arXiv subjects

Giuseppe De Giacomo

Publications and source records attributed to Giuseppe De Giacomo.

At least 19 recordsLinked to original sources

arXiv2026

Semantically Labelled Automata for Multi-Task Reinforcement Learning with LTL Instructions

We study multi-task reinforcement learning (RL), a setting in which an agent learns a single, universal policy capable of generalising to arbitrary, possibly unseen tasks. We consider tasks specified as linear temporal logic (LTL) formulae, which are commonly used in formal methods to specify properties of systems, and have recently been successfully adopted in RL. In this setting, we present a novel task embedding technique leveraging a new generation of semantic LTL-to-automata translations, originally developed for temporal synthesis. The resulting semantically labelled automata contain rich, structured information in each state that allow us to (i) compute the automaton efficiently on-the-fly, (ii) extract expressive task embeddings used to condition the policy, and (iii) naturally support full LTL. Experimental results in a variety of domains demonstrate that our approach achieves state-of-the-art performance and is able to scale to complex specifications where existing methods fail.

cs.AI↗

arXiv2026

Infinite Trace Objectives with Finite Trace Techniques: Translating LTL to LTLf+

Linear Temporal Logic (LTL) is one of the most widely adopted languages for specifying temporal extended objectives in AI, with applications ranging from reactive synthesis to stochastic planning in Markov decision processes and reinforcement learning. Traditionally, solving any of these problems requires translating the LTL specification to a nondeterministic automata on infinite words and then determinizing it, a step that is notoriously difficult in theory and in practice. Recent work has introduced LTLf+, which lifts the finite-trace logic LTLf to infinite traces. LTLf+ has the same expressive power as LTL, yet it retains most of the crucial advantages of its base logic LTLf. Most reasoning in LTLf+ rests on finite automata on finite words, for which we have not only a canonical minimal representation but also an efficient determinization procedure. In this work we present the first translation from LTL to LTLf+. We first normalize an LTL formula into the syntactic reactivity fragment of the Manna-Pnueli hierarchy, to create the general fragment-based shape of LTLf+. We then present linear translations for each individual component of that fragment. As a consequence of this translation, the expanding body of techniques developed for LTLf+ now becomes available to many AI problems currently formulated in LTL. We further show that this comes at no asymptotic cost, as the pipeline from LTL to automaton via LTLf+ remains doubly exponential.

cs.AI↗

arXiv2026

Fast Obligation Translation and Synthesis

Syntactic obligations are a fragment of LTL formulas that translate to deterministic weak $ω$-automata (DWA). We show that syntactic obligations can be very efficiently converted to minimal DWA represented using multi-terminal binary decision diagrams (MTBDDs), and that synthesis of such specifications can be solved directly on the MTBDD representation on the fly. Our implementation in Spot shows substantial runtime improvements in translation and synthesis.

cs.FL↗

arXiv2026

Symbolic Synthesis for LTLf+ Obligations

We study synthesis for obligation properties expressed in LTLfp, the extension of LTLf to infinite traces. Obligation properties are positive Boolean combinations of safety and guarantee (co-safety) properties and form the second level of the temporal hierarchy of Manna and Pnueli. Although obligation properties are expressed over infinite traces, they retain most of the simplicity of LTLf. In particular, we show that they admit a translation into symbolically represented deterministic weak automata (DWA) obtained directly from the symbolic deterministic finite automata (DFA) for the underlying LTLf properties on trace prefixes. DWA inherit many of the attractive algorithmic features of DFA, including Boolean closure and polynomial-time minimization. Moreover, we show that synthesis for LTLfp obligation properties is theoretically highly efficient - solvable in linear time once the DWA is constructed. We investigate several symbolic algorithms for solving DWA games that arise in the synthesis of obligation properties and evaluate their effectiveness experimentally. Overall, the results indicate that synthesis for LTLfp obligation properties can be performed with virtually the same effectiveness as LTLf synthesis.

cs.LO↗

arXiv2026

Formal Foundations of Agentic Business Process Management

Just like traditional BPM systems, agentic BPM systems are built around a specification of the process under consideration. Their distinguishing feature, however, is that the execution of the process is driven by multiple autonomous decision-makers, referred to as agents. Since such agents cannot be fully controlled, the process specification is augmented with explicit objectives, or goals, assigned to the participating agents. Agents then pursue these goals, at least to the best of their efforts, under suitable assumptions on the behavior of others, by adopting appropriate strategies. Centrally, the organization enacting the process can use these specifications to provide guardrails on the decision-making capabilities of agents at the strategy level. This paper sets up the mathematical foundations of such systems in three key settings and analyzes four foundational problems of agentic BPM.

