LTLf and LDLf Synthesis under Partial Observability

In this paper, we study synthesis under partial observability for logical specifications over finite traces expressed in LTLf/LDLf. This form of synthesis can be seen as a generalization of planning under partial observability in nondeterministic domains, which is known to be 2EXPTIME-complete. We start by showing that the usual "belief-state construction" used in planning under partial observability works also for general LTLf/LDLf synthesis, though with a jump in computational complexity from 2EXPTIME to 3EXPTIME. Then we show that the belief-state construction can be avoided in favor of a direct automata construction which exploits projection to hide unobservable propositions. This allow us to prove that the problem remains 2EXPTIME-complete. The new synthesis technique proposed is effective and readily implementable

Clock specifications for temporal tasks in planning and learning

Recently, Linear Temporal Logics on finite traces, such as LTL (or LDL ), have been advocated as high-level formalisms to express dynamic properties, such as goals in planning domains or rewards in Reinforcement Learning (RL). This paper addresses the challenge of separating high-level temporal specifications from the low-level details of the underlying environment (domain or MDP), by allowing for expressing the specifications at a different time granularity than the environment. We study the notion of a clock which progresses the high-level LTL specification, whose ticks are triggered by dynamic (low-level) properties defined on the underlying environment. The obtained separation enables terse high-level specifications while allowing for very expressive forms of clock expressed as general LTL properties over low-level features, such as counting or occurrence/alternation of special events. We devise an automata-based construction to compile away the clock into a deterministic automaton that is polynomial in the size of the automata characterizing the high-level and clock specifications. We show the correctness of the approach and discuss its application in several contexts, including FOND planning, RL with LTL Restraining Bolts, and Reward Machines

Service composition in stochastic settings

With the growth of the Internet-of-Things and online Web services, more services with more capabilities are available to us. The ability to generate new, more useful services from existing ones has been the focus of much research for over a decade. The goal is, given a specification of the behavior of the target service, to build a controller, known as an orchestrator, that uses existing services to satisfy the requirements of the target service. The model of services and requirements used in most work is that of a finite state machine. This implies that the specification can either be satisfied or not, with no middle ground. This is a major drawback, since often an exact solution cannot be obtained. In this paper we study a simple stochastic model for service composition: we annotate the tar- get service with probabilities describing the likelihood of requesting each action in a state, and rewards for being able to execute actions. We show how to solve the resulting problem by solving a certain Markov Decision Process (MDP) derived from the service and requirement specifications. The solution to this MDP induces an orchestrator that coincides with the exact solution if a composition exists. Otherwise it provides an approximate solution that maximizes the expected sum of values of user requests that can be serviced. The model studied although simple shades light on composition in stochastic settings and indeed we discuss several possible extensions

LTLf/LDLf Non-Markovian Rewards

In Markov Decision Processes (MDPs), the reward obtained in a state is Markovian, i.e., depends on the last state and action. This dependency makes it difficult to reward more interesting long-term behaviors, such as always closing a door after it has been opened, or providing coffee only following a request. Extending MDPs to handle non-Markovian reward functions was the subject of two previous lines of work. Both use LTL variants to specify the reward function and then compile the new model back into a Markovian model. Building on recent progress in temporal logics over finite traces, we adopt LDLf for specifying non-Markovian rewards and provide an elegant automata construction for building a Markovian model, which extends that of previous work and offers strong minimality and compositionality guarantees

Multi-Player Games with LDL Goals over Finite Traces

Linear Dynamic Logic on finite traces LDLf is a powerful logic for reasoning about the behaviour of concurrent and multi-agent systems. In this paper, we investigate techniques for both the characterisation and verification of equilibria in multi-player games with goals/objectives expressed using logics based on LDLf. This study builds upon a generalisation of Boolean games, a logic-based game model of multi-agent systems where players have goals succinctly represented in a logical way. Because LDLf goals are considered, in the settings we study -- Reactive Modules games and iterated Boolean games with goals over finite traces -- players' goals can be defined to be regular properties while achieved in a finite, but arbitrarily large, trace. In particular, using alternating automata, the paper investigates automata-theoretic approaches to the characterisation and verification of (pure strategy Nash) equilibria, shows that the set of Nash equilibria in multi-player games with LDLf objectives is regular, and provides complexity results for the associated automata constructions