Recognition of Topological Invariants by Modular Arrays
In this paper we study recognition of topological invariant properties of patterns by use of finite, rectangular 2-dimensional, interactive arrays of finite state automata (hereafter called modular arrays). The use of modular arrays as pattern recognition devices has been studied by Atrubin [1] and...
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| Language: | en_US |
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2004
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| Online Access: | http://hdl.handle.net/1721.1/6169 |
| _version_ | 1811075866791247872 |
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| author | Beyer, Terry |
| author_facet | Beyer, Terry |
| author_sort | Beyer, Terry |
| collection | MIT |
| description | In this paper we study recognition of topological invariant properties of patterns by use of finite, rectangular 2-dimensional, interactive arrays of finite state automata (hereafter called modular arrays). The use of modular arrays as pattern recognition devices has been studied by Atrubin [1] and by Unger [2]. Our aim is to show that modular arrays can not only recognize a large variety of topological invariants, but can do so in times that are almost minimal for a certain class of machines. We begin by describing our model of the modular array as a pattern recognition connectivity. Next, we introduce a fundamental transformation of patterns and prove several interesting properties of the transformation. Finally, we apply the transformation to modular arrays to obtain fast methods of recognizing a wide variety of topological invariants. |
| first_indexed | 2024-09-23T10:13:02Z |
| id | mit-1721.1/6169 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:13:02Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/61692019-04-12T07:44:03Z Recognition of Topological Invariants by Modular Arrays Beyer, Terry In this paper we study recognition of topological invariant properties of patterns by use of finite, rectangular 2-dimensional, interactive arrays of finite state automata (hereafter called modular arrays). The use of modular arrays as pattern recognition devices has been studied by Atrubin [1] and by Unger [2]. Our aim is to show that modular arrays can not only recognize a large variety of topological invariants, but can do so in times that are almost minimal for a certain class of machines. We begin by describing our model of the modular array as a pattern recognition connectivity. Next, we introduce a fundamental transformation of patterns and prove several interesting properties of the transformation. Finally, we apply the transformation to modular arrays to obtain fast methods of recognizing a wide variety of topological invariants. 2004-10-04T14:43:58Z 2004-10-04T14:43:58Z 1968-09-01 AIM-166 http://hdl.handle.net/1721.1/6169 en_US AIM-166 7489364 bytes 539367 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | Beyer, Terry Recognition of Topological Invariants by Modular Arrays |
| title | Recognition of Topological Invariants by Modular Arrays |
| title_full | Recognition of Topological Invariants by Modular Arrays |
| title_fullStr | Recognition of Topological Invariants by Modular Arrays |
| title_full_unstemmed | Recognition of Topological Invariants by Modular Arrays |
| title_short | Recognition of Topological Invariants by Modular Arrays |
| title_sort | recognition of topological invariants by modular arrays |
| url | http://hdl.handle.net/1721.1/6169 |
| work_keys_str_mv | AT beyerterry recognitionoftopologicalinvariantsbymodulararrays |