Shufang Zhu

Shenghui Chen, Shufang Zhu, Giuseppe De Giacomo et al. · oxford

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.

Benjamin Aminof, Giuseppe De Giacomo, Antonio Di Stasio et al. · oxford

In this paper, we study LTLf synthesis under environment specifications for arbitrary reachability and safety properties. We consider both kinds of properties for both agent tasks and environment specifications, providing a complete landscape of synthesis algorithms. For each case, we devise a specific algorithm (optimal wrt complexity of the problem) and prove its correctness. The algorithms combine common building blocks in different ways. While some cases are already studied in literature others are studied here for the first time.

Shufang Zhu, Giuseppe De Giacomo · oxford

Most of the synthesis literature has focused on studying how to synthesize a strategy to fulfill a task. This task is a duty for the agent. In this paper, we argue that intelligent agents should also be equipped with rights, that is, tasks that the agent itself can choose to fulfill (e.g., the right of recharging the battery). The agent should be able to maintain these rights while acting for its duties. We study this issue in the context of LTLf synthesis: we give duties and rights in terms of LTLf specifications, and synthesize a suitable strategy to achieve the duties that can be modified on-the-fly to achieve also the rights, if the agent chooses to do so. We show that handling rights does not make synthesis substantially more difficult, although it requires a more sophisticated solution concept than standard LTLf synthesis. We also extend our results to the case in which further duties and rights are given to the agent while already executing.

Giuseppe De Giacomo, Gianmarco Parretti, Shufang Zhu · oxford

We study best-effort strategies (aka plans) in fully observable nondeterministic domains (FOND) for goals expressed in Linear Temporal Logic on Finite Traces (LTLf). The notion of best-effort strategy has been introduced to also deal with the scenario when no agent strategy exists that fulfills the goal against every possible nondeterministic environment reaction. Such strategies fulfill the goal if possible, and do their best to do so otherwise. We present a game-theoretic technique for synthesizing best-effort strategies that exploit the specificity of nondeterministic planning domains. We formally show its correctness and demonstrate its effectiveness experimentally, exhibiting a much greater scalability with respect to a direct best-effort synthesis approach based on re-expressing the planning domain as generic environment specifications.

Giuseppe De Giacomo, Dror Fried, Fabio Patrizi et al. · oxford

Devising a strategy to make a system mimicking behaviors from another system is a problem that naturally arises in many areas of Computer Science. In this work, we interpret this problem in the context of intelligent agents, from the perspective of LTLf, a formalism commonly used in AI for expressing finite-trace properties. Our model consists of two separated dynamic domains, D_A and D_B, and an LTLf specification that formalizes the notion of mimicking by mapping properties on behaviors (traces) of D_A into properties on behaviors of D_B. The goal is to synthesize a strategy that step-by-step maps every behavior of D_A into a behavior of D_B so that the specification is met. We consider several forms of mapping specifications, ranging from simple ones to full LTLf, and for each we study synthesis algorithms and computational properties.

Giuseppe De Giacomo, Gianmarco Parretti, Shufang Zhu · oxford

We consider an agent acting to fulfil tasks in a nondeterministic environment. When a strategy that fulfills the task regardless of how the environment acts does not exist, the agent should at least avoid adopting strategies that prevent from fulfilling its task. Best-effort synthesis captures this intuition. In this paper, we devise and compare various symbolic approaches for best-effort synthesis in Linear Temporal Logic on finite traces (LTLf). These approaches are based on the same basic components, however they change in how these components are combined, and this has a significant impact on the performance of the approaches as confirmed by our empirical evaluations.

Shengping Xiao, Yongkang Li, Shufang Zhu et al. · oxford

We present an on-the-fly synthesis framework for Linear Temporal Logic over finite traces (LTLf) based on top-down deterministic automata construction. Existing approaches rely on constructing a complete Deterministic Finite Automaton (DFA) corresponding to the LTLf specification, a process with doubly exponential complexity relative to the formula size in the worst case. In this case, the synthesis procedure cannot be conducted until the entire DFA is constructed. This inefficiency is the main bottleneck of existing approaches. To address this challenge, we first present a method for converting LTLf into Transition-based DFA (TDFA) by directly leveraging LTLf semantics, incorporating intermediate results as direct components of the final automaton to enable parallelized synthesis and automata construction. We then explore the relationship between LTLf synthesis and TDFA games and subsequently develop an algorithm for performing LTLf synthesis using on-the-fly TDFA game solving. This algorithm traverses the state space in a global forward manner combined with a local backward method, along with the detection of strongly connected components. Moreover, we introduce two optimization techniques -- model-guided synthesis and state entailment -- to enhance the practical efficiency of our approach. Experimental results demonstrate that our on-the-fly approach achieves the best performance on the tested benchmarks and effectively complements existing tools and approaches.

Alexandre Duret-Lutz, Giuseppe De Giacomo, Marcin Jurdzinski et al.

