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How Do Cryptocurrencies without Proof-of-Work (PoW) Consensus Address the Double-Spending Problem?

Cryptocurrencies without PoW, such as those using Proof-of-Stake (PoS), address the double-spending problem by requiring validators to "stake" their own capital (the native coin) as collateral. If a validator attempts a double-spend by signing two conflicting blocks, they are penalized by having their staked coins "slashed" or forfeited.

This financial disincentive replaces the computational cost of PoW, ensuring that malicious behavior results in a direct, quantifiable loss of capital.

What Is the Risk of “Slashing” in a Proof-of-Stake Protocol?
What Is the “Slashing” Mechanism in Proof-of-Stake and How Does It Deter Attacks?
What Is ‘Slashing’ in a Proof-of-Stake (PoS) System and How Does It Prevent Malicious Behavior?
What Is the Concept of “Slashing” in a Proof-of-Stake Consensus Mechanism?