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Iteration and Summability in Semirings

DOI: 10.1016/s0304-0208(08)72965-7
  • Linguistics
  • Logic
  • Mathematics


An algebraic treatment of various questions in linear algebra, automata and formal language theory, combinatorial optimization, data flow analysis, graph theory, semantics and others has exhibited the importance of transitive closure over semirings and the broad applicability of Gauss-Jordan elimination method. In view of these applications we study the solvability of equations of the form x=l+ax, called iteration, and introduct a concept of summability in positive semirings.

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