Spectre is a DAG based (directed acyclic graph) distributed ledger (a structure as an alternative to blockchain based distributed ledger).
Is there any mechanism in Spectre to prevent sending spam transactions?
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Sure, there is a desire to avoid unnecessary load. But it is futile apart from cautioning people to avoid hurting the system during its growth phase.
In a system without identities there is no way to apply quota or ratelimiting per participant, and global ratelimiting only results in a denial-of-service attack. In practice the only thing that prevents spam is a free market; if people want to pay more for something than others, it will get in. This is independent of the type of consensus algorithm used to construct the chain.