On morphically generated formal power series
A decision method for the recognizability of sets defined by number systems
A Kleene-Schützenberger theorem for Lindenmayerian rational power series
On sequences defined by D0L power series
The cyclicity problem for the images of Q-rational series
We show that it is decidable whether or not a given Q-rational series in several noncommutative variables has a cyclic image. By definition, a series has a cyclic image if there is a rational number such that all nonzero coefficients of are integer powers of .
A bound for the -equivalence problem of polynomial D0L systems
We give a bound for the -equivalence problem of polynomially bounded D0L systems which depends only on the size of the underlying alphabet.
The cyclicity problem for the images of Q-rational series
We show that it is decidable whether or not a given Q-rational series in several noncommutative variables has a cyclic image. By definition, a series has a cyclic image if there is a rational number such that all nonzero coefficients of are integer powers of .
A bound for the -equivalence problem of polynomial D0L systems
We give a bound for the -equivalence problem of polynomially bounded D0L systems which depends only on the size of the underlying alphabet.
A periodicity property of iterated morphisms
Suppose is a morphism and . For every nonnegative integer , let be the longest common prefix of ƒ and ƒ, and let be words such that ƒ and ƒ. We prove that there is a positive integer such that for any positive integer , the prefixes of (resp. ) of length form an ultimately periodic sequence having period . Further, there is a value of which works for all words .
On Sequences Defined by D0L Power Series
We study D0L power series over commutative semirings. We show that a sequence () of nonzero elements of a field A is the coefficient sequence of a D0L power series if and only if there exist a positive integer and integers for 1 ≤ ≤ such that for all ≥ 0. As a consequence we solve the equivalence problem of D0L power series over computable fields.
A Kleene-Schützenberger theorem for Lindenmayerian rational power series
We define L rational and L recognizable power series, and establish a Kleene-Schützenberger theorem for Lindenmayerian power series by showing that a power series is L rational if and only if it is L recognizable.
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