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Self-affine fractals of finite type

Christoph Bandt, Mathias Mesing (2009)

Banach Center Publications

In the class of self-affine sets on ℝⁿ we study a subclass for which the geometry is rather tractable. A type is a standardized position of two intersecting pieces. For a self-affine tiling, this can be identified with an edge or vertex type. We assume that the number of types is finite. We study the topology of such fractals and their boundary sets, and we show how new finite type fractals can be constructed. For finite type self-affine tiles in the plane we give an algorithm which decides whether...

Semigroups defined by automaton extension mapping

Mirosław Osys (2005)

Discussiones Mathematicae - General Algebra and Applications

We study semigroups generated by the restrictions of automaton extension (see, e.g., [3]) and give a characterization of automaton extensions that generate finite semigroups.

Series which are both max-plus and min-plus rational are unambiguous

Sylvain Lombardy, Jean Mairesse (2006)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Consider partial maps Σ * → ℝ with a rational domain. We show that two families of such series are actually the same: the unambiguous rational series on the one hand, and the max-plus and min-plus rational series on the other hand. The decidability of equality was known to hold in both families with different proofs, so the above unifies the picture. We give an effective procedure...

Series which are both max-plus and min-plus rational are unambiguous

Sylvain Lombardy, Jean Mairesse (2010)

RAIRO - Theoretical Informatics and Applications

Consider partial maps ∑* → ℝ with a rational domain. We show that two families of such series are actually the same: the unambiguous rational series on the one hand, and the max-plus and min-plus rational series on the other hand. The decidability of equality was known to hold in both families with different proofs, so the above unifies the picture. We give an effective procedure to build an unambiguous automaton from a max-plus automaton and a min-plus one that recognize the same series.

Some results on C-varieties

Jean-Éric Pin, Howard Straubing (2010)

RAIRO - Theoretical Informatics and Applications

In an earlier paper, the second author generalized Eilenberg's variety theory by establishing a basic correspondence between certain classes of monoid morphisms and families of regular languages. We extend this theory in several directions. First, we prove a version of Reiterman's theorem concerning the definition of varieties by identities, and illustrate this result by describing the identities associated with languages of the form (a1a2...ak)+, where a1,...,ak are distinct letters. Next,...

Some results on 𝒞 -varieties

Jean-Éric Pin, Howard Straubing (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

In an earlier paper, the second author generalized Eilenberg’s variety theory by establishing a basic correspondence between certain classes of monoid morphisms and families of regular languages. We extend this theory in several directions. First, we prove a version of Reiterman’s theorem concerning the definition of varieties by identities, and illustrate this result by describing the identities associated with languages of the form ( a 1 a 2 ⋯ a k ) + , where a 1 , ... , a k are distinct letters. Next, we generalize the notions...

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