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The Sequence Equivalence Problem for Marked DT0L Systems

100%

Honkala J.

Fundamenta Informaticae

2011

tom Vol. 110, nr 1-4

175-182

We study the DT0L sequence equivalence problem for marked morphisms. We show that to decide this problem it is enough to consider initial terms involving at most 2n morphisms where n is the cardinality of the underlying alphabet.

The equivalence problem of DOL and DFOL power series

100%

Honkala J.

Fundamenta Informaticae

1999

tom Vol. 38, Nr 1,2

201-208

We show that it is decidable whether or not a given D0L power series and a given DF0L power series over a computable field are equal. This generalizes to power series the result of Ruohonen stating that DF0L-D0L language equivalence is decidable.

D0L Sequences and their Equality Sets

100%

Honkala J.

Fundamenta Informaticae

2017

tom Vol. 154, nr 1/4

201--206

We study D0L sequences and their equality sets. If s = (s(n))n≥0 and t = (t(n))n≥0 are D0L sequences, their equality set is defined by E(s, t) = {n ≥ 0 | s(n) = t(n)}. It is an open problem whether such equality sets are always eventually periodic. Using methods developed by Ehrenfeucht and Rozenberg we show that a D0L equality set is eventually periodic if it contains at least one infinite arithmetic progression. As a main tool we use elementary morphisms introduced by Ehrenfeucht and Rozenberg.

A Characterization of Regular Languages as Equality Sets of HDT0L Sequences

100%

Honkala J.

Fundamenta Informaticae

2012

tom Vol. 116, nr 1-4

123-128

We characterize regular languages as the equality sets of sequences generated by compatible uniform HDT0L systems.

On the Problem Whether the Image of an N-Rational Series Equals N

100%

Honkala J.

Fundamenta Informaticae

2006

tom Vol. 73, nr 1-2

127-132

We show that it is undecidable whether or not a given N-rational series assumes all nonnegative values. As a consequence we see that it is undecidable whether the image of a given N-rational series equals the image of a given N-rational sequence. We discuss also related results concerning DT0L and D0L length sets.

A New Class of Algebraic Series Having a Decidable Equivalence Problem

100%

Honkala J.

Fundamenta Informaticae

2002

tom Vol. 53, nr 3,4

315-320

We introduce a new class of algebraic series with noncommuting variables having a decidable equivalence problem. As a tool we consider star roots of formal power series.