Strong alternating moduli (chosen-input) assumption ⇒ Weak alternating moduli (random-input) assumption

Strong alternating moduli (chosen-input) assumption implies Weak alternating moduli (random-input) assumption.

Statement

Migrated verbatim from alternating-moduli:

is negligible. AM hardness implies Weak-AM hardness (the strong assumption implies the weak one).

Notes

source: folklore: the claim carried no citation on the page it was migrated from, and none was invented.

class: unstated: no citing page says which notion of reduction is meant. Recording a class the wiki does not state would add a claim.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

• Neither strong-AM nor weak-AM has its own page; both identifiers are ad hoc (the slug alternating-moduli covers both games).
• Uncited and not flagged as folklore or standard.