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.

Yujian Cao, Sven Schewe, Qiyi Tang et al.

Strategy synthesis typically follows an all-or-nothing paradigm, returning unrealisable whenever a specification cannot be guaranteed in an uncertain environment. In this paper, we introduce optimal LTLf synthesis, where the goal is to realise as many objectives as possible from a given specification consisting of multiple objectives, especially for the case that they are not all jointly realisable. We first consider max-guarantee synthesis, which commits to a maximal set of objectives that we can a priori guarantee to realise. We then introduce max-observation synthesis, which maximises a posteriori realised objectives that may be incomparable on different executions. Finally, we present incremental max-observation synthesis, which further improves strategies by exploiting opportunities for stronger guarantees when they arise during an execution. Experimental results show that different variations of optimal synthesis scale broadly equally well, solving a large fraction of the benchmark instances within the given timeout, demonstrating the practical feasibility of the approach.

Nadav Alon, Supratik Chakraborty, Alexandre Duret-Lutz et al.

LTLf synthesis under partial observability requires reasoning about unobservable environment variables, which is typically handled by constructing a belief-state DFA via subset construction that universally quantifies these variables. Existing approaches perform this construction as a separate step prior to game solving, often generating belief states that are unnecessary in practice. We propose an on-the-fly approach to LTLf synthesis under partial observability based on observable progression. Our method incrementally builds the belief-state DFA by progressing the specification with respect to observable variables only, universally quantifying unobservable variables on the fly. We prove the correctness of the construction and show that it naturally enables on-the-fly game solving, leading to a fully on-the-fly synthesis framework. Our implementation leverages DFAs represented using Multi-Terminal Binary Decision Diagrams: a compact representation that has proven highly effective for LTLf synthesis under full observability. Experimental results demonstrate that our approach significantly outperforms existing methods and further highlight the practical benefits of integrating on-the-fly game solving with belief-state construction.

Daniel Hausmann, Shufang Zhu, Gianmarco Parretti et al. · oxford

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.

Yongkang Li, Shengping Xiao, Shufang Zhu et al. · oxford

Reactive synthesis from Linear Temporal Logic over finite traces (LTLf) can be reduced to a two-player game over a Deterministic Finite Automaton (DFA) of the LTLf specification. The primary challenge here is DFA construction, which is 2EXPTIME-complete in the worst case. Existing techniques either construct the DFA compositionally before solving the game, leveraging automata minimization to mitigate state-space explosion, or build the DFA incrementally during game solving to avoid full DFA construction. However, neither is dominant. In this paper, we introduce a compositional on-the-fly synthesis framework that integrates the strengths of both approaches, focusing on large conjunctions of smaller LTLf formulas common in practice. This framework applies composition during game solving instead of automata (game arena) construction. While composing all intermediate results may be necessary in the worst case, pruning these results simplifies subsequent compositions and enables early detection of unrealizability. Specifically, the framework allows two composition variants: pruning before composition to take full advantage of minimization or pruning during composition to guide on-the-fly synthesis. Compared to state-of-the-art synthesis solvers, our framework is able to solve a notable number of instances that other solvers cannot handle. A detailed analysis shows that both composition variants have unique merits.

Giuseppe De Giacomo, Gianmarco Parretti, Shufang Zhu · oxford

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.

Shufang Zhu, Giuseppe De Giacomo, Geguang Pu et al.

In synthesis, assumptions are constraints on the environment that rule out certain environment behaviors. A key observation here is that even if we consider systems with LTLf goals on finite traces, environment assumptions need to be expressed over infinite traces, since accomplishing the agent goals may require an unbounded number of environment action. To solve synthesis with respect to finite-trace LTLf goals under infinite-trace assumptions, we could reduce the problem to LTL synthesis. Unfortunately, while synthesis in LTLf and in LTL have the same worst-case complexity (both 2EXPTIME-complete), the algorithms available for LTL synthesis are much more difficult in practice than those for LTLf synthesis. In this work we show that in interesting cases we can avoid such a detour to LTL synthesis and keep the simplicity of LTLf synthesis. Specifically, we develop a BDD-based fixpoint-based technique for handling basic forms of fairness and of stability assumptions. We show, empirically, that this technique performs much better than standard LTL synthesis.

Shufang Zhu, Lucas M. Tabajara, Jianwen Li et al.

LTLf synthesis is the process of finding a strategy that satisfies a linear temporal specification over finite traces. An existing solution to this problem relies on a reduction to a DFA game. In this paper, we propose a symbolic framework for LTLf synthesis based on this technique, by performing the computation over a representation of the DFA as a boolean formula rather than as an explicit graph. This approach enables strategy generation by utilizing the mechanism of boolean synthesis. We implement this symbolic synthesis method in a tool called Syft, and demonstrate by experiments on scalable benchmarks that the symbolic approach scales better than the explicit one.