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  1. Linear Temporal Logic (LTL) synthesis aims at automatically synthesizing a program that complies with desired properties expressed in LTL. Unfortunately it has been proved to be too difficult computationally to perform full LTL synthesis. There have been two success stories with LTL synthesis, both having to do with the form of the specification. The first is the GR(1) approach: use safety conditions to determine the possible transitions in a game between the environment and the agent, plus one powerful notion of fairness, Generalized Reactivity(1), or GR(1). The second, inspired by AI planning, is focusing on finite-trace temporal synthesis, with LTLfmore »(LTL on finite traces) as the specification language. In this paper we take these two lines of work and bring them together. We first study the case in which we have an LTLf agent goal and a GR(1) assumption. We then add to the framework safety conditions for both the environment and the agent, obtaining a highly expressive yet still scalable form of LTL synthesis.« less
  2. Silva, A. ; Leino, K.R.M. (Ed.)
    In the Adapter-Design Pattern, a programmer implements a Target interface by constructing an Adapter that accesses an existing Adaptee code. In this work, we presented a reactive synthesis interpretation to the adapter design pattern, wherein an algorithm takes an Adaptee and a Target transducers, and the aim is to synthesize an Adapter transducer that, when composed with the Adaptee, generates a behavior that is equivalent to the behavior of the Target. One use of such an algorithm is to synthesize controllers that achieve similar goals on different hardware platforms. While this problem can be solved with existing synthesis algorithms, currentmore »state-of-the-art tools fail to scale. To cope with the computational complexity of the problem, we introduced a special form of specification format, called Separated GR(k), which can be solved with a scalable synthesis algorithm but still allows for a large set of realistic specifications. We solved the realizability and the synthesis problems for Separated GR(k), and showed how to exploit the separated nature of our specification to construct better algorithms, in terms of time complexity, than known algorithms for GR(k) synthesis. We then described a tool, called SGR(k), which we have implemented based on the above approach and showed, by experimental evaluation, how our tool outperforms current state-of-the-art tools on various benchmarks and test-cases.« less
  3. Robots have begun operating and collaborating with humans in industrial and social settings. This collaboration introduces challenges: the robot must plan while taking the human’s actions into account. In prior work, the problem was posed as a 2-player deterministic game, with a limited number of human moves. The limit on human moves is unintuitive, and in many settings determinism is undesirable. In this paper, we present a novel planning method for collaborative human-robot manipulation tasks via probabilistic synthesis. We introduce a probabilistic manipulation domain that captures the interaction by allowing for both robot and human actions with states that representmore »the configurations of the objects in the workspace. The task is specified using Linear Temporal Logic over finite traces (LTLf ). We then transform our manipulation domain into a Markov Decision Process (MDP) and synthesize an optimal policy to satisfy the specification on this MDP. We present two novel contributions: a formalization of probabilistic manipulation domains allowing us to apply existing techniques and a comparison of different encodings of these domains. Our framework is validated on a physical UR5 robot.« less
  4. This work proposes a novel method of incorporating calls to a motion planner inside a potential field control policy for safe multi-robot navigation with uncertain dynamics. The proposed framework can handle more general scenes than the control policy and has low computational costs. Our work is robust to uncertain dynamics and quickly finds high-quality paths in scenarios generated from real-world floor plans. In the proposed approach, we attempt to follow the control policy as much as possible, and use calls to the motion planner to escape local minima. Trajectories returned from the motion planner are followed using a path-following controllermore »guaranteeing robustness. We demonstrate the utility of our approach with experiments based on floor plans gathered from real buildings.« less
