The Cost of Exactness in Quantitative Reachability

  title={The Cost of Exactness in Quantitative Reachability},
  author={Krishnendu Chatterjee and Laurent Doyen and Thomas A. Henzinger},
  booktitle={Models, Algorithms, Logics and Tools},
In the analysis of reactive systems a quantitative objective assigns a real value to every trace of the system. The value decision problem for a quantitative objective requires a trace whose value is at least a given threshold, and the exact value decision problem requires a trace whose value is exactly the threshold. We compare the computational complexity of the value and exact value decision problems for classical quantitative objectives, such as sum, discounted sum, energy, and mean-payoff… 

Reachability Games with Relaxed Energy Constraints

It is proved that when considering weak upper bound, reachability objectives require memory, but can still be solved in polynomial-time for one-player arenas; it is also proved that they are in co-NP in the two-player setting.

Probabilistic causes in Markov chains

By combining two of the central paradigms of causality, namely counterfactual reasoning and probability-raising, a probabilistic notion of cause in Markov chains is introduced and can be used for monitoring purposes where the aim is to detect faulty behavior before it actually occurs.



On The Complexity of Counter Reachability Games

This work considers the problem of deciding the winner in counter reachability games and shows that, in most cases, it has the same complexity under all semantics.

Reachability Games on Extended Vector Addition Systems with States

Several decidable and even tractable subcases of this problem of deciding thewinner in two-player turn-based games with zero-reachability and zero-safety objectives obtained by restricting the number of counters and/or the sets of target configurations are identified.

To Reach or not to Reach? Efficient Algorithms for Total-Payoff Games

This work gives an efficient value iteration algorithm to compute the values and optimal strategies (when they exist), that runs in pseudo-polynomial time for quantitative games, and proposes heuristics allowing one to possibly speed up the computations in both cases.

Optimal cost almost-sure reachability in POMDPs

Infinite Runs in Weighted Timed Automata with Energy Constraints

This work considers automata equipped with positive and negative weights on transitions and locations, corresponding to the production and consumption of some resource, and asks the question whether there exists an infinite path for which the accumulated weight for any finite prefix satisfies certain constraints.

Reachability in Succinct One-Counter Games

It is shown that the winner-determination problem is EXPSPACE-complete regardless of whether transitions are guarded by constraints on the counter or if the counter is restricted to non-negative values.

Playing Stochastic Games Precisely

It is shown that precise value games are not determined, and the memory requirements for winning strategies are compared, and necessary and sufficient conditions for the existence of a winning strategy of the controller for a large class of functions are established.

Multi-objective Discounted Reward Verification in Graphs and MDPs

This work considers a generalised version of discounted reward objectives, in which the amount of discounting depends on the states visited and on the objective, which extends the usual definition of discounted rewards.

Reachability in Succinct and Parametric One-Counter Automata

One of the main results of this paper is to show that the reachability problem for parametric one-counter automata is in fact in NP, and is thus NP -complete.

Quantitative Languages Defined by Functional Automata

This paper investigates functional weighted automata for four different measures: the sum, the mean, the discounted sum of weights along edges and the ratio between rewards and costs, and shows that functionality is decidable for the four measures.