas of computing.

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1969-present

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A multidimensional forest is a data structure which is a generalization of the conventionally-defined forest. One- and two-dimensional forests correspond to strings and conventional forests respectively. Regular forest grammars can be written to produce sets of n-dimensional forests, and a frontier operation can be applied to sets of n-dimensional forests to yield sets of strings. Thus, n-dimensional regular forest grammars define a class of string languages for each value of n;One-dimensional forest grammars yield exactly the regular languages. Two dimensional forest grammars yield all the context-free languages and perhaps some non-context-free languages which can be produced without copying substrings. Three-dimensional forests grammars yield all the IO macro languages and at least some of the OI macro languages. The frontier operation on three-dimensional forests has the same copying power as the derivation operation in macro grammars, but it has more deleting power. The enhanced deleting power of a three-dimensional forest grammar allows both IO and OI macro derivations to be simulated in a single formal system.

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Tue Jan 01 00:00:00 UTC 1985