EXTENDING LEAN CELLULAR AUTOMATA FRAMEWORK – BOUNDARY CONDITIONS AND PROPERTIES OF CANONICAL FORMS
We present several extensions to our Lean–based formal mechanized framework for computing with cellular automata (CA). First we extend the definition of CAs to allow for specification of arbitrary boundary conditions. We use this addition to represent constant and periodic boundaries. We then form...
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| Format: | Article |
| Language: | English |
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Sciendo
2020-05-01
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| Series: | Acta Electrotechnica et Informatica |
| Subjects: | |
| Online Access: | http://www.aei.tuke.sk/papers/2020/1/5_Silvasi.pdf |
| _version_ | 1827838958257569792 |
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| author | Frantisek SILVASI Martin TOMASEK |
| author_facet | Frantisek SILVASI Martin TOMASEK |
| author_sort | Frantisek SILVASI |
| collection | DOAJ |
| description | We present several extensions to our Lean–based formal mechanized framework for computing with cellular automata (CA). First
we extend the definition of CAs to allow for specification of arbitrary boundary conditions. We use this addition to represent constant
and periodic boundaries. We then formulate and prove numerous missing properties pertaining to canonical forms of cellular automata,
culminating in a theorem stating that canonical forms preserve counts of nonempty cell states. |
| first_indexed | 2024-03-12T07:14:22Z |
| format | Article |
| id | doaj.art-934d125163b34b109f65ae91df13bff8 |
| institution | Directory Open Access Journal |
| issn | 1335-8243 1338-3957 |
| language | English |
| last_indexed | 2024-03-12T07:14:22Z |
| publishDate | 2020-05-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Acta Electrotechnica et Informatica |
| spelling | doaj.art-934d125163b34b109f65ae91df13bff82023-09-02T22:55:07ZengSciendoActa Electrotechnica et Informatica1335-82431338-39572020-05-01201323810.15546/aeei-2020-0005EXTENDING LEAN CELLULAR AUTOMATA FRAMEWORK – BOUNDARY CONDITIONS AND PROPERTIES OF CANONICAL FORMSFrantisek SILVASI0Martin TOMASEK1Department of Computers and Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Kosice, Letna 9, 042 00 Kosice, SlovakiaDepartment of Computers and Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Kosice, Letna 9, 042 00 Kosice, SlovakiaWe present several extensions to our Lean–based formal mechanized framework for computing with cellular automata (CA). First we extend the definition of CAs to allow for specification of arbitrary boundary conditions. We use this addition to represent constant and periodic boundaries. We then formulate and prove numerous missing properties pertaining to canonical forms of cellular automata, culminating in a theorem stating that canonical forms preserve counts of nonempty cell states.http://www.aei.tuke.sk/papers/2020/1/5_Silvasi.pdfcellular automataformalizationlean |
| spellingShingle | Frantisek SILVASI Martin TOMASEK EXTENDING LEAN CELLULAR AUTOMATA FRAMEWORK – BOUNDARY CONDITIONS AND PROPERTIES OF CANONICAL FORMS Acta Electrotechnica et Informatica cellular automata formalization lean |
| title | EXTENDING LEAN CELLULAR AUTOMATA FRAMEWORK – BOUNDARY CONDITIONS AND PROPERTIES OF CANONICAL FORMS |
| title_full | EXTENDING LEAN CELLULAR AUTOMATA FRAMEWORK – BOUNDARY CONDITIONS AND PROPERTIES OF CANONICAL FORMS |
| title_fullStr | EXTENDING LEAN CELLULAR AUTOMATA FRAMEWORK – BOUNDARY CONDITIONS AND PROPERTIES OF CANONICAL FORMS |
| title_full_unstemmed | EXTENDING LEAN CELLULAR AUTOMATA FRAMEWORK – BOUNDARY CONDITIONS AND PROPERTIES OF CANONICAL FORMS |
| title_short | EXTENDING LEAN CELLULAR AUTOMATA FRAMEWORK – BOUNDARY CONDITIONS AND PROPERTIES OF CANONICAL FORMS |
| title_sort | extending lean cellular automata framework boundary conditions and properties of canonical forms |
| topic | cellular automata formalization lean |
| url | http://www.aei.tuke.sk/papers/2020/1/5_Silvasi.pdf |
| work_keys_str_mv | AT frantiseksilvasi extendingleancellularautomataframeworkboundaryconditionsandpropertiesofcanonicalforms AT martintomasek extendingleancellularautomataframeworkboundaryconditionsandpropertiesofcanonicalforms |