In 2007, Abdulla et al. introduced the elegant concept of decisive Markov chain. Intuitively, decisiveness allows one to lift the good properties of finite Markov chains to infinite Markov chains. For instance, the approximate quantitative reachability problem can be solved for decisive Markov chains (enjoying reasonable effectiveness assumptions) including probabilistic lossy channel systems a...

We consider qualitative and quantitative verification problems for infinitestate Markov chains. We call a Markov chain decisive w.r.t. a given set of target states F if it almost certainly eventually reaches either F or a state from which F can no longer be reached. While all finite Markov chains are trivially decisive (for every set F ), this also holds for many classes of infinite Markov chai...

We present a theory that rationalizes voters’ preference for decisive leaders. Common definitions of decisiveness reference the speed of decision making. Although greater speed can be good or bad, agency problems between voters and politicians create a natural preference among voters for leaders who have a greater aversion to delay or more self-knowledge than the voters, and hence who make deci...

A crucial day for the future of European research will be 26 November 2004. The European Council of Ministers (ECM), representing the 25 member states of the European Union (EU), will discuss whether and how the EU will support basic research in the years to come. Ultimately, the question of whether to establish a European Research Council (ERC) will have to be answered, and it is the hope of E...

Increasingly, biologists are constructing evolutionary trees on large numbers of overlapping sets of taxa, and then combining them into a ‘supertree’ that classifies all the taxa. In this paper, we ask how much coverage of the total set of taxa is required by these subsets in order to ensure that we have enough information to reconstruct the supertree uniquely. We describe two results — a combi...