{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/139249"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/139249","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Tolerant Testing of Regular Languages in Sublinear Time","abstract":"A classic problem in property testing is to test whether a binary input word 𝑤 is in regular language 𝐿. Such testers distinguish the case that 𝑤 is in 𝐿 from the case where 𝑤 is 𝜖-far from 𝐿 (𝜖-far means that at least 𝜖 fraction of the bits in 𝑤 must be modified to change 𝑤 into a word in 𝐿. Otherwise, 𝑤 is 𝜖-close). When it is known that 𝑤 is noisy, it can be useful to provide tolerant testers: algorithms that accept when 𝑤 is 𝛿-close and reject when 𝑤 is 𝜖-far, for 𝛿 < 𝜖. We build on the work of Alon, Krivelevich, Newman and Szegedy [1] to provide a tolerant, constant time property tester for regular languages. Our main result is that given a regular language 𝐿 ∈ {0, 1} * and an integer 𝑛, there exists a randomized algorithm which accepts a word 𝑤 of length 𝑛 if it is 𝛿-close (𝛿 < 𝜖) to a word in 𝐿 and rejects with high probability if 𝑤 is 𝜖-far from a word in 𝐿. The algorithm queries polynomial in 1 𝜖 bits in 𝑤.","abstract_html":"A classic problem in property testing is to test whether a binary input word 𝑤 is in regular language 𝐿. Such testers distinguish the case that 𝑤 is in 𝐿 from the case where 𝑤 is 𝜖-far from 𝐿 (𝜖-far means that at least 𝜖 fraction of the bits in 𝑤 must be modified to change 𝑤 into a word in 𝐿. Otherwise, 𝑤 is 𝜖-close). When it is known that 𝑤 is noisy, it can be useful to provide tolerant testers: algorithms that accept when 𝑤 is 𝛿-close and reject when 𝑤 is 𝜖-far, for 𝛿 &lt; 𝜖. We build on the work of Alon, Krivelevich, Newman and Szegedy [1] to provide a tolerant, constant time property tester for regular languages. Our main result is that given a regular language 𝐿 ∈ {0, 1} * and an integer 𝑛, there exists a randomized algorithm which accepts a word 𝑤 of length 𝑛 if it is 𝛿-close (𝛿 &lt; 𝜖) to a word in 𝐿 and rejects with high probability if 𝑤 is 𝜖-far from a word in 𝐿. The algorithm queries polynomial in 1 𝜖 bits in 𝑤.","abstract_has_math":false,"creators":["Gong, Linda"],"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":["Rubinfeld, Ronitt"],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-06","date_published":"2021-06","updated_at":"2026-07-22T22:21:09Z","subjects":[],"languages":[],"rights":["In Copyright - Educational Use Permitted","Copyright MIT"],"rights_urls":["http://rightsstatements.org/page/InC-EDU/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1721.1/139249","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Rubinfeld, Ronitt"]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science"]},{"key":"dc:creator","label":"Author","values":["Gong, Linda"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2022-01-14T14:59:22Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-01-14T14:59:22Z"]},{"key":"dc:date.issued","label":"Date","values":["2021-06"]},{"key":"dc:publisher","label":"Institution","values":["Massachusetts Institute of Technology"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master","Master of Engineering in Electrical Engineering and Computer Science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright - Educational Use Permitted","Copyright MIT"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/page/InC-EDU/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1721.1/139249"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A classic problem in property testing is to test whether a binary input word 𝑤 is in regular language 𝐿. Such testers distinguish the case that 𝑤 is in 𝐿 from the case where 𝑤 is 𝜖-far from 𝐿 (𝜖-far means that at least 𝜖 fraction of the bits in 𝑤 must be modified to change 𝑤 into a word in 𝐿. Otherwise, 𝑤 is 𝜖-close). When it is known that 𝑤 is noisy, it can be useful to provide tolerant testers: algorithms that accept when 𝑤 is 𝛿-close and reject when 𝑤 is 𝜖-far, for 𝛿 < 𝜖. We build on the work of Alon, Krivelevich, Newman and Szegedy [1] to provide a tolerant, constant time property tester for regular languages. Our main result is that given a regular language 𝐿 ∈ {0, 1} * and an integer 𝑛, there exists a randomized algorithm which accepts a word 𝑤 of length 𝑛 if it is 𝛿-close (𝛿 < 𝜖) to a word in 𝐿 and rejects with high probability if 𝑤 is 𝜖-far from a word in 𝐿. The algorithm queries polynomial in 1 𝜖 bits in 𝑤."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["M.Eng."]},{"key":"dc:title","label":"Title","values":["Tolerant Testing of Regular Languages in Sublinear Time"]}]}],"canonical_facts":{"dc:contributor.advisor":["Rubinfeld, Ronitt"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science"],"dc:creator":["Gong, Linda"],"dc:date.accessioned":["2022-01-14T14:59:22Z"],"dc:date.available":["2022-01-14T14:59:22Z"],"dc:date.issued":["2021-06"],"dc:description.abstract":["A classic problem in property testing is to test whether a binary input word 𝑤 is in regular language 𝐿. Such testers distinguish the case that 𝑤 is in 𝐿 from the case where 𝑤 is 𝜖-far from 𝐿 (𝜖-far means that at least 𝜖 fraction of the bits in 𝑤 must be modified to change 𝑤 into a word in 𝐿. Otherwise, 𝑤 is 𝜖-close). When it is known that 𝑤 is noisy, it can be useful to provide tolerant testers: algorithms that accept when 𝑤 is 𝛿-close and reject when 𝑤 is 𝜖-far, for 𝛿 < 𝜖. We build on the work of Alon, Krivelevich, Newman and Szegedy [1] to provide a tolerant, constant time property tester for regular languages. Our main result is that given a regular language 𝐿 ∈ {0, 1} * and an integer 𝑛, there exists a randomized algorithm which accepts a word 𝑤 of length 𝑛 if it is 𝛿-close (𝛿 < 𝜖) to a word in 𝐿 and rejects with high probability if 𝑤 is 𝜖-far from a word in 𝐿. The algorithm queries polynomial in 1 𝜖 bits in 𝑤."],"dc:description.degree":["M.Eng."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/139249"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright MIT"],"dc:rights.uri":["http://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Tolerant Testing of Regular Languages in Sublinear Time"],"dc:type":["Thesis"],"thesis:degree_name":["Master","Master of Engineering in Electrical Engineering and Computer Science"]},"updated_at":"2026-07-22T22:21:09Z"}