cs.AI↗

arXiv2026

Agentic Business Process Management: A Research Manifesto

This paper presents a manifesto that articulates the conceptual foundations of Agentic Business Process Management (APM), an extension of Business Process Management (BPM) for governing autonomous agents executing processes in organizations. From a management perspective, APM represents a paradigm shift from the traditional process view of the business process, driven by the realization of process awareness and an agent-oriented abstraction, where software and human agents act as primary functional entities that perceive, reason, and act within explicit process frames. This perspective marks a shift from traditional, automation-oriented BPM toward systems in which autonomy is constrained, aligned, and made operational through process awareness. We introduce the core abstractions and architectural elements required to realize APM systems and elaborate on four key capabilities that such APM agents must support: framed autonomy, explainability, conversational actionability, and self-modification. These capabilities jointly ensure that agents' goals are aligned with organizational goals and that agents behave in a framed yet proactive manner in pursuing those goals. We discuss the extent to which the capabilities can be realized and identify research challenges whose resolution requires further advances in BPM, AI, and multi-agent systems. The manifesto thus serves as a roadmap for bridging these communities and for guiding the development of APM systems in practice.

cs.AI↗

arXiv2026

Incremental LTLf Synthesis

In this paper, we study incremental LTLf synthesis -- a form of reactive synthesis where the goals are given incrementally while in execution. In other words, the protagonist agent is already executing a strategy for a certain goal when it receives a new goal: at this point, the agent has to abandon the current strategy and synthesize a new strategy still fulfilling the original goal, which was given at the beginning, as well as the new goal, starting from the current instant. In this paper, we formally define the problem of incremental synthesis and study its solution. We propose a solution technique that efficiently performs incremental synthesis for multiple LTLf goals by leveraging auxiliary data structures constructed during automata-based synthesis. We also consider an alternative solution technique based on LTLf formula progression. We show that, in spite of the fact that formula progression can generate formulas that are exponentially larger than the original ones, their minimal automata remain bounded in size by that of the original formula. On the other hand, we show experimentally that, if implemented naively, i.e., by actually computing the automaton of the progressed LTLf formulas from scratch every time a new goal arrives, the solution based on formula progression is not competitive.

cs.AI↗

arXiv2026

Multi-Property Synthesis

We study LTLf synthesis with multiple properties, where satisfying all properties may be impossible. Instead of enumerating subsets of properties, we compute in one fixed-point computation the relation between product-game states and the goal sets that are realizable from them, and we synthesize strategies achieving maximal realizable sets. We develop a fully symbolic algorithm that introduces Boolean goal variables and exploits monotonicity to represent exponentially many goal combinations compactly. Our approach substantially outperforms enumeration-based baselines, with speedups of up to two orders of magnitude.

cs.AI↗

arXiv2025

Best-Effort Policies for Robust Markov Decision Processes

We study the common generalization of Markov decision processes (MDPs) with sets of transition probabilities, known as robust MDPs (RMDPs). A standard goal in RMDPs is to compute a policy that maximizes the expected return under an adversarial choice of the transition probabilities. If the uncertainty in the probabilities is independent between the states, known as s-rectangularity, such optimal robust policies can be computed efficiently using robust value iteration. However, there might still be multiple optimal robust policies, which, while equivalent with respect to the worst-case, reflect different expected returns under non-adversarial choices of the transition probabilities. Hence, we propose a refined policy selection criterion for RMDPs, drawing inspiration from the notions of dominance and best-effort in game theory. Instead of seeking a policy that only maximizes the worst-case expected return, we additionally require the policy to achieve a maximal expected return under different (i.e., not fully adversarial) transition probabilities. We call such a policy an optimal robust best-effort (ORBE) policy. We prove that ORBE policies always exist, characterize their structure, and present an algorithm to compute them with a manageable overhead compared to standard robust value iteration. ORBE policies offer a principled tie-breaker among optimal robust policies. Numerical experiments show the feasibility of our approach.

