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Tally ERP.9
TALLY is contained in P/poly - the class of languages that can be recognized in polynomial time given an advice function that depends only on the input length. In this case, the required advice function is very simple - it returns a single bit for each input length k specifying whether 1k is in the language or not.
A unary language is necessarily a sparse language, since for each n it contains at most one value of length n and at most n values of length at most n, but not all sparse languages are unary; thus TALLY is contained in SPARSE.
If there exists a unary language that is NP-complete, then P = NP.
This result can be extended to sparse languages.
If L is a unary language, then L (the Kleene star of L) is a regular language
