Languages of higher-dimensional automata

We introduce languages of higher-dimensional automata (HDAs) and develop some of their properties. To this end, we define a new category of precubical sets, uniquely naturally isomorphic to the standard one, and introduce a notion of event consistency. HDAs are then finite, labeled, event-consistent...

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Published inMathematical structures in computer science Vol. 31; no. 5; pp. 575 - 613
Main Authors Fahrenberg, Uli, Johansen, Christian, Struth, Georg, Ziemiański, Krzysztof
Format Journal Article
LanguageEnglish
Published Cambridge University Press (CUP) 01.05.2021
Subjects
Computer Science
Formal Languages and Automata Theory
concurrency theory
pomset
Higher-dimensional automaton
directed topology
Online AccessGet full text
ISSN0960-1295
1469-8072
1469-8072
DOI10.1017/S0960129521000293

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Abstract We introduce languages of higher-dimensional automata (HDAs) and develop some of their properties. To this end, we define a new category of precubical sets, uniquely naturally isomorphic to the standard one, and introduce a notion of event consistency. HDAs are then finite, labeled, event-consistent precubical sets with distinguished subsets of initial and accepting cells. Their languages are sets of interval orders closed under subsumption; as a major technical step, we expose a bijection between interval orders and a subclass of HDAs. We show that any finite subsumption-closed set of interval orders is the language of an HDA, that languages of HDAs are closed under binary unions and parallel composition, and that bisimilarity implies language equivalence.
AbstractList We introduce languages of higher-dimensional automata (HDAs) and develop some of their properties. To this end, we define a new category of precubical sets, uniquely naturally isomorphic to the standard one, and introduce a notion of event consistency. HDAs are then finite, labeled, event-consistent precubical sets with distinguished subsets of initial and accepting cells. Their languages are sets of interval orders closed under subsumption; as a major technical step, we expose a bijection between interval orders and a subclass of HDAs. We show that any finite subsumption-closed set of interval orders is the language of an HDA, that languages of HDAs are closed under binary unions and parallel composition, and that bisimilarity implies language equivalence.
Author Ziemiański, Krzysztof
Fahrenberg, Uli
Struth, Georg
Johansen, Christian
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Cites_doi 10.1145/5383.5384
10.1145/78969.78972
10.3233/FI-1981-4210
10.1017/S0960129503004031
10.1016/0020-0190(77)90021-7
10.1007/s10817-018-9472-6
10.1145/99583.99625
10.1109/LICS.1995.523257
10.1007/978-3-030-43520-2_6
10.1093/comjnl/28.5.449
10.1016/j.tcs.2009.06.014
10.1007/s00200-017-0316-0
10.1007/3-540-55767-9
10.1016/j.jlamp.2015.10.009
10.1016/j.apal.2018.08.002
10.1007/BF01379149
10.1007/3-540-45694-5_27
10.1007/978-3-319-15398-8
10.1007/978-3-540-31982-5_12
10.1007/BF01798961
10.2307/1969485
10.1017/S0960129500003169
10.1016/0012-365X(85)90042-1
10.1007/s002360000041
10.1007/BF01786227
10.1016/j.tcs.2006.02.012
10.1016/0304-3975(81)90112-2
10.1016/j.tcs.2006.06.024
10.1006/inco.1996.0057
10.1016/0304-3975(93)90238-O
10.1016/0022-2496(70)90062-3
10.1016/j.ic.2016.12.009
10.1016/j.aam.2005.02.003
10.1016/0304-3975(88)90124-7
10.1007/s41468-019-00040-z
10.1016/j.tcs.2006.03.022
10.1007/BFb0015256
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Issue 5
Keywords concurrency theory
pomset
Higher-dimensional automaton
directed topology
Language English
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References S0960129521000293_ref30
S0960129521000293_ref21
S0960129521000293_ref23
S0960129521000293_ref22
S0960129521000293_ref25
S0960129521000293_ref24
S0960129521000293_ref27
S0960129521000293_ref26
Lane (S0960129521000293_ref28) 1998
Winskel (S0960129521000293_ref50) 1995
S0960129521000293_ref41
S0960129521000293_ref40
S0960129521000293_ref39
Fahrenberg (S0960129521000293_ref10) 2021; 17
S0960129521000293_ref32
S0960129521000293_ref31
S0960129521000293_ref34
S0960129521000293_ref33
S0960129521000293_ref36
S0960129521000293_ref35
S0960129521000293_ref38
S0960129521000293_ref37
S0960129521000293_ref1
S0960129521000293_ref52
S0960129521000293_ref51
