Pub Date : 2022-07-14DOI: 10.48550/arXiv.2207.07229
E. Demaine, R. Hearn, D. Hendrickson, J. Lynch
We prove PSPACE-completeness of several reversible, fully deterministic systems. At the core, we develop a framework for such proofs (building on a result of Tsukiji and Hagiwara and a framework for motion planning through gadgets), showing that any system that can implement three basic gadgets is PSPACE-complete. We then apply this framework to four different systems, showing its versatility. First, we prove that Deterministic Constraint Logic is PSPACE-complete, fixing an error in a previous argument from 2008. Second, we give a new PSPACE-hardness proof for the reversible ‘billiard ball’ model of Fredkin and Toffoli from 40 years ago, newly establishing hardness when only two balls move at once. Third, we prove PSPACE-completeness of zero-player motion planning with any reversible deterministic interacting [Formula: see text]-tunnel gadget and a ‘rotate clockwise’ gadget (a zero-player analog of branching hallways). Fourth, we give simpler proofs that zero-player motion planning is PSPACE-complete with just a single gadget, the 3-spinner. These results should in turn make it even easier to prove PSPACE-hardness of other reversible deterministic systems.
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Pub Date : 2018-06-28DOI: 10.1007/978-3-319-92402-1_1
R. Freund
{"title":"Control Mechanisms for Array Grammars on Cayley Grids","authors":"R. Freund","doi":"10.1007/978-3-319-92402-1_1","DOIUrl":"https://doi.org/10.1007/978-3-319-92402-1_1","url":null,"abstract":"","PeriodicalId":340847,"journal":{"name":"Machines, Computations, and Universality","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125089435","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 : 2018-06-28DOI: 10.1007/978-3-319-92402-1_6
V. Geffert, Z. Bednárová
{"title":"Minimal Useful Size of Counters for (Real-Time) Multicounter Automata","authors":"V. Geffert, Z. Bednárová","doi":"10.1007/978-3-319-92402-1_6","DOIUrl":"https://doi.org/10.1007/978-3-319-92402-1_6","url":null,"abstract":"","PeriodicalId":340847,"journal":{"name":"Machines, Computations, and Universality","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130142381","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 : 2018-06-28DOI: 10.1007/978-3-319-92402-1_5
H. Fernau, Lakshmanan Kuppusamy, R. O. Oladele, Indhumathi Raman
{"title":"Minimizing Rules and Nonterminals in Semi-conditional Grammars: Non-trivial for the Simple Case","authors":"H. Fernau, Lakshmanan Kuppusamy, R. O. Oladele, Indhumathi Raman","doi":"10.1007/978-3-319-92402-1_5","DOIUrl":"https://doi.org/10.1007/978-3-319-92402-1_5","url":null,"abstract":"","PeriodicalId":340847,"journal":{"name":"Machines, Computations, and Universality","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130996644","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 : 2018-06-28DOI: 10.1007/978-3-319-92402-1_3
A. Alhazov, R. Freund, Sergiu Ivanov
{"title":"Sequential Grammars with Activation and Blocking of Rules","authors":"A. Alhazov, R. Freund, Sergiu Ivanov","doi":"10.1007/978-3-319-92402-1_3","DOIUrl":"https://doi.org/10.1007/978-3-319-92402-1_3","url":null,"abstract":"","PeriodicalId":340847,"journal":{"name":"Machines, Computations, and Universality","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127009704","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 : 2018-06-28DOI: 10.1007/978-3-319-92402-1_2
M. Raynal, Jiannong Cao
{"title":"A Pleasant Stroll Through the Land of Distributed Machines, Computation, and Universality","authors":"M. Raynal, Jiannong Cao","doi":"10.1007/978-3-319-92402-1_2","DOIUrl":"https://doi.org/10.1007/978-3-319-92402-1_2","url":null,"abstract":"","PeriodicalId":340847,"journal":{"name":"Machines, Computations, and Universality","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131809234","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 : 2018-06-28DOI: 10.1007/978-3-319-92402-1_8
B. Nagy, S. Vályi
{"title":"An Extension of Interval-Valued Computing Equivalent to Red-Green Turing Machines","authors":"B. Nagy, S. Vályi","doi":"10.1007/978-3-319-92402-1_8","DOIUrl":"https://doi.org/10.1007/978-3-319-92402-1_8","url":null,"abstract":"","PeriodicalId":340847,"journal":{"name":"Machines, Computations, and Universality","volume":"40 11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131317789","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 : 2018-02-09DOI: 10.1007/978-3-319-92402-1_4
C. Bonchis, Gabriel Istrate, Vlad Rochian
{"title":"The language (and series) of Hammersley-type processes","authors":"C. Bonchis, Gabriel Istrate, Vlad Rochian","doi":"10.1007/978-3-319-92402-1_4","DOIUrl":"https://doi.org/10.1007/978-3-319-92402-1_4","url":null,"abstract":"","PeriodicalId":340847,"journal":{"name":"Machines, Computations, and Universality","volume":"357 18","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132340148","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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