Strictifying and taming directed paths in Higher Dimensional Automata
| Autor: | Martin Raussen |
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| Rok vydání: | 2020 |
| Předmět: |
Higher Dimensional Automata [Keywords]
Theoretical computer science nerve lemma serial Computer science tame Algebraic topology Space (mathematics) 68Q85 55P10 55U10 Computer Science Applications Automaton Computational topology Mathematics (miscellaneous) parallel Lemma (logic) homotopy equivalence FOS: Mathematics State space Algebraic Topology (math.AT) Mathematics - Algebraic Topology Algebra over a field d-path Computer Science::Operating Systems strict |
| Zdroj: | Raussen, M 2021, ' Strictifying and taming directed paths in Higher Dimensional Automata ', Mathematical Structures in Computer Science, vol. 31, no. 2, pp. 193-213 . https://doi.org/10.1017/S0960129521000128 |
| DOI: | 10.48550/arxiv.2006.05797 |
| Popis: | Directed paths have been used by several authors to describe concurrent executions of a program. Spaces of directed paths in an appropriate state space contain executions with all possible legal schedulings. It is interesting to investigate whether one obtains different topological properties of such a space of executions if one restricts attention to schedulings with "nice" properties, eg involving synchronizations. This note shows that this is not the case, ie that one may operate with nice schedulings without inflicting any harm. Several of the results in this note had previously been obtained by Ziemianski. We attempt to make them accessible for a wider audience by giving an easier proof for these findings by an application of quite elementary results from algebraic topology; notably the nerve lemma. Comment: 21 pages, 9 figures |
| Databáze: | OpenAIRE |
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