Cartesian Monoids

On Cartesian Monoids

Some Undecidability Results Related to the Star Problem in Trace Monoids

This paper deals with decision problems related to the star problem in trace monoids, which means to determine whether the iteration of a recognizable trace language is recognizable. Due to a theorem by Richomme from 1994 30, 31], we know that the Star Problem is decidable in trace monoids which do not contain a C4-submonoid. The C4 is (isomorphic to) the Cartesian Product of two free monoids o...

A Connection between the Star Problem and the Finite Power Property in Trace Monoids

This paper deals with a connection between two decision problems for recognizable trace languages: the star problem and the nite power property problem. Due to a theorem by Richomme from 1994 26, 28], we know that both problems are decidable in trace monoids which do not contain a C4 submonoid. It is not known, whether the star problem or the nite power property are decidable in the C4 or in tr...

Space-Efficient Bimachine Construction Based on the Equalizer Accumulation Principle

Algorithms for building bimachines from functional transducers found in the literature in a run of the bimachine imitate one successful path of the input transducer. Each single bimachine output exactly corresponds to the output of a single transducer transition. Here we introduce an alternative construction principle where bimachine steps take alternative parallel transducer paths into account...

On some categorical-algebraic conditions in S-protomodular categories

In the context of semi-abelian categories, several additional conditions have been considered in order to obtain a closer group-like behavior. Among them are locally algebraic cartesian closedness and algebraic coherence. The recent notion of S-protomodular categories, whose main examples are the category of monoids and, more generally, categories of monoids with operations and Jónsson-Tarski v...