Minimum Circuit Size, Graph Isomorphism, and Related Problems
| Autor: | Andrew Morgan, Eric Allender, Joshua A. Grochow, Cristopher Moore, Dieter van Melkebeek |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
FOS: Computer and information sciences 000 Computer science knowledge general works General Computer Science General Mathematics 010102 general mathematics Truth table 0102 computer and information sciences Computational Complexity (cs.CC) 01 natural sciences Time-bounded Kolmogorov complexity Power (physics) Computer Science::Hardware Architecture Computer Science - Computational Complexity Computer Science::Emerging Technologies Minimum Circuit Size Problem 010201 computation theory & mathematics Graph Isomorphism Computer Science 0101 mathematics Graph isomorphism Reductions between NP-intermediate problems Mathematics |
| Zdroj: | BASE-Bielefeld Academic Search Engine |
| DOI: | 10.4230/lipics.itcs.2018.20 |
| Popis: | We study the computational power of deciding whether a given truth-table can be described by a circuit of a given size (the Minimum Circuit Size Problem, or MCSP for short), and of the variant denoted as MKTP where circuit size is replaced by a polynomially-related Kolmogorov measure. All prior reductions from supposedly-intractable problems to MCSP / MKTP hinged on the power of MCSP / MKTP to distinguish random distributions from distributions produced by hardness-based pseudorandom generator constructions. We develop a fundamentally different approach inspired by the well-known interactive proof system for the complement of Graph Isomorphism (GI). It yields a randomized reduction with zero-sided error from GI to MKTP. We generalize the result and show that GI can be replaced by any isomorphism problem for which the underlying group satisfies some elementary properties. Instantiations include Linear Code Equivalence, Permutation Group Conjugacy, and Matrix Subspace Conjugacy. Along the way we develop encodings of isomorphism classes that are efficiently decodable and achieve compression that is at or near the information-theoretic optimum; those encodings may be of independent interest. Comment: 35 pages |
| Databáze: | OpenAIRE |
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