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This paper studies language-based opacity enforcement in a two-player, zero-sum game on a graph. In this game, player 1 (P1) wins if he can achieve a secret temporal goal described by the language of a finite automaton, no matter what strategy the opponent player 2 (P2) selects. In addition, P1 aims to win while making its goal opaque to a passive observer with imperfect information. However, P2 colludes with the observer to reveal P1's secret whenever P2 cannot prevent P1 from achieving its goal, and therefore, opacity must be enforced against P2. We show that a winning and opacity-enforcing strategy for P1 can be computed by reducing the problem to solving a reachability game augmented with the observer's belief states. Furthermore, if such a strategy does not exist, winning for P1 must entail the price of revealing his secret to the observer. We demonstrate our game-theoretic solution of opacity-enforcement control through a small illustrative example and in a robot motion planning problem. 

This paper studies temporal planning in probabilistic environments, modeled as labeled Markov decision processes (MDPs), with user preferences over multiple temporal goals. Existing works reflect such preferences as a prioritized list of goals. This paper introduces a new specification language, termed prioritized qualitative choice linear temporal logic on finite traces, which augments linear temporal logic on finite traces with prioritized conjunction and ordered disjunction from prioritized qualitative choice logic. This language allows for succinctly specifying temporal objectives with corresponding preferences accomplishing each temporal task. The finite traces that describe the system's behaviors are ranked based on their dissatisfaction scores with respect to the formula. We propose a systematic translation from the new language to a weighted deterministic finite automaton. Utilizing this computational model, we formulate and solve a problem of computing an optimal policy that minimizes the expected score of dissatisfaction given user preferences. We demonstrate the efficacy and applicability of the logic and the algorithm on several case studies with detailed analyses for each. 

In this paper, we study planning in stochastic systems, modeled as Markov decision processes (MDPs), with preferences over temporally extended goals. Prior work on temporal planning with preferences assumes that the user preferences form a total order, meaning that every pair of outcomes are comparable with each other. In this work, we consider the case where the preferences over possible outcomes are a partial order rather than a total order. We first introduce a variant of deterministic finite automaton, referred to as a preference DFA, for specifying the user's preferences over temporally extended goals. Based on the order theory, we translate the preference DFA to a preference relation over policies for probabilistic planning in a labeled MDP. In this treatment, a most preferred policy induces a weak-stochastic nondominated probability distribution over the finite paths in the MDP. The proposed planning algorithm hinges on the construction of a multi-objective MDP. We prove that a weak-stochastic nondominated policy given the preference specification is Pareto-optimal in the constructed multi-objective MDP, and vice versa. Throughout the paper, we employ a running example to demonstrate the proposed preference specification and solution approaches. We show the efficacy of our algorithm using the example with detailed analysis, and then discuss possible future directions. 

One important class of applications entails a robot scrutinizing, monitoring, or recording the evolution of an uncertain time-extended process. This sort of situation leads to an interesting family of active perception problems that can be cast as planning problems in which the robot is limited in what it sees and must, thus, choose what to pay attention to. The distinguishing characteristic of this setting is that the robot has influence over what it captures via its sensors, but exercises no causal authority over the process evolving in the world. As such, the robot’s objective is to observe the underlying process and to produce a “chronicle” of occurrent events, subject to a goal specification of the sorts of event sequences that may be of interest. This paper examines variants of such problems in which the robot aims to collect sets of observations to meet a rich specification of their sequential structure. We study this class of problems by modeling a stochastic process via a variant of a hidden Markov model and specify the event sequences of interest as a regular language, developing a vocabulary of “mutators” that enable sophisticated requirements to be expressed. Under different suppositions on the information gleaned about the event model, we formulate and solve different planning problems. The core underlying idea is the construction of a product between the event model and a specification automaton. Using this product, we compute a policy that minimizes the expected number of steps to reach a goal state. We introduce a general algorithm for this problem as well as several more efficient algorithms for important special cases. The paper reports and compares performance metrics by drawing on some small case studies analyzed in depth via simulation. Specifically, we study the effect of the robot’s observation model on the average time required for the robot to record a desired story. We also compare our algorithm with a baseline greedy algorithm, showing that our algorithm outperforms the greedy algorithm in terms of the average time to record a desired story. In addition, experiments show that the algorithms tailored to specialized variants of the problem are rather more efficient than the general algorithm.