The US government and the ancient government of the Roman Republic share the following concepts:
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Separation of Powers: Both systems have a form of separation of powers among different branches of government. In the Roman Republic, power was divided among the consuls, the Senate, and popular assemblies, while in the US, it is divided among the legislative, executive, and judicial branches.
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Checks and Balances: Both systems incorporate checks and balances to prevent any one branch from becoming too powerful. In the Roman Republic, various offices had powers that could limit or check the actions of other offices, while in the US, each branch has the ability to check the powers of the other branches.
These principles are foundational in both governments, though the specific structures and functions differ. The other terms you mentioned, such as "written consultations," "one year time limit," and "who serves at judges," are not core concepts that reflect similarities between the two systems in the way that separation of powers and checks and balances do.