Pub Date : 2023-02-21DOI: 10.48550/arXiv.2302.10670
Maximilian Kotowsky, Jan Philipp Wächter
A finitary automaton group is a group generated by an invertible, deterministic finite-state letter-to-letter transducer whose only cycles are self-loops at an identity state. We show that, for this presentation of finite groups, the uniform word problem is coNP-complete. Here, the input consists of a finitary automaton together with a finite state sequence and the question is whether the sequence acts trivially on all input words. Additionally, we also show that the respective compressed word problem, where the state sequence is given as a straight-line program, is PSPACE-complete. In both cases, we give a direct reduction from the satisfiablity problem for (quantified) boolean formulae.
{"title":"The Word Problem for Finitary Automaton Groups","authors":"Maximilian Kotowsky, Jan Philipp Wächter","doi":"10.48550/arXiv.2302.10670","DOIUrl":"https://doi.org/10.48550/arXiv.2302.10670","url":null,"abstract":"A finitary automaton group is a group generated by an invertible, deterministic finite-state letter-to-letter transducer whose only cycles are self-loops at an identity state. We show that, for this presentation of finite groups, the uniform word problem is coNP-complete. Here, the input consists of a finitary automaton together with a finite state sequence and the question is whether the sequence acts trivially on all input words. Additionally, we also show that the respective compressed word problem, where the state sequence is given as a straight-line program, is PSPACE-complete. In both cases, we give a direct reduction from the satisfiablity problem for (quantified) boolean formulae.","PeriodicalId":305919,"journal":{"name":"Workshop on Descriptional Complexity of Formal Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126299063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-27DOI: 10.48550/arXiv.2205.13916
Duncan Adamson
Unlabelled Necklaces are an equivalence class of cyclic words under both the rotation (cyclic shift) and the relabelling operations. The relabelling of a word is a bijective mapping from the alphabet to itself. The main result of the paper is the first polynomial-time algorithm for ranking unlabelled necklaces of a binary alphabet. The time-complexity of the algorithm is O ( n 6 log 2 n ), where n is the length of the considered necklaces. The key part of the algorithm is to compute the rank of any word with respect to the set of unlabelled necklaces by finding three other ranks: the rank over all necklaces, the rank over symmetric unlabelled necklaces, and the rank over necklaces with an enclosing labelling. The last two concepts are introduced in this paper.
{"title":"Ranking Binary Unlabelled Necklaces in Polynomial Time","authors":"Duncan Adamson","doi":"10.48550/arXiv.2205.13916","DOIUrl":"https://doi.org/10.48550/arXiv.2205.13916","url":null,"abstract":"Unlabelled Necklaces are an equivalence class of cyclic words under both the rotation (cyclic shift) and the relabelling operations. The relabelling of a word is a bijective mapping from the alphabet to itself. The main result of the paper is the first polynomial-time algorithm for ranking unlabelled necklaces of a binary alphabet. The time-complexity of the algorithm is O ( n 6 log 2 n ), where n is the length of the considered necklaces. The key part of the algorithm is to compute the rank of any word with respect to the set of unlabelled necklaces by finding three other ranks: the rank over all necklaces, the rank over symmetric unlabelled necklaces, and the rank over necklaces with an enclosing labelling. The last two concepts are introduced in this paper.","PeriodicalId":305919,"journal":{"name":"Workshop on Descriptional Complexity of Formal Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115358835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-24DOI: 10.1007/978-3-031-34326-1_12
Josef Rukavicka
{"title":"Construction of a Bi-infinite Power Free Word with a Given Factor and a Non-recurrent Letter","authors":"Josef Rukavicka","doi":"10.1007/978-3-031-34326-1_12","DOIUrl":"https://doi.org/10.1007/978-3-031-34326-1_12","url":null,"abstract":"","PeriodicalId":305919,"journal":{"name":"Workshop on Descriptional Complexity of Formal Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117165104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-26DOI: 10.1007/978-3-030-93489-7_4
Stefan Hoffmann
{"title":"Sync-Maximal Permutation Groups Equal Primitive Permutation Groups","authors":"Stefan Hoffmann","doi":"10.1007/978-3-030-93489-7_4","DOIUrl":"https://doi.org/10.1007/978-3-030-93489-7_4","url":null,"abstract":"","PeriodicalId":305919,"journal":{"name":"Workshop on Descriptional Complexity of Formal Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133054533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-26DOI: 10.1007/978-3-030-93489-7_5
Stefan Hoffmann
{"title":"Commutative Regular Languages with Product-Form Minimal Automata","authors":"Stefan Hoffmann","doi":"10.1007/978-3-030-93489-7_5","DOIUrl":"https://doi.org/10.1007/978-3-030-93489-7_5","url":null,"abstract":"","PeriodicalId":305919,"journal":{"name":"Workshop on Descriptional Complexity of Formal Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116528204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-26DOI: 10.1007/978-3-030-93489-7_6
Stefan Hoffmann
{"title":"State Complexity Investigations on Commutative Languages - The Upward and Downward Closure, Commutative Aperiodic and Commutative Group Languages","authors":"Stefan Hoffmann","doi":"10.1007/978-3-030-93489-7_6","DOIUrl":"https://doi.org/10.1007/978-3-030-93489-7_6","url":null,"abstract":"","PeriodicalId":305919,"journal":{"name":"Workshop on Descriptional Complexity of Formal Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123521751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-02DOI: 10.1007/978-3-030-93489-7_15
S. Kiefer, C. Widdershoven
{"title":"Image-Binary Automata","authors":"S. Kiefer, C. Widdershoven","doi":"10.1007/978-3-030-93489-7_15","DOIUrl":"https://doi.org/10.1007/978-3-030-93489-7_15","url":null,"abstract":"","PeriodicalId":305919,"journal":{"name":"Workshop on Descriptional Complexity of Formal Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121584879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-30DOI: 10.1007/978-3-030-93489-7_16
A. Yakaryılmaz
{"title":"Improved constructions for succinct affine automata","authors":"A. Yakaryılmaz","doi":"10.1007/978-3-030-93489-7_16","DOIUrl":"https://doi.org/10.1007/978-3-030-93489-7_16","url":null,"abstract":"","PeriodicalId":305919,"journal":{"name":"Workshop on Descriptional Complexity of Formal Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128302866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-24DOI: 10.1007/978-3-030-93489-7_2
Sabine Broda, António Machiavelo, Nelma Moreira, Rogério Reis
{"title":"On the Uniform Distribution of Regular Expressions","authors":"Sabine Broda, António Machiavelo, Nelma Moreira, Rogério Reis","doi":"10.1007/978-3-030-93489-7_2","DOIUrl":"https://doi.org/10.1007/978-3-030-93489-7_2","url":null,"abstract":"","PeriodicalId":305919,"journal":{"name":"Workshop on Descriptional Complexity of Formal Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130487392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-31DOI: 10.1007/978-3-030-62536-8_3
Ehud Cseresnyes, Hannes Seiwert
{"title":"Regular Expression Length via Arithmetic Formula Complexity","authors":"Ehud Cseresnyes, Hannes Seiwert","doi":"10.1007/978-3-030-62536-8_3","DOIUrl":"https://doi.org/10.1007/978-3-030-62536-8_3","url":null,"abstract":"","PeriodicalId":305919,"journal":{"name":"Workshop on Descriptional Complexity of Formal Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115327254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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