Deterministic Circuit Range Avoidance is (Likely) Intractable
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ilango-rilango-sm-eecs-2025-thesis.pdf
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Thesis PDF
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312.28 KB
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Author(s)
Ilango, Rahul
Advisor(s)
Williams, Ryan
Date Issued
September 2025
Publisher
Massachusetts Institute of Technology
Abstract
Circuit Range Avoidance (denoted Avoid) is a computational problem where, given a Boolean circuit with more output bits than input bits, one must output a string outside of the range of the circuit. A simple counting argument implies that such a string must always exist and also guarantees that outputting a uniformly random string is correct with good probability. A natural question is whether this can be derandomized: does there exist an efficient deterministic algorithm for Avoid? We give the first evidence that deterministically solving Avoid is intractable. We show that there is no polynomial-time algorithm for Avoid under plausible assumptions in complexity theory and cryptography. Specifically, our assumptions are that NP ≠ coNP and that subexponentially-secure indistinguishability obfuscation exists.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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