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Binary Operations on Automatic Functions

Juhani Karhumäki, Jarkko Kari, Joakim Kupke, Binary Operations on Automatic Functions. RAIRO Informatique Theorique et Applications 42, 217-236, 2008.

Abstract:

Real functions on the domain [0,1)^n – often used to describe digital images – allow for different well-known types of binary operations. In this note, we recapitulate how weighted finite automata can be used in order to represent those functions and how certain binary operations are reflected in the theory of these automata. Different types of products of automata are employed, including the seldomly-used full Cartesian product. We show, however, the infeasibility of functional composition; simple examples yield that the class of automatic functions (i.e., functions computable by automata) is not closed under this operation.

BibTeX entry:

@ARTICLE{jKaKaKu08a,
  title = {Binary Operations on Automatic Functions},
  author = {Karhumäki, Juhani and Kari, Jarkko and Kupke, Joakim},
  journal = {RAIRO Informatique Theorique et Applications},
  volume = {42},
  pages = {217-236},
  year = {2008},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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