Further Results on Hierarchies of Canonic Systems
MASSACHUSETTS INST OF TECH CAMBRIDGE PROJECT MAC
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The thesis outlines a new way of presenting the theory of canonic systems, including a distinction for methodic reasons between simple canonic systems and general canonic systems, and proves a series of results on hierarchies of canonic systems. After a brief summary of Doyles results on a partial hierarchy of canonic systems, a new hierarchy is developed which relates the general canonic systems not only to all 4 types of formal grammars defined by Chomsky but also to any class of formal grammars definable in terms of productions. It is also shown that all attempts to define a mathematical system which exactly corresponds to the recursive sets are necessarily fruitless.
- Theoretical Mathematics
- Computer Programming and Software