{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/164654"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/164654","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Deterministic Circuit Range Avoidance is (Likely) Intractable","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_html":"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_has_math":false,"creators":["Ilango, Rahul"],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science","school":null,"contributors":[],"advisors":["Williams, Ryan"],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-09","date_published":"2025-09","updated_at":"2026-07-22T22:22:31Z","subjects":[],"languages":[],"rights":["In Copyright - Educational Use Permitted","Copyright retained by author(s)"],"rights_urls":["https://rightsstatements.org/page/InC-EDU/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1721.1/164654","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Williams, Ryan"]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. 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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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["Deterministic Circuit Range Avoidance is (Likely) Intractable"]}]}],"canonical_facts":{"dc:contributor.advisor":["Williams, Ryan"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science"],"dc:creator":["Ilango, Rahul"],"dc:date.accessioned":["2026-01-29T15:06:11Z"],"dc:date.available":["2026-01-29T15:06:11Z"],"dc:date.issued":["2025-09"],"dc:description.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."],"dc:description.degree":["S.M."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/164654"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright retained by author(s)"],"dc:rights.uri":["https://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Deterministic Circuit Range Avoidance is (Likely) Intractable"],"dc:type":["Thesis"],"thesis:degree_name":["Master","Master of Science in Electrical Engineering and Computer Science"]},"updated_at":"2026-07-22T22:22:31Z"}