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Actually not all routers are stateless devices. There are stateful routers also. The definition depends on the IP filtering and routing algorithms used. Routers which have static IP filters and routing tables are of the stateless type. Routers with Static IP filters allow direct connections from the external network to hosts on the internal network and typically there is no authentication. More intelligent and secure routers with dynamic IP address and packet based filtering are known as stateful type. Stateful routers can also have application proxies or gateways. These have more overheads for processing packets passing through the routers. - Neeraj Sharma

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Q: Why is a router called a stateless device?
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