Eilenberg's Volume C

Samuel Eilenberg did not finish the third volume of his treatise. Preliminary versions of some of the chapters circulated at the end of the seventies. Here are copies of three handwritten chapters. A separate paper deals with the example of the Dyck set. The documents were scanned with the help of Luc Boasson.

Additional informations are of course welcome.

Chapter I (34 pages)
  1. Algebraic grammars
  2. Examples
  3. Weights
  4. Loose semigroups and positive grammars
  5. Linguistic interpretation:parsing
  6. Introduction to the fixed point approach
ChapterII (21 pages)
  1. The filtered fixed-point theorem
  2. Polynomials and paranomials
  3. Polynomial and paranomial transformation
  4. The main theorem
Chapter III (33 pages)
  1. The category C
  2. The continuous fixed-point theorem
  3. C-semirings
  4. The main theorem
  5. Lattice semirings and fuzzy sets
The D1 example (8 pages)