Subgraphs Satisfying MSO Properties on z-Topologically Orderable Digraphs

@article{Oliveira2013SubgraphsSM,
  title={Subgraphs Satisfying MSO Properties on z-Topologically Orderable Digraphs},
  author={Mateus de Oliveira Oliveira},
  journal={ArXiv},
  year={2013},
  volume={abs/1303.4443}
}
We introduce the notion of z-topological orderings for digraphs. We prove that given a digraph G on n vertices admitting a z-topological order- ing, together with such an ordering, one may count the number of subgraphs of G that at the same time satisfy a monadic second order formula {\phi} and are the union of k directed paths, in time f ({\phi}, k, z) * n^O(k*z) . Our result implies the polynomial time solvability of many natural counting problems on digraphs admitting z-topological orderings… 
A Slice Theoretic Approach for Embedding Problems on Digraphs
TLDR
In this work, parameterized algorithms for embedding problems on digraphs in the setting in which the host digraph G has directed pathwidth w and the pattern digraph H can be covered by k paths are devised.
Width Parameterizations for Knot-free Vertex Deletion on Digraphs
TLDR
This paper investigates parameterization bydfv and shows that {\sc KFVD} can be solved in FPT-time parameterized by either $dfv+\kappa$ or $dfV+p$; and it admits a Turing kernel by the distance to a DAG having an Hamiltonian path.
An algorithmic metatheorem for directed treewidth
Parameterized and Exact Computation
TLDR
This paper gives a simple deterministic polynomial-time algorithm for finding a fixed point free element in a transitive permutation group, answering an open question of Cameron.
Reachability in Graph Transformation Systems and Slice Languages
TLDR
This work shows that for any set \(\mathcal {R}\) of graph transformation rules, one can determine in time whether a graph G of cutwidth c can be transformed into a graph H in depth at most d by the application ofGraph transformation rules from \(\mathCal {R}\).
Causality in Bounded Petri Nets is MSO Definable
TLDR
It is shown that a family of k-coverable DAGs is recognizable by a saturated slice automaton if and only if $$\mathfrak {G}$$ is definable in monadic second order logic.
Automated Verification, Synthesis and Correction of Concurrent Systems via MSO Logic
TLDR
Algorithmic solutions to five fundamental problems concerning the verification, synthesis and correction of concurrent systems that can be modeled by bounded p/t-nets are provided.
MSO Logic and the Partial Order Semantics of Place/Transition-Nets
TLDR
This work shows that given any MSO sentence, one can automatically construct a bounded Petri net whose behaviour minimally includes the set of partial orders specified by $$\varphi $$.
Combinatorial Slice Theory
Slices are digraphs that can be composed together to form larger digraphs.In this thesis we introduce the foundations of a theory whose aim is to provide ways of defining and manipulating infinite ...

References

SHOWING 1-10 OF 51 REFERENCES
Digraph Complexity Measures and Applications in Formal Language Theory
TLDR
The cycle rank problem is investigated, and it is shown that computing the cycle rank is NP-complete, even for sparse digraphs of maximum outdegree 2, and both a polynomial-time approximation and an exponential-time exact algorithm are provided for this problem.
Are There Any Good Digraph Width Measures?
TLDR
It is shown that any reasonable digraph measure cannot be substantially different from the treewidth of the underlying undirected graph, and it is argued that directed topological minors are the weakest useful notion of minors for digraphs.
Easy Problems for Tree-Decomposable Graphs
Canonizable Partial Order Generators
TLDR
It is shown that any slice graph can be transitive reduced into a Hasse diagram generator representing the same set of partial orders, allowing us to establish unknown connections between the true concurrent behavior of bounded p/t-nets and traditional approaches for representing infinite families ofpartial orders.
Finite Automata, Digraph Connectivity, and Regular Expression Size
TLDR
This work develops a different, more versatile lower bound technique that is based on the star height of regular languages, which is tied to cycle rank, a structural complexity measure for digraphs proposed by Eggan and Buchi, which measures the degree of connectivity of directed graphs.
On the Algorithmic Effectiveness of Digraph Decompositions and Complexity Measures
TLDR
The question of why this gap exists is answered by giving two hardness results: it is shown that Directed Hamiltonian Circuit is W[2]-hard when the parameter is the width of the input graph, for any of these widths, and that Max Di Cut remains NP-hard even when restricted to DAGs.
...
1
2
3
4
5
...