Checking [tilings with] constraints

A set of allowed templates can be specified by a Mathematica pattern of the form t₁ | t₂ | t₃

\!\(\*SubscriptBox[\(t\),\(1\)]\)|\!\(\*SubscriptBox[\(t\),\(2\)]\)|\!\(\*SubscriptBox[\(t\),\(3\)]\) etc. where the t_i

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\!\(\*SubscriptBox[\(t\),\(i\)]\) are for example {{_, 1, _}, {0, 0, 1}, {_, 0, _}}

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{{_, 1, _}, {0, 0, 1}, {_, 0, _}}. To check whether an array list

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list contains only arrangements of colors corresponding to allowed templates one can then use

SatisfiedQ[list_, allowed_] := Apply[And, Map[MatchQ[#, allowed] &, Partition[list, {3, 3}, {1, 1}], {2}], {0, 1}]