POMDPs are standard models for probabilistic planning problems, where an agent interacts with an uncertain environment. We study the problem of almost-sure reachability, where given a set of target states, the question is to decide whether there is a policy to ensure that the target set is reached with probability 1 (almost-surely). While in general the problem is EXPTIME-complete, in many practical cases policies with a small amount of memory suffice. Moreover, the existing solution to the problem is explicit, which first requires to construct explicitly an exponential reduction to a belief-support MDP. In this work, we first study the existence of observation-stationary strategies, which is NP-complete, and then small-memory strategies. We present a symbolic algorithm by an efficient encoding to SAT and using a SAT solver for the problem. We report experimental results demonstrating the scalability of our symbolic (SAT-based) approach.

A number of problems involve managing a set of optional clauses. For example, the soft clauses in a MAXSAT formula are optional—they can be falsified for a cost. Similarly, when computing a Minimum Correction Set for an unsatisfiable formula, all clauses are optional—some can be falsified in order to satisfy the remaining. In both of these cases the task is to find a subset of the optional clauses that achieves some criteria, and whose removal leaves a satisfiable formula. Relaxation search is a simple method of using a standard SAT solver to solve this task. Relaxation search is easy to implement, sometimes requiring only a simple modification of the variable selection heuristic in the SAT solver; it offers considerable flexibility and control over the order in which subsets of optional clauses are examined; and it automatically exploits clause learning to exchange information between the two phases of finding a suitable subset of optional clauses and checking if their removal yields satisfiability. We demonstrate how relaxation search can be used to solve MAXSAT and to compute Minimum Correction Sets. In both cases relaxation search is able to achieve state-of-the-art performance and solve some instances other solvers are not able to solve.

Successive elimination of candidates is often a route to making manipulation intractable to compute. We prove that eliminating candidates does not necessarily increase the computational complexity of manipulation. However, for many voting rules used in practice, the computational complexity increases. For example, it is already known that it is NP-hard to compute how a single voter can manipulate the result of single transferable voting (the elimination version of plurality voting). We show here that it is NP-hard to compute how a single voter can manipulate the result of the elimination version of veto voting, of the closely related Coombs’ rule, and of the elimination versions of a general class of scoring rules.

We prove that it is NP-hard for a coalition of two manipulators to compute how to manipulate the Borda voting rule. This resolves one of the last open problems in the computational complexity of manipulating common voting rules. Because of this NP-hardness, we treat computing a manipulation as an approximation problem where we try to minimize the number of manipulators. Based on ideas from bin packing and multiprocessor scheduling, we propose two new approximation methods to compute manipulations of the Borda rule. Experiments show that these methods significantly outperform the previous best known approximation method. We are able to find optimal manipulations in almost all the randomly generated elections tested. Our results suggest that, whilst computing a manipulation of the Borda rule by a coalition is NP-hard, computational complexity may provide only a weak barrier against manipulation in practice.

When model-checking reports that a property holds on a model, vacuity detection increases user confidence in this result by checking that the property is satisfied in the intended way. While vacuity detection is effective, it is a relatively expensive technique requiring many additional model-checking runs. We address the problem of efficient vacuity detection for Bounded Model Checking (BMC) of LTL properties, presenting three partial vacuity detection methods based on the efficient analysis of the resolution proof produced by a successful BMC run. In particular, we define a characteristic of resolution proofs - peripherality - and prove that if a variable is a source of vacuity, then there exists a resolution proof in which this variable is peripheral. Our vacuity detection tool, VaqTree, uses these methods to detect vacuous variables, decreasing the total number of model-checking runs required to detect all sources of vacuity.