Revision #3 Authors: Martin Lück, Arne Meier, Irina Schindler

Accepted on: 24th March 2015 16:15

Downloads: 1003

Keywords:

We present a complete classification of the parameterized complexity of all operator fragments of the satisfiability problem in computation tree logic CTL. The investigated parameterization is temporal depth and pathwidth. Our results show a dichotomy between W[1]-hard and fixed-parameter tractable fragments. The two real operator fragments which are in FPT are the fragments containing solely AF, or AX. Also we prove a generalization of Courcelle's theorem to infinite vocabularies which will be used to proof the FPT-membership cases.

Corrected the W[1]-hardness reductions.

Revision #2 Authors: Martin Lück, Arne Meier, Irina Schindler

Accepted on: 23rd November 2014 16:40

Downloads: 1402

Keywords:

We present an almost complete classification of the parameterized complexity of all operator fragments of the satisfiability problem in computation tree logic CTL. The investigated parameterization is the sum of temporal depth and structural pathwidth. The classification shows a dichotomy between W[1]-hard and fixed-parameter tractable fragments. The only real operator fragment which is confirmed to be in FPT is the fragment containing solely AX. Also we prove a generalization of Courcelle's theorem to infinite signatures which will be used to proof the FPT-membership case.

More detailed proofs, explanations, and visualizations added.

Revision #1 Authors: Martin Lück, Arne Meier, Irina Schindler

Accepted on: 24th October 2014 11:16

Downloads: 1011

Keywords:

We present an almost complete classification of the parameterized complexity of all operator fragments of the satisfiability problem in computation tree logic CTL. The investigated parameterization is temporal depth and pathwidth. The classification shows a dichotomy between W[1]-hard and fixed-parameter tractable fragments. The only real operator fragments which is in FPT is the fragment containing solely AX. Also we prove a generalization of Courcelle's theorem to infinite signatures which will be used to proof the FPT-membership cases.

TR14-134 Authors: Martin Lück, Arne Meier, Irina Schindler

Publication: 24th October 2014 11:00

Downloads: 1194

Keywords:

We present a complete classification of the parameterized complexity of all operator fragments of the satisfiability problem in computation tree logic CTL. The investigated parameterization is temporal depth and pathwidth. Our results show a dichotomy between W[1]-hard and fixed-parameter tractable fragments. The two real operator fragments which are in FPT are the fragments containing solely AF, or AX. Also we prove a generalization of Courcelle's theorem to infinite vocabularies which will be used to proof the FPT-membership cases.