Most parameterizedcomplexity classes are defined in terms of a parameterized version of the Boolean satisfiability problem(the so-called weighted satisfiability problem). For example, Downey and Fellow'sW-hierarc...
详细信息
Most parameterizedcomplexity classes are defined in terms of a parameterized version of the Boolean satisfiability problem(the so-called weighted satisfiability problem). For example, Downey and Fellow'sW-hierarchy is of this form. But there are also classes such as the A-hierarchy, that are more naturally characterised in terms of model-checking problems for certain fragments of first-order logic. Downey, Fellows, and Regan(1998) were the first to establish a connection between the two formalisms by giving a characterisation of the W-hierarchy in terms of first-order model-checking problems. We improve their result and then prove a similar correspondence between weighted satisfiability and model-checking problems for the A-hierarchy and the W*-hierarchy. Thus we obtain very uniform characterisations of many of the most important parameterizedcomplexity classes in both formalisms. Our results can be used to give new, simple proofs of some of the core results of structural parameterized complexity theory.
The existential k-pebble game characterizes the expressive power of the existential- positive k-variable fragment of first-order logic on finite structures. The winner of the existential k-pebble game on two given fin...
详细信息
The existential k-pebble game characterizes the expressive power of the existential- positive k-variable fragment of first-order logic on finite structures. The winner of the existential k-pebble game on two given finite structures can be determined in time O(n(2k)) by dynamic programming on the graph of game configurations. We show that there is no O(n((k-3)/12))-time algorithm that decides which player can win the existential k-pebble game on two given structures. This lower bound is unconditional and does not rely on any complexity-theoretic assumptions. Establishing strong k-consistency is a well-known heuristic for solving the constraint satisfaction problem (CSP). By the game characterization of Kolaitis and Vardi [14] our result implies that there is no O(n((k-3)/12))-time algorithm that decides if strong k-consistency can be established for a given CSP-instance.
暂无评论