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Formations of finite monoids and formal languages: Eilenberg's variety theorem revisited
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Adolfo Ballester-Bolinches
Published/Copyright:
June 19, 2012
Abstract
We present an extension of Eilenberg's variety theorem, a well-known result connecting algebra to formal languages. We prove that there is a bijective correspondence between formations of finite monoids and certain classes of languages, the formations of languages. Our result permits to treat classes of finite monoids which are not necessarily closed under taking submonoids, contrary to the original theory. We also prove a similar result for ordered monoids.
Funding source: MICINN (Spain)
Award Identifier / Grant number: Proyecto MTM2010-19938-C03-01
Funding source: ANR 2010 BLAN 0202 02 FREC
Funding source: Universitat Politècnica de València
Award Identifier / Grant number: PAID-02-09
Received: 2011-9-19
Revised: 2012-5-13
Published Online: 2012-6-19
Published in Print: 2014-11-1
© 2015 by De Gruyter
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Articles in the same Issue
- Frontmatter
- On certain optimal diffeomorphisms between closed curves
- On the existence of non-trivial finitely injective modules
- Eisenstein series, cohomology of arithmetic groups, and automorphic L-functions at half integral arguments
- Separable ultrametric spaces and their isometry groups
- On the domain of meromorphy of a multivariate Euler product of Igusa type
- Formations of finite monoids and formal languages: Eilenberg's variety theorem revisited
- Spectral theory on 3-dimensional hyperbolic space and Hermitian modular forms
- On the zeros of Epstein zeta functions
- A note on formulas transmuting mixed multiplicities
- Dressians, tropical Grassmannians, and their rays
- The lifespan for 3-dimensional quasilinear wave equations in exterior domains
- Free products and wild nearfields à la B. H. Neumann and Hans Zassenhaus
