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finite automata have no storage and no computing capability????

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Finite automata have no auxiliary storage. It remembers something by changing a state. So we may say it has finite storage capability. 

Memory in finite automata is present in the form of states Q only and according to automata principal: any automata can have only finite set of states. hence finite automata has finite memory, this is the reason automata for regular language is called finite automata.

Source: https://cs.stackexchange.com/questions/23460/i-need-clarification-about-dfas-and-dfa-acceptable-languages

Regarding Computing capability, it is more appropriate to say it has limited computing capability rather than saying it has no computing capability.

The finite state machine has less computational power than some other models of computation such as the Turing machine.[2] The computational power distinction means there are computational tasks that a Turing machine can do but a FSM cannot. This is because a FSM's memory is limited by the number of states it has.

Souce: https://en.wikipedia.org/wiki/Finite-state_machine

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