Relationships To Other Complexity Classes
TALLY is contained in P/poly, with a single-bit advice string 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. Piotr Berman showed in 1978 that if any unary language is NP-complete, then P = NP, which Mahaney generalized to sparse languages.
Read more about this topic: Unary Language
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