cs.AI↗

arXiv2025

Good-for-MDP State Reduction for Stochastic LTL Planning

We study stochastic planning problems in Markov Decision Processes (MDPs) with goals specified in Linear Temporal Logic (LTL). The state-of-the-art approach transforms LTL formulas into good-for-MDP (GFM) automata, which feature a restricted form of nondeterminism. These automata are then composed with the MDP, allowing the agent to resolve the nondeterminism during policy synthesis. A major factor affecting the scalability of this approach is the size of the generated automata. In this paper, we propose a novel GFM state-space reduction technique that significantly reduces the number of automata states. Our method employs a sophisticated chain of transformations, leveraging recent advances in good-for-games minimisation developed for adversarial settings. In addition to our theoretical contributions, we present empirical results demonstrating the practical effectiveness of our state-reduction technique. Furthermore, we introduce a direct construction method for formulas of the form $\mathsf{G}\mathsf{F}φ$, where $φ$ is a co-safety formula. This construction is provably single-exponential in the worst case, in contrast to the general doubly-exponential complexity. Our experiments confirm the scalability advantages of this specialised construction.

cs.FL↗

arXiv2025

Learning to Coordinate without Communication under Incomplete Information

Achieving seamless coordination in cooperative games is a crucial challenge in artificial intelligence, particularly when players operate under incomplete information. While communication helps, it is not always feasible. In this paper, we explore how effective coordination can be achieved without verbal communication, relying solely on observing each other's actions. Our method enables an agent to develop a strategy by interpreting its partner's action sequences as intent signals, constructing a finite-state transducer built from deterministic finite automata, one for each possible action the agent can take. Experiments show that these strategies significantly outperform uncoordinated ones and closely match the performance of coordinating via direct communication.

cs.AI↗

arXiv2025

Emerson-Lei and Manna-Pnueli Games for LTLf+ and PPLTL+ Synthesis

Recently, the Manna-Pnueli Hierarchy has been used to define the temporal logics LTLfp and PPLTLp, which allow to use finite-trace LTLf/PPLTL techniques in infinite-trace settings while achieving the expressiveness of full LTL. In this paper, we present the first actual solvers for reactive synthesis in these logics. These are based on games on graphs that leverage DFA-based techniques from LTLf/PPLTL to construct the game arena. We start with a symbolic solver based on Emerson-Lei games, which reduces lower-class properties (guarantee, safety) to higher ones (recurrence, persistence) before solving the game. We then introduce Manna-Pnueli games, which natively embed Manna-Pnueli objectives into the arena. These games are solved by composing solutions to a DAG of simpler Emerson-Lei games, resulting in a provably more efficient approach. We implemented the solvers and practically evaluated their performance on a range of representative formulas. The results show that Manna-Pnueli games often offer significant advantages, though not universally, indicating that combining both approaches could further enhance practical performance.

cs.LO↗

arXiv2025

Solving MDPs with LTLf+ and PPLTL+ Temporal Objectives

The temporal logics LTLf+ and PPLTL+ have recently been proposed to express objectives over infinite traces. These logics are appealing because they match the expressive power of LTL on infinite traces while enabling efficient DFA-based techniques, which have been crucial to the scalability of reactive synthesis and adversarial planning in LTLf and PPLTL over finite traces. In this paper, we demonstrate that these logics are also highly effective in the context of MDPs. Introducing a technique tailored for probabilistic systems, we leverage the benefits of efficient DFA-based methods and compositionality. This approach is simpler than its non-probabilistic counterparts in reactive synthesis and adversarial planning, as it accommodates a controlled form of nondeterminism (``good for MDPs") in the automata when transitioning from finite to infinite traces. Notably, by exploiting compositionality, our solution is both implementation-friendly and well-suited for straightforward symbolic implementations.

cs.FL↗

arXiv2025

LTLf Adaptive Synthesis for Multi-Tier Goals in Nondeterministic Domains

We study a variant of LTLf synthesis that synthesizes adaptive strategies for achieving a multi-tier goal, consisting of multiple increasingly challenging LTLf objectives in nondeterministic planning domains. Adaptive strategies are strategies that at any point of their execution (i) enforce the satisfaction of as many objectives as possible in the multi-tier goal, and (ii) exploit possible cooperation from the environment to satisfy as many as possible of the remaining ones. This happens dynamically: if the environment cooperates (ii) and an objective becomes enforceable (i), then our strategies will enforce it. We provide a game-theoretic technique to compute adaptive strategies that is sound and complete. Notably, our technique is polynomial, in fact quadratic, in the number of objectives. In other words, it handles multi-tier goals with only a minor overhead compared to standard LTLf synthesis.

