Reachability in graph transformation systems and slice languages

0454008 - MÚ 2017 RIV CH eng C - Conference Paper (international conference)
de Oliveira Oliveira, Mateus
Reachability in graph transformation systems and slice languages.
Graph Transformation. Cham: Springer, 2015 - (Parisi-Presicce, F.; Westfechtel, B.), s. 121-137. Lecture Notes in Computer Science, 9151. ISBN 978-3-319-21144-2. ISSN 0302-9743.
[International Conference on Graph Transformation, ICGT 2015. L'Aquila (IT), 21.06.2015-23.06.2015]
EU Projects: European Commission(XE) 339691 - FEALORA
Institutional support: RVO:67985840
Keywords : graph transformation systems * reachability * slice languages
Subject RIV: BA - General Mathematics
http://link.springer.com/chapter/10.1007%2F978-3-319-21145-9_8

In this work we show that the reachability problem for graph transformation systems is in the complexity class XP when parameterized with respect to the depth of derivations and the cutwidth of the source graph. More precisely, we show that for any set R of graph transformation rules, one can determine in time f(c,d)G H g(c,d) whether a graph G of cutwidth c can be transformed into a graph H in depth at most d by the application of graph transformation rules from R . In particular, our algorithm runs in polynomial time when c and d are constants. On the other hand, we show that the problem becomes NP-hard if we allow c=O(G) and d=5 . In the case in which all transformation rules are monotone we get an algorithm running in time f(c,d)⋅G O(c) ⋅H . To prove our main theorems we will establish an interesting connection between graph transformation systems and regular slice languages.
Permanent Link: http://hdl.handle.net/11104/0254722