Many combinatorial problems are NP-complete for general graphs, but are not NP-complete for partial k-trees (graphs of treewidth bounded by a constant k) and can be efficiently solved in polynomial time or mostly in linear time for partial k-trees. On the other hand, very few problems are known to be NP-complete for partial k-trees with bounded k. These include the subgraph isomorphism problem ...

We convert, within polynomial-time and sequential processing, NP-Complete Problems into a problem of deciding feasibility of a given system S of linear equations with constants and coefficients of binary-variables that are 0, 1, or -1. S is feasible, if and only if, the NP-Complete problem has a feasible solution. We show separate polynomialtime conversions to S, from the SUBSET-SUM and 3-SAT p...

We are interested in implementing a fully automated software development process starting from sequence charts, which have proven their naturalness and usefulness in industry. We show in this paper that even for the simplest variants of sequence charts, there are strong impediments to the implementability of this dream. In the case of a manual development, we have to check the final implementat...

We study Coalitional Resource Games (CRGs), a variation of Qualitative Coalitional Games (QCGs) in which each agent is endowed with a set of resources, and the ability of a coalition to bring about a set of goals depends on whether they are collectively endowed with the necessary resources. We investigate and classify the computational complexity of a number of natural decision problems for CRG...

Qualitative coalitional games (QCGs) are a variation of conventional coalitional games in which each coalition may choose to cooperate in a number of different ways, with different choices resulting in potentially different sets of goals being achieved; each agent is associated with a set of goals, the intuition being that an agent is “satisfied” if any of its goals are achieved, but is indiffe...

We study the model checking problem, for fixed structures A, over positive equality-free first-order logic – a natural generalisation of the non-uniform quantified constraint satisfaction problem QCSP(A). We prove a complete complexity classification for this problem when A ranges over 1.) boolean structures and 2.) digraphs of size (less than or equal to) three. The former class displays dicho...

We consider a natural family of motion planning problems with movable obstacles and obtain hardness results for them. Some members of the family are shown to be PSPACE-complete thus improving and extending (and also simplifying) a previous NP-hardness result of Wilfong. The family considered includes a motion planning problem which forms the basis of a popular computer game called SOKOBAN. The ...

We propose to study concurrent games on a new extension of Vector Addition Systems with States, where inhibition conditions are added for modeling purposes. Games are a well-suited framework to solve control problems, and concurrent semantics reflect realistic situations where the environment can always produce a move before the controller, although it is never required to do so. This is in con...

We analyze the computational complexity of various twodimensional platform games. We identify common properties of these games that allow us to state several meta-theorems: general constructions that allow us to identify a class of these games for which the set of solvable levels is NP-hard, and another class for which the set is even PSPACE-hard. Notably CommanderKeen is shown to be NP-hard, a...