cs.AI↗

arXiv2024

LTLf+ and PPLTL+: Extending LTLf and PPLTL to Infinite Traces

We introduce LTLf+ and PPLTL+, two logics to express properties of infinite traces, that are based on the linear-time temporal logics LTLf and PPLTL on finite traces. LTLf+/PPLTL+ use levels of Manna and Pnueli's LTL safety-progress hierarchy, and thus have the same expressive power as LTL. However, they also retain a crucial characteristic of the reactive synthesis problem for the base logics: the game arena for strategy extraction can be derived from deterministic finite automata (DFA). Consequently, these logics circumvent the notorious difficulties associated with determinizing infinite trace automata, typical of LTL reactive synthesis. We present DFA-based synthesis techniques for LTLf+/PPLTL+, and show that synthesis is 2EXPTIME-complete for LTLf+ (matching LTLf) and EXPTIME-complete for PPLTL+ (matching PPLTL). Notably, while PPLTL+ retains the full expressive power of LTL, reactive synthesis is EXPTIME-complete instead of 2EXPTIME-complete. The techniques are also adapted to optimally solve satisfiability, validity, and model-checking, to get EXPSPACE-complete for LTLf+ (extending a recent result for the guarantee level using LTLf), and PSPACE-complete for PPLTL+.

cs.LO↗

arXiv2024

Computational Grounding of Responsibility Attribution and Anticipation in LTLf

Responsibility is one of the key notions in machine ethics and in the area of autonomous systems. It is a multi-faceted notion involving counterfactual reasoning about actions and strategies. In this paper, we study different variants of responsibility in a strategic setting based on LTLf. We show a connection with notions in reactive synthesis, including synthesis of winning, dominant, and best-effort strategies. This connection provides the building blocks for a computational grounding of responsibility including complexity characterizations and sound, complete, and optimal algorithms for attributing and anticipating responsibility.

cs.AI↗

arXiv2024

Abstracting Situation Calculus Action Theories

We develop a general framework for agent abstraction based on the situation calculus and the ConGolog agent programming language. We assume that we have a high-level specification and a low-level specification of the agent, both represented as basic action theories. A refinement mapping specifies how each high-level action is implemented by a low-level ConGolog program and how each high-level fluent can be translated into a low-level formula. We define a notion of sound abstraction between such action theories in terms of the existence of a suitable bisimulation between their respective models. Sound abstractions have many useful properties that ensure that we can reason about the agent's actions (e.g., executability, projection, and planning) at the abstract level, and refine and concretely execute them at the low level. We also characterize the notion of complete abstraction where all actions (including exogenous ones) that the high level thinks can happen can in fact occur at the low level. To facilitate verifying that one has a sound/complete abstraction relative to a mapping, we provide a set of necessary and sufficient conditions. Finally, we identify a set of basic action theory constraints that ensure that for any low-level action sequence, there is a unique high-level action sequence that it refines. This allows us to track/monitor what the low-level agent is doing and describe it in abstract terms (i.e., provide high-level explanations, for instance, to a client or manager).

cs.LO↗

arXiv2024

The Trembling-Hand Problem for LTLf Planning

Consider an agent acting to achieve its temporal goal, but with a "trembling hand". In this case, the agent may mistakenly instruct, with a certain (typically small) probability, actions that are not intended due to faults or imprecision in its action selection mechanism, thereby leading to possible goal failure. We study the trembling-hand problem in the context of reasoning about actions and planning for temporally extended goals expressed in Linear Temporal Logic on finite traces (LTLf), where we want to synthesize a strategy (aka plan) that maximizes the probability of satisfying the LTLf goal in spite of the trembling hand. We consider both deterministic and nondeterministic (adversarial) domains. We propose solution techniques for both cases by relying respectively on Markov Decision Processes and on Markov Decision Processes with Set-valued Transitions with LTLf objectives, where the set-valued probabilistic transitions capture both the nondeterminism from the environment and the possible action instruction errors from the agent. We formally show the correctness of our solution techniques and demonstrate their effectiveness experimentally through a proof-of-concept implementation.

cs.RO↗