Diamond Subgraphs in the Reduction Graph of a One-Rule String Rewriting System
| Autor: | Adinayev, Arthur, Stein, Itamar |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we study a certain case of a subgraph isomorphism problem. We consider the Hasse diagram of the lattice $M_{k}$ (the unique lattice with $k+2$ elements and one anti-chain of length $k$) and want to find the maximal $k$ for which it is isomorphic to a subgraph of the reduction graph of a given one-rule string rewriting system. We obtain a complete characterization for this problem and show that there is a dichotomy. There are one-rule string rewriting systems for which the maximal such $k$ is $2$ and there are cases where there is no maximum. No other intermediate option is possible. Comment: 14 pages |
| Databáze: | arXiv |
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