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De?nition Instantaneous Description of an FSA:
An instantaneous description (ID) of a FSA A = (Q,Σ, T, q0, F) is a pair (q,w) ∈ Q×Σ* , where q the current state and w is the portion of the input under and to the right of the read head.
w is the portion of the string remaining to be processed. The symbol being currently being read by the FSA is the ?rst symbol of w. If w is empty then the entire input has been scanned and the FSA has halted.
To see this, note that if there are any cycles in the Myhill graph of A then L(A) will be infinite, since any such cycle can be repeated arbitrarily many times. Conversely, if the
Proof (sketch): Suppose L 1 and L 2 are recognizable. Then there are DFAs A 1 = (Q,Σ, T 1 , q 0 , F 1 ) and A 2 = (P,Σ, T 2 , p 0 , F 2 ) such that L 1 = L(A 1 ) and L 2 = L(
These assumptions hold for addition, for instance. Every instance of addition has a unique solution. Each instance is a pair of numbers and the possible solutions include any third
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