Related papers: On Decidability of Time-bounded Reachability in CT…
We study the problem of formalizing and checking probabilistic hyperproperties for models that allow nondeterminism in actions. We extend the temporal logic \HyperPCTL, which has been previously introduced for discrete-time Markov chains,…
Autonomous systems often have logical constraints arising, for example, from safety, operational, or regulatory requirements. Such constraints can be expressed using temporal logic specifications. The system state is often partially…
The reachability analysis of recursive programs that communicate asynchronously over reliable FIFO channels calls for restrictions to ensure decidability. Our first result characterizes communication topologies with a decidable reachability…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…
Partially observable Markov decision processes (POMDPs) are a central model for uncertainty in sequential decision making. The most basic objective is the reachability objective, where a target set must be eventually visited, and the more…
In this paper we consider the problem of obtaining sharp bounds for the performance of temporal difference (TD) methods with linear function approximation for policy evaluation in discounted Markov decision processes. We show that a simple…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
The \emph{Entscheidungsproblem}, or the classical decision problem, asks whether a given formula of first-order logic is satisfiable. In this work, we consider an extension of this problem to regular first-order \emph{theories}, i.e.,…
We give a new proof of the decidability of reachability in alternating pushdown systems, showing that it is a simple consequence of a cut-elimination theorem for some natural-deduction style inference systems. Then, we show how this result…
The paper addresses the problem of computing maximal conditional expected accumulated rewards until reaching a target state (briefly called maximal conditional expectations) in finite-state Markov decision processes where the condition is…
The synthesis problem for partially observable Markov decision processes (POMDPs) is to compute a policy that satisfies a given specification. Such policies have to take the full execution history of a POMDP into account, rendering the…
We show the first unconditional pseudo-determinism result for all of search-BPP. Specifically, we show that every BPP search problem can be computed pseudo-deterministically on average for infinitely many input lengths. In other words, for…
Calculating optimal policies is known to be computationally difficult for Markov decision processes (MDPs) with Borel state and action spaces. This paper studies finite-state approximations of discrete time Markov decision processes with…
This paper studies Markov Decision Processes (MDPs) with atomless initial state distributions and atomless transition probabilities. Such MDPs are called atomless. The initial state distribution is considered to be fixed. We show that for…
Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been…
Assuming Schanuel's conjecture, we prove that any polynomial exponential equation in one variable must have a solution that is transcendental over a given finitely generated field. With the help of some recent results in Diophantine…
The probabilistic reachability problems of nondeterministic systems are studied. Based on the existing studies, the definition of probabilistic reachable sets is generalized by taking into account time-varying target set and obstacle. A…
We consider the problem of computing minimum and maximum probabilities of satisfying an $\omega$-regular property in a bounded-parameter Markov decision process (BMDP). BMDP arise from Markov decision processes (MDP) by allowing for…
We study the reachability problem for networks of timed communicating processes. Each process is a timed automaton communicating with other processes by exchanging messages over unbounded FIFO channels. Messages carry clocks which are…
In recent years, there has been increasing interest in explanation methods for neural model predictions that offer precise formal guarantees. These include abductive (respectively, contrastive) methods, which aim to compute minimal subsets…