Related papers: Ranking and Repulsing Supermartingales for Reachab…
This paper shows how to harness existing theorem provers for first-order logic to automatically verify safety properties of imperative programs that perform dynamic storage allocation and destructive updating of pointer-valued structure…
We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented for different types of systems generating the data. First, an algorithm for computing…
Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…
Evaluating performance across optimization algorithms on many problems presents a complex challenge due to the diversity of numerical scales involved. Traditional data processing methods, such as hypothesis testing and Bayesian inference,…
Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for…
We apply the method of defensive forecasting, based on the use of game-theoretic supermartingales, to prediction with expert advice. In the traditional setting of a countable number of experts and a finite number of outcomes, the Defensive…
This paper over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing…
Computing the reachability probability in infinite state probabilistic models has been the topic of numerous works. Here we introduce a new property called \emph{divergence} that when satisfied allows to compute reachability probabilities…
A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…
Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and…
The classic model of computable randomness considers martingales that take real or rational values. Recent work by Bienvenu et al. (2012) and Teutsch (2014) shows that fundamental features of the classic model change when the martingales…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…
In the theory of algorithmic randomness, one of the central notions is that of computable randomness. An infinite binary sequence X is computably random if no recursive martingale (strategy) can win an infinite amount of money by betting on…
Probabilistic programming combines general computer programming, statistical inference, and formal semantics to help systems make decisions when facing uncertainty. Probabilistic programs are ubiquitous, including having a significant…
Simple stochastic games are turn-based 2.5-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a…
Computing tight over-approximation of reach sets of a controlled uncertain dynamical system is a common practice in verification of safety-critical cyber-physical systems (CPS). While several algorithms are available for this purpose, they…
Games on graphs provide a natural and powerful model for reactive systems. In this paper, we consider generalized reachability objectives, defined as conjunctions of reachability objectives. We first prove that deciding the winner in such…
This paper presents optimizations to improve the scalability of reachability analysis on a subclass of hybrid automata extended with stochasticity. The optimizations target different components of the analysis, such as quantifier…
Rankings are central to decision-making in fields ranging from education to online platforms, yet classical deterministic methods such as the Borda count method or Copeland-type pairwise methods ignore uncertainty due to sampling noise or…
Validating and controlling safety-critical systems in uncertain environments necessitates probabilistic reachable sets of future state evolutions. The existing methods of computing probabilistic reachable sets normally assume that…