A Note on Avoid vs MCSP
Edward A. Hirsch, Ilya Volkovich
TL;DR
This paper explores the relationship between the Minimal Circuit Size Problem and the class AM ∩ coAM, proposing a new approach to understanding the complexity of languages reducible to the Range Avoidance Problem.
Contribution
It introduces a novel method using the Minimal Circuit Size Problem to potentially replicate known results about the complexity class containment of certain languages.
Findings
Potential new avenue for complexity class containment proofs
Connection between Minimal Circuit Size Problem and AM ∩ coAM
Alternative approach to previous results by Ghentiyala, Li, and Stephens-Davidowitz
Abstract
A recent result of Ghentiyala, Li, and Stephens-Davidowitz (ECCC TR 25-210) shows that any language reducible to the Range Avoidance Problem via deterministic or randomized Turing reductions is contained in AM coAM. In this note, we present a different potential avenue for obtaining the same result via the Minimal Circuit Size Problem.
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Taxonomy
TopicsComplexity and Algorithms in Graphs · DNA and Biological Computing · semigroups and automata theory