{"id":"https://openalex.org/W239882307","doi":"https://doi.org/10.1007/978-0-387-35608-2_28","title":"Probabilistically Checkable Proofs the Easy Way","display_name":"Probabilistically Checkable Proofs the Easy Way","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W239882307","doi":"https://doi.org/10.1007/978-0-387-35608-2_28","mag":"239882307"},"language":"en","primary_location":{"id":"doi:10.1007/978-0-387-35608-2_28","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-0-387-35608-2_28","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-0-387-35608-2_28.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Information Technology in the Era of Network and Mobile Computing","raw_type":"book-chapter"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1007/978-0-387-35608-2_28.pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046763801","display_name":"Marius Zimand","orcid":"https://orcid.org/0000-0002-5938-6599"},"institutions":[{"id":"https://openalex.org/I4322298","display_name":"Towson University","ror":"https://ror.org/044w7a341","country_code":"US","type":"education","lineage":["https://openalex.org/I4322298"]},{"id":"https://openalex.org/I141595442","display_name":"University of Bucharest","ror":"https://ror.org/02x2v6p15","country_code":"RO","type":"education","lineage":["https://openalex.org/I141595442"]}],"countries":["RO","US"],"is_corresponding":true,"raw_author_name":"Marius Zimand","raw_affiliation_strings":["Department of Computer Science, University of Bucharest, Bucharest, Romania","Department of Computer and Information Sciences, Towson University, Baltimore, MD, USA","University of Bucharest","Towson University"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Bucharest, Bucharest, Romania","institution_ids":["https://openalex.org/I141595442"]},{"raw_affiliation_string":"Department of Computer and Information Sciences, Towson University, Baltimore, MD, USA","institution_ids":["https://openalex.org/I4322298"]},{"raw_affiliation_string":"University of Bucharest","institution_ids":["https://openalex.org/I141595442"]},{"raw_affiliation_string":"Towson University","institution_ids":["https://openalex.org/I4322298"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046763801"],"corresponding_institution_ids":["https://openalex.org/I141595442","https://openalex.org/I4322298"],"apc_list":null,"apc_paid":null,"fwci":0.3333,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55476529,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":null,"first_page":"337","last_page":"351"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.98580002784729,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.98580002784729,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.982200026512146,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10181","display_name":"Natural Language Processing Techniques","score":0.96670001745224,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6907534599304199},{"id":"https://openalex.org/keywords/gas-meter-prover","display_name":"Gas meter prover","score":0.6847438812255859},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6337872743606567},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.6144886612892151},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.5724791288375854},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.5450201630592346},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5065916776657104},{"id":"https://openalex.org/keywords/boolean-satisfiability-problem","display_name":"Boolean satisfiability problem","score":0.4872552454471588},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.48610568046569824},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.44867491722106934},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.4203302562236786},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4072422385215759},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39310216903686523},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.06251534819602966}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6907534599304199},{"id":"https://openalex.org/C159718280","wikidata":"https://www.wikidata.org/wiki/Q5526353","display_name":"Gas meter prover","level":3,"score":0.6847438812255859},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6337872743606567},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.6144886612892151},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.5724791288375854},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.5450201630592346},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5065916776657104},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.4872552454471588},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.48610568046569824},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.44867491722106934},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.4203302562236786},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4072422385215759},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39310216903686523},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.06251534819602966},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/978-0-387-35608-2_28","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-0-387-35608-2_28","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-0-387-35608-2_28.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Information Technology in the Era of Network and Mobile Computing","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.24.7953","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.7953","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://136.160.185.82/pub/pcp.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.32.7991","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.7991","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://136.160.184.109/pub/pcp.ps","raw_type":"text"},{"id":"mag:239882307","is_oa":false,"landing_page_url":"http://dblp.uni-trier.de/db/journals/eccc/eccc8.html#ECCC-TR01-027","pdf_url":null,"source":{"id":"https://openalex.org/S11189987","display_name":"Electronic colloquium on computational complexity","issn_l":"1433-8092","issn":["1433-8092"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Electronic colloquium on computational complexity","raw_type":null}],"best_oa_location":{"id":"doi:10.1007/978-0-387-35608-2_28","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-0-387-35608-2_28","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-0-387-35608-2_28.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Information Technology in the Era of Network and Mobile Computing","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W239882307.pdf","grobid_xml":"https://content.openalex.org/works/W239882307.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1569885018","https://openalex.org/W1970808997","https://openalex.org/W1996183456","https://openalex.org/W1998918799","https://openalex.org/W2015880590","https://openalex.org/W2040438296","https://openalex.org/W2107764994","https://openalex.org/W2117362057","https://openalex.org/W2143391442","https://openalex.org/W2151433956","https://openalex.org/W2166980335","https://openalex.org/W6657410821"],"related_works":["https://openalex.org/W1571969663","https://openalex.org/W2404853397","https://openalex.org/W1483170929","https://openalex.org/W2401934382","https://openalex.org/W184142732","https://openalex.org/W2021586362","https://openalex.org/W2806763105","https://openalex.org/W3214593854","https://openalex.org/W1490233153","https://openalex.org/W2148352980","https://openalex.org/W1571856917","https://openalex.org/W2400612744","https://openalex.org/W2395412869","https://openalex.org/W1555946936","https://openalex.org/W2950148416","https://openalex.org/W935592923","https://openalex.org/W2139594012","https://openalex.org/W2914525031","https://openalex.org/W2742040237","https://openalex.org/W1497086998"],"abstract_inverted_index":{"We":[0,45],"present":[1],"a":[2,11,52,58,64,70,95,129,144,148],"weaker":[3],"variant":[4,17],"of":[5,29,61,74,120,132,143],"the":[6,18,80,92,102,114,117,121,126,141],"PCP":[7,122],"Theorem":[8,123],"that":[9,47,56,94],"admits":[10],"significantly":[12],"easier":[13],"proof.":[14],"In":[15],"this":[16],"prover":[19,99],"only":[20],"has":[21],"n":[22,76,96],"t":[23,97],"time":[24],"to":[25,41],"compute":[26],"each":[27],"bit":[28],"his":[30],"answer,":[31],"for":[32],"an":[33,135],"arbitrary":[34],"but":[35],"fixed":[36],"constant":[37,59,130],"t,":[38],"in":[39,113,124],"contrast":[40],"being":[42],"all":[43],"powerful.":[44],"show":[46],"3SAT":[48],"is":[49,77,88,104],"accepted":[50],"by":[51],"polynomial-time":[53],"probabilistic":[54],"verifier":[55,81,103,127],"queries":[57],"number":[60,131],"bits":[62,133],"from":[63,134,147],"polynomially":[65],"long":[66,137],"proof":[67,115,138],"string.":[68],"If":[69,86],"boolean":[71],"formula":[72],"\u00f8":[73,87],"length":[75],"satisfiable,":[78,90],"then":[79,91],"accepts":[82],"with":[83],"probability":[84,93],"1.":[85],"not":[89],"-bounded":[98],"can":[100],"fool":[101],"at":[105],"most":[106],"1/2.":[107],"The":[108],"main":[109],"technical":[110],"tools":[111],"used":[112],"are":[116],"\u201ceasy\u201d":[118],"part":[119],"which":[125],"reads":[128],"exponentially":[136],"string,":[139],"and":[140],"construction":[142],"pseudo-random":[145],"generator":[146],"one-way":[149],"permutation.":[150]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}