Size-varying reversible causal graph dynamics
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866911013907988480 |
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| author | Arrighi, Pablo Durbec, Amélia Emmanuel, Aurélien |
| author_facet | Arrighi, Pablo Durbec, Amélia Emmanuel, Aurélien |
| contents | Consider a network that evolves according to a reversible, nearest neighbours dynamics. Is the dynamics allowed to vary the size of the network? On the one hand it seems that, being the principal carriers of information, nodes cannot be destroyed without jeopardising bijectivity. On the other hand, there are plenty of bijective functions from the set of graphs to the set of graphs that are non-vertex-preserving. The question has been settled negatively -- for three different reasons. Yet, in this paper we do obtain reversible local node creation/destruction -- in three relaxed settings, whose equivalence we prove for robustness. We motivate our work both by theoretical computer science considerations (reversible computing, cellular automata extensions) and theoretical physics concerns (basic formalisms towards discrete quantum gravity). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1805_10330 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Size-varying reversible causal graph dynamics Arrighi, Pablo Durbec, Amélia Emmanuel, Aurélien Discrete Mathematics Consider a network that evolves according to a reversible, nearest neighbours dynamics. Is the dynamics allowed to vary the size of the network? On the one hand it seems that, being the principal carriers of information, nodes cannot be destroyed without jeopardising bijectivity. On the other hand, there are plenty of bijective functions from the set of graphs to the set of graphs that are non-vertex-preserving. The question has been settled negatively -- for three different reasons. Yet, in this paper we do obtain reversible local node creation/destruction -- in three relaxed settings, whose equivalence we prove for robustness. We motivate our work both by theoretical computer science considerations (reversible computing, cellular automata extensions) and theoretical physics concerns (basic formalisms towards discrete quantum gravity). |
| title | Size-varying reversible causal graph dynamics |
| topic | Discrete Mathematics |
| url | https://arxiv.org/abs/1805.10330 |