On Aperiodic Trace Languages

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On Aperiodic Trace Languages
Formal power series over non-commuting variables have been investigated as representations of the behavior of automata with multiplicities. Here we introduce and investigate the concepts of aperiodic and of star-free formal power series over semirings and partially commuting variables. We prove that if the semiring K is idempotent and commutative, or if K is idempotent and the variables are non-commuting, then the product of any two aperiodic series is again aperiodic. We also show that if K is idempotent and the matrix monoids over K have a Burnside property (satisfied, e.g. by the tropical semiring), then the aperiodic and the star-free series coincide. This generalizes a classical result of Sch¨utzenberger (1961) for aperiodic regular languages and contains a result of Guaiana, Restivo and Salemi (1992) on aperiodic trace languages.
Giovanna Guaiana, Antonio Restivo, Sergio Salemi
Added 27 Aug 2010
Updated 27 Aug 2010
Type Conference
Year 1991
Authors Giovanna Guaiana, Antonio Restivo, Sergio Salemi
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