Christian Pech

A Kleene Theorem for Weighted Tree Automata

Abstract In this paper we prove Kleene’s result for formal tree series over a commutative semiring A (which is not necessarily complete or continuous or idempotent), i.e., the class of formal tree series over A which are accepted by weighted tree automata, and the class of rational tree series over A are equal. We show the result by direct automata-theoretic constructions and prove their correctness.

A new construction of antipodal distance regular covers of complete graphs through the use of Godsil-Hensel matrices

New constructions of regular distance regular antipodal covers (in the sense of Godsil-Hensel) of complete graphs K n are presented. The main source of these constructions are skew generalized Hadamard matrices. It is described how to produce such a matrix of order n 2 over a group T from an arbitrary given generalized Hadamard matrix of order n over the same group T . Further, a new regular cover of K 45 on 135 vertices is produced with the aid of a decoration of the alternating group A 6 .

Examples of computer experimentation in algebraic combinatorics

We introduce certain paradigms for procuring computer-free explanations from data acquired via computer algebra experimentation. Our established context is the field of algebraic combinatorics, with special focus on coherent configurations and association schemes. All results presented here were obtained by the authors with the aid of computer algebra systems, especially COCO and GAP. A number of examples are explored, in particular of objects on 28, 50, 63, and 210 points. In a few cases, initial experimental data pointed to appropriate theoretical generalizations that yielded an infinite class of related combinatorial structures. Special attention is paid to algebraic automorphisms (of a coherent algebra), a fairly new concept that has already proved to have far-reaching consequences. Finally, we focus on the Doyle-Holt graph on 27 vertices, and some of its related structures.

On automatic homeomorphicity for transformation monoids

Transformation monoids carry a canonical topology—the topology of point-wise convergence. A closed transformation monoid

Towards a Ryll‐Nardzewski‐type theorem for weakly oligomorphic structures

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Reconstructing the Topology of the Elementary Self-embedding Monoids of Countable Saturated Structures

M is said to have automatic homeomorphicity with respect to a class

ON POLYMORPHISM-HOMOGENEOUS RELATIONAL STRUCTURES AND THEIR CLONES

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