Abstract
The problem we mainly deal with is the existence of a coding between two trace monoids. We introduce a new notion of coding: the strong coding (independent letters are mapped into independent traces). We prove that the existence of a strong coding between two trace monoids is decidable when the first monoid belongs to one of two large families of trace monoids that we specify. Our decision conditions are based on graph-theoretical properties of the dependence relations. A related question of Ochmański (1988) is completely solved for strong codings.
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