Affiliation:
1. Deptartment of Computing Science, Umeå University, 90836 Umeå, Sweden
Abstract
A regular unranked tree folding consists of a regular unranked tree language and a folding operation that merges (i.e., folds) selected nodes of a tree to form a graph; the combination is a formal device for representing graph languages. If, in the process of folding, the order among edges is discarded so that the result is an unordered graph, then two applications of a fold operation are enough to make the associated parsing problem NP-complete. However, if the order is kept, then the problem is solvable in non-uniform polynomial time. In this paper, we address the remaining case, where only one fold operation is applied, but the order among the edges is discarded. We show that, under these conditions, the problem is solvable in non-uniform polynomial time.
Funder
Swedish Research Council
Knut and Alice Wallenberg Foundation
Reference27 articles.
1. Tang, L., and Liu, H. (2010). Graph mining applications to social network analysis. Managing and Mining Graph Data, Springer.
2. Plump, D. (2009). The graph programming language GP. Algebraic Informatics, Proceedings of the 3rd International Conference on Algebraic Informatics, CAI 2009, Thessaloniki, Greece, 19–22 May 2009, Springer.
3. You, J., Leskovec, J., He, K., and Xie, S. (2020, January 13–18). Graph structure of neural networks. Proceedings of the International Conference on Machine Learning, PMLR, Virtual.
4. Björklund, H., Björklund, J., and Ericson, P. (2017). On the regularity and learnability of ordered DAG languages. Implementation and Application of Automata, Proceedings of the 22nd International Conference, CIAA 2017, Marne-la-Vallée, France, 27–30 June 2017, Springer.
5. The complexity of graph languages generated by hyperedge replacement;Lautemann;Acta Inform.,1990