Related papers: Undecidable Cases of Model Checking Probabilistic …
In a seminal paper from 1985, Sistla and Clarke showed that the model-checking problem for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If, in contrast, the set of…
We study the complexity of predicate logics based on team semantics. We show that the satisfiability problems of two-variable independence logic and inclusion logic are both NEXPTIME-complete. Furthermore, we show that the validity problem…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
In temporal logics, a central question is about the choice of modalities and their relative expressive power, in comparison to the complexity of decision problems such as satisfiability. In this tutorial, we will illustrate the study of…
Clock-dependent probabilistic timed automata extend classical timed automata with discrete probabilistic choice, where the probabilities are allowed to depend on the exact values of the clocks. Previous work has shown that the quantitative…
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…
We show that for several variations of partially observable Markov decision processes, polynomial-time algorithms for finding control policies are unlikely to or simply don't have guarantees of finding policies within a constant factor or a…
We consider the model checking problem for Gap-order Constraint Systems (GCS) w.r.t. the branching-time temporal logic CTL, and in particular its fragments EG and EF. GCS are nondeterministic infinitely branching processes described by…
The formal verification and controller synthesis for Markov decision processes that evolve over uncountable state spaces are computationally hard and thus generally rely on the use of approximations. In this work, we consider the…
In this paper, we introduce a restriction of Timed Automata (TA), called non-resetting test Timed Automata (nrtTA). An nrtTA does not allow to test and reset the same clock on the same transition. The model has the same expressive power of…
We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and…
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…
Given two labelled Markov decision processes (MDPs), the trace-refinement problem asks whether for all strategies of the first MDP there exists a strategy of the second MDP such that the induced labelled Markov chains are trace-equivalent.…
Metric temporal logic (MTL) and timed propositional temporal logic (TPTL) are quantitative extensions of linear temporal logic, which are prominent and widely used in the verification of real-timed systems. It was recently shown that the…
This article surveys some of the recent work in verification of temporal epistemic logic via symbolic model checking, focusing on OBDD-based and SAT-based approaches for epistemic logics built on discrete and real-time branching time…
The notion of a non-deterministic logical matrix (where connectives are interpreted as multi-functions) extends the traditional semantics for propositional logics based on logical matrices (where connectives are interpreted as functions).…
Partially observable Markov decision processes (POMDPs) form a prominent model for uncertainty in sequential decision making. We are interested in constructing algorithms with theoretical guarantees to determine whether the agent has a…
Sound and complete axiomatizations are provided for a number of different logics involving modalities for knowledge and time. These logics arise from different choices for various parameters. All the logics considered involve the discrete…
Labeled continuous-time Markov chains (CTMCs) describe processes subject to random timing and partial observability. In applications such as runtime monitoring, we must incorporate past observations. The timing of these observations matters…
Given a Markov decision process (MDP) $M$ and a formula $\Phi$, the strategy synthesis problem asks if there exists a strategy $\sigma$ s.t. the resulting Markov chain $M[\sigma]$ satisfies $\Phi$. This problem is known to be undecidable…