Abstract
We show that several reducibility notions coincide when applied to the Graph Isomorphism (GI) problem. In particular we show that if a set is many-one logspace reducible to GI, then it is in fact many-one AC 0 reducible to GI. For the case of Turing reducibilities we show that for any k ≥ 0 an NC k + 1 reduction to GI can be transformed into an AC k reduction to the same problem.
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Torán, J. (2007). Reductions to Graph Isomorphism. In: Arvind, V., Prasad, S. (eds) FSTTCS 2007: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2007. Lecture Notes in Computer Science, vol 4855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77050-3_13
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DOI: https://doi.org/10.1007/978-3-540-77050-3_13
Publisher Name: Springer, Berlin, Heidelberg
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