2026-09-19T04:08:33Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1646542026-01-30T03:24:47Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Williams, Ryan
Ilango, Rahul
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2026-01-29T15:06:11Z
2026-01-29T15:06:11Z
2025-09
2025-09-15T14:40:55.245Z
https://hdl.handle.net/1721.1/164654
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.
S.M.
Massachusetts Institute of Technology
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https://rightsstatements.org/page/InC-EDU/1.0/
Deterministic Circuit Range Avoidance is (Likely) Intractable
Thesis
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Master
Master of Science in Electrical Engineering and Computer Science
Publication
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<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.</Abstract>
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