{"id":"https://openalex.org/W2151068277","doi":"https://doi.org/10.2178/jsl/1096901758","title":"On spectra of sentences of monadic second order logic with counting","display_name":"On spectra of sentences of monadic second order logic with counting","publication_year":2004,"publication_date":"2004-09-01","ids":{"openalex":"https://openalex.org/W2151068277","doi":"https://doi.org/10.2178/jsl/1096901758","mag":"2151068277"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1096901758","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1096901758","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036603247","display_name":"E. Fischer","orcid":"https://orcid.org/0009-0001-4721-356X"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"E. Fischer","raw_affiliation_strings":["Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel, E-mail:","Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel, E-mail: eldar@cs.technion.ac.il"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel, E-mail:","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel, E-mail: eldar@cs.technion.ac.il","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090746300","display_name":"Johann A. Makowsky","orcid":"https://orcid.org/0000-0002-3550-4271"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"J. A. Makowsky","raw_affiliation_strings":["Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel, E-mail:","Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel, E-mail: janos@cs.technion.ac.il"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel, E-mail:","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel, E-mail: janos@cs.technion.ac.il","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":null,"apc_paid":null,"fwci":2.0518,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.87184116,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"69","issue":"3","first_page":"617","last_page":"640"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9983000159263611,"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/T11567","display_name":"semigroups and automata theory","score":0.9983000159263611,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9972000122070312,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.8820104598999023},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6810513734817505},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5555369257926941},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5306562185287476},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4945206344127655},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.45927247405052185},{"id":"https://openalex.org/keywords/binary-relation","display_name":"Binary relation","score":0.45024654269218445},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4427400231361389},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.4412250518798828}],"concepts":[{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.8820104598999023},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6810513734817505},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5555369257926941},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5306562185287476},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4945206344127655},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.45927247405052185},{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.45024654269218445},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4427400231361389},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.4412250518798828},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1096901758","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1096901758","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1096901758","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1096901758","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.6000000238418579,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":70,"referenced_works":["https://openalex.org/W163370848","https://openalex.org/W192864959","https://openalex.org/W200063938","https://openalex.org/W278258255","https://openalex.org/W596942210","https://openalex.org/W657835803","https://openalex.org/W1482193060","https://openalex.org/W1511526676","https://openalex.org/W1512428151","https://openalex.org/W1537449969","https://openalex.org/W1549757712","https://openalex.org/W1563892973","https://openalex.org/W1576906924","https://openalex.org/W1579049696","https://openalex.org/W1582408114","https://openalex.org/W1658080915","https://openalex.org/W1966875984","https://openalex.org/W1975241591","https://openalex.org/W1976120600","https://openalex.org/W1993328543","https://openalex.org/W1994887153","https://openalex.org/W2003895694","https://openalex.org/W2004142949","https://openalex.org/W2004663163","https://openalex.org/W2005659848","https://openalex.org/W2007091370","https://openalex.org/W2022499468","https://openalex.org/W2025087469","https://openalex.org/W2028357390","https://openalex.org/W2031764672","https://openalex.org/W2036648964","https://openalex.org/W2036740975","https://openalex.org/W2043071947","https://openalex.org/W2043711611","https://openalex.org/W2045399132","https://openalex.org/W2053534720","https://openalex.org/W2054167510","https://openalex.org/W2062792526","https://openalex.org/W2063063505","https://openalex.org/W2066026450","https://openalex.org/W2082778556","https://openalex.org/W2085467680","https://openalex.org/W2085923075","https://openalex.org/W2087083200","https://openalex.org/W2089107726","https://openalex.org/W2089928579","https://openalex.org/W2093898714","https://openalex.org/W2105435789","https://openalex.org/W2109716789","https://openalex.org/W2131834772","https://openalex.org/W2138716118","https://openalex.org/W2157390113","https://openalex.org/W2159003936","https://openalex.org/W2165273951","https://openalex.org/W2551720480","https://openalex.org/W2798588639","https://openalex.org/W2911295106","https://openalex.org/W2913344232","https://openalex.org/W2953095747","https://openalex.org/W2954327716","https://openalex.org/W2986773320","https://openalex.org/W3127113455","https://openalex.org/W4212959352","https://openalex.org/W4236835455","https://openalex.org/W4241604193","https://openalex.org/W4285719527","https://openalex.org/W4292230561","https://openalex.org/W6636739396","https://openalex.org/W6672861001","https://openalex.org/W6683227944"],"related_works":["https://openalex.org/W2888918612","https://openalex.org/W2166285859","https://openalex.org/W3148597776","https://openalex.org/W1561765852","https://openalex.org/W230743427","https://openalex.org/W1603558256","https://openalex.org/W3037447502","https://openalex.org/W2050480346","https://openalex.org/W2070614493","https://openalex.org/W1988459304"],"abstract_inverted_index":{"Abstract.":[0],"We":[1,52,108],"show":[2],"that":[3,179],"the":[4,35,74,77,90,95,155,180],"spectrum":[5,156],"of":[6,37,40,66,79,82,92,123,154,159,184],"a":[7,54,64],"sentence":[8],"\u03d5":[9,38,80],"in":[10],"Counting":[11],"Monadic":[12,160],"Second":[13,103,161],"Order":[14,104,162],"Logic":[15,105,163],"(":[16],"CMSOL":[17],")":[18],"using":[19],"one":[20,171],"binary":[21],"relation":[22,28],"symbol":[23],"and":[24,63,129,139,147,170,190],"finitely":[25,166],"many":[26,167],"unary":[27,168,172],"symbols,":[29],"is":[30,98],"ultimately":[31],"periodic,":[32],"provided":[33],"all":[34,183],"models":[36,78,181],"are":[39,81,174,182],"clique":[41,67],"width":[42,68,84,186],"at":[43,85,187],"most":[44,86,188],"k":[45,50,87],",":[46],"for":[47,57,69,101,132,157],"some":[48],"fixed":[49],".":[51,88,107],"prove":[53],"similar":[55],"statement":[56],"arbitrary":[58],"finite":[59],"relational":[60],"vocabularies":[61],"\u03c4":[62,70],"variant":[65],"-structures.":[71],"This":[72,176],"includes":[73],"cases":[75],"where":[76,164],"tree":[83,185],"For":[89],"case":[91],"bounded":[93],"tree-width,":[94],"ultimate":[96,152],"periodicity":[97,153],"even":[99],"proved":[100],"Guarded":[102],"GSOL":[106],"also":[109],"generalize":[110],"this":[111],"result":[112],"to":[113,137],"many-sorted":[114],"spectra,":[115],"which":[116],"can":[117],"be":[118],"viewed":[119],"as":[120],"an":[121],"analogue":[122],"Parikh's":[124],"Theorem":[125],"on":[126],"context-free":[127,133],"languages,":[128],"its":[130],"analogues":[131],"graph":[134],"grammars":[135],"due":[136],"Habel":[138],"Courcelle.":[140],"Our":[141],"work":[142],"was":[143],"inspired":[144],"by":[145],"Gurevich":[146],"Shelah":[148],"(2003),":[149],"who":[150],"showed":[151],"sentences":[158],"only":[165],"predicates":[169],"function":[173],"allowed.":[175],"restriction":[177],"implies":[178],"2,":[189],"hence":[191],"it":[192],"follows":[193],"from":[194],"our":[195],"result.":[196]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}