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.

• Type: Conference
• Year: 1991
• Where: STACS
• Authors: Giovanna Guaiana, Antonio Restivo, Sergio Salemi
• Keywords: Aperiodic, Aperiodic Series, Formal Power Series, STACS 1991, Theoretical Computer Science