Chapter

Algebraic Informatics

Volume 5725 of the series Lecture Notes in Computer Science pp 1-12

Cycle-Free Finite Automata in Partial Iterative Semirings

  • Stephen L. BloomAffiliated withDept. of Computer Science, Stevens Institute of Technology
  • , Zoltan ÉsikAffiliated withDept. of Computer Science, University of Szeged
  • , Werner KuichAffiliated withInstitut für Diskrete Mathematik und Geometrie, Technische Universität Wien

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Abstract

We consider partial Conway semirings and partial iteration semirings, both introduced by Bloom, Ésik, Kuich [2]. We develop a theory of cycle-free elements in partial iterative semirings that allows us to define cycle-free finite automata in partial iterative semirings and to prove a Kleene Theorem. We apply these results to power series over a graded monoid with discounting.