Ésik (S0960129521000293_ref5) 2004; 9
Grandis (S0960129521000293_ref19) 2009
S0960129521000293_ref6
S0960129521000293_ref43
S0960129521000293_ref7
S0960129521000293_ref42
S0960129521000293_ref8
S0960129521000293_ref45
S0960129521000293_ref44
S0960129521000293_ref9
S0960129521000293_ref2
S0960129521000293_ref47
S0960129521000293_ref3
S0960129521000293_ref46
S0960129521000293_ref4
S0960129521000293_ref49
S0960129521000293_ref48
Grandis (S0960129521000293_ref20) 1990; 11
Milner (S0960129521000293_ref29) 1989
S0960129521000293_ref18
S0960129521000293_ref17
S0960129521000293_ref12
S0960129521000293_ref11
S0960129521000293_ref14
S0960129521000293_ref13
S0960129521000293_ref16
S0960129521000293_ref15
References_xml – ident: S0960129521000293_ref2
– ident: S0960129521000293_ref26
  doi: 10.1145/5383.5384
– ident: S0960129521000293_ref31
– ident: S0960129521000293_ref21
  doi: 10.1145/78969.78972
– ident: S0960129521000293_ref6
– ident: S0960129521000293_ref40
– ident: S0960129521000293_ref18
  doi: 10.3233/FI-1981-4210
– ident: S0960129521000293_ref37
  doi: 10.1017/S0960129503004031
– ident: S0960129521000293_ref49
  doi: 10.1016/0020-0190(77)90021-7
– ident: S0960129521000293_ref4
  doi: 10.1007/s10817-018-9472-6
– ident: S0960129521000293_ref3
– ident: S0960129521000293_ref34
  doi: 10.1145/99583.99625
– ident: S0960129521000293_ref45
  doi: 10.1109/LICS.1995.523257
– ident: S0960129521000293_ref9
  doi: 10.1007/978-3-030-43520-2_6
– ident: S0960129521000293_ref39
  doi: 10.1093/comjnl/28.5.449
– ident: S0960129521000293_ref46
  doi: 10.1016/j.tcs.2009.06.014
– ident: S0960129521000293_ref51
  doi: 10.1007/s00200-017-0316-0
– volume: 9
  start-page: 3
  year: 2004
  ident: S0960129521000293_ref5
  article-title: Higher dimensional automata
  publication-title: Journal of Automata, Languages and Combinatorics
– ident: S0960129521000293_ref41
– ident: S0960129521000293_ref48
  doi: 10.1007/3-540-55767-9
– ident: S0960129521000293_ref24
  doi: 10.1016/j.jlamp.2015.10.009
– volume-title: Communication and Concurrency
  year: 1989
  ident: S0960129521000293_ref29
– volume-title: Categories for the Working Mathematician
  year: 1998
  ident: S0960129521000293_ref28
– ident: S0960129521000293_ref1
  doi: 10.1016/j.apal.2018.08.002
– volume: 17
  year: 2021
  ident: S0960129521000293_ref10
  article-title: Sculptures in concurrency
  publication-title: Logical Methods in Computer Science
– ident: S0960129521000293_ref33
  doi: 10.1007/BF01379149
– volume-title: Handbook of Logic in Computer Science
  year: 1995
  ident: S0960129521000293_ref50
– ident: S0960129521000293_ref14
  doi: 10.1007/3-540-45694-5_27
– ident: S0960129521000293_ref12
  doi: 10.1007/978-3-319-15398-8
– ident: S0960129521000293_ref8
  doi: 10.1007/978-3-540-31982-5_12
– ident: S0960129521000293_ref47
  doi: 10.1007/BF01798961
– ident: S0960129521000293_ref38
  doi: 10.2307/1969485
– ident: S0960129521000293_ref36
  doi: 10.1017/S0960129500003169
– ident: S0960129521000293_ref16
  doi: 10.1016/0012-365X(85)90042-1
– ident: S0960129521000293_ref7
– ident: S0960129521000293_ref44
  doi: 10.1007/s002360000041
– ident: S0960129521000293_ref27
  doi: 10.1007/BF01786227
– ident: S0960129521000293_ref32
– ident: S0960129521000293_ref42
  doi: 10.1016/j.tcs.2006.02.012
– ident: S0960129521000293_ref30
  doi: 10.1016/0304-3975(81)90112-2
– ident: S0960129521000293_ref43
  doi: 10.1016/j.tcs.2006.06.024
– ident: S0960129521000293_ref25
  doi: 10.1006/inco.1996.0057
– ident: S0960129521000293_ref22
  doi: 10.1016/0304-3975(93)90238-O
– ident: S0960129521000293_ref15
  doi: 10.1016/0022-2496(70)90062-3
– ident: S0960129521000293_ref23
  doi: 10.1016/j.ic.2016.12.009
– ident: S0960129521000293_ref11
  doi: 10.1016/j.aam.2005.02.003
– volume: 11
  start-page: 185
  year: 1990
  ident: S0960129521000293_ref20
  article-title: Cubical sets and their site
  publication-title: Theory and Applications of Categories
– ident: S0960129521000293_ref17
  doi: 10.1016/0304-3975(88)90124-7
– ident: S0960129521000293_ref52
  doi: 10.1007/s41468-019-00040-z
– ident: S0960129521000293_ref13
  doi: 10.1016/j.tcs.2006.03.022
– volume-title: New Mathematical Monographs
  year: 2009
  ident: S0960129521000293_ref19
– ident: S0960129521000293_ref35
  doi: 10.1007/BFb0015256
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Title Languages of higher-dimensional automata
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