Comtraces (combined traces) are extensions of Mazurkiewicz traces that can model the "not later than" relationship. In this paper, we first introduce the novel concept of generalized comtraces, extensions of comtraces that can additionally model the "non-simultaneously" relationship. Then we study some basic algebraic properties as well as canonical reprentations of comtraces and generalized comtraces. Finally we analyze the relationship between generalized comtraces and generalized stratified order structures. The major technical contribution of this paper is a proof showing that generalized comtraces can be represented by generalized stratified order structures.
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