  5. Many systems are naturally modeled as Markov Decision Processes (MDPs), combining probabilities and strategic actions. Given a model of a system as an MDP and some logical specification of system behavior, the goal of synthesis is to find a policy that maximizes the probability of achieving this behavior. A popular choice for defining behaviors is Linear Temporal Logic (LTL). Policy synthesis on MDPs for properties specified in LTL has been well studied. LTL, however, is defined over infinite traces, while many properties of interest are inherently finite. Linear Temporal Logic over finite traces (LTLf ) has been used to expressmore »such properties, but no tools exist to solve policy synthesis for MDP behaviors given finite-trace properties. We present two algorithms for solving this synthesis problem: the first via reduction of LTLf to LTL and the second using native tools for LTLf . We compare the scalability of these two approaches for synthesis and show that the native approach offers better scalability compared to existing automaton generation tools for LTL.« less
  6. LTL synthesis is the problem of synthesizing a reactive system from a formal specification in Linear Temporal Logic. The extension of allowing for partial observability, where the system does not have direct access to all relevant information about the environment, allows generalizing this problem to a wider set of real-world applications, but the difficulty of implementing such an extension in practice means that it has remained in the realm of theory. Recently, it has been demonstrated that restricting LTL synthesis to systems with finite executions by using LTL with finite-horizon semantics (LTLf) allows for significantly simpler implementations in practice. Withmore »the conceptual simplicity of LTLf, it becomes possible to explore extensions such as partial observability in practice for the first time. Previous work has analyzed the problem of LTLf synthesis under partial observability theoretically and suggested two possible algorithms, one with 3EXPTIME and another with 2EXPTIME complexity. In this work, we first prove a complexity lower bound conjectured in earlier work. Then, we complement the theoretical analysis by showing how the two algorithms can be integrated in practice into an established framework for LTLf synthesis. We furthermore identify a third, MSO-based, approach enabled by this framework. Our experimental evaluation reveals very different results from what the theory seems to suggest, with the 3EXPTIME algorithm often outperforming the 2EXPTIME approach. Furthermore, as long as it is able to overcome an initial memory bottleneck, the MSO-based approach can often outperforms the others.« less
  7. LTLf synthesis is the automated construction of a reactive system from a high-level description, expressed in LTLf, of its finite-horizon behavior. So far, the conversion of LTLf formulas to deterministic finite-state automata (DFAs) has been identified as the primary bottleneck to the scalabity of synthesis. Recent investigations have also shown that the size of the DFA state space plays a critical role in synthesis as well.Therefore, effective resolution of the bottleneck for synthesis requires the conversion to be time and memory performant, and prevent state-space explosion. Current conversion approaches, however, which are based either on explicit-state representation or symbolic-state representation,more »fail to address these necessities adequately at scale: Explicit-state approaches generate minimal DFA but are slow due to expensive DFA minimization. Symbolic-state representations can be succinct, but due to the lack of DFA minimization they generate such large state spaces that even their symbolic representations cannot compensate for the blow-up.This work proposes a hybrid representation approach for the conversion. Our approach utilizes both explicit and symbolic representations of the state-space, and effectively leverages their complementary strengths. In doing so, we offer an LTLf to DFA conversion technique that addresses all three necessities, hence resolving the bottleneck. A comprehensive empirical evaluation on conversion and synthesis benchmarks supports the merits of our hybrid approach.« less
  8. Decomposition is a general principle in computational thinking, aiming at decomposing a problem instance into easier subproblems. Indeed, decomposing a transition system into a partitioned transition relation was critical to scaling BDD-based model checking to large state spaces. Since then, it has become a standard technique for dealing with related problems, such as Boolean synthesis. More recently, partitioning has begun to be explored in the synthesis of reactive systems. LTLf synthesis, a finite-horizon version of reactive synthesis with applications in areas such as robotics, seems like a promising candidate for partitioning techniques. After all, the state of the art ismore »based on a BDD-based symbolic algorithm similar to those from model checking, and partitioning could be a potential solution to the current bottleneck of this approach, which is the construction of the state space. In this work, however, we expose fundamental limitations of partitioning that hinder its effective application to symbolic LTLf synthesis. We not only provide evidence for this fact through an extensive experimental evaluation, but also perform an in depth analysis to identify the reason for these results. We trace the issue to an overall increase in the size of the explored state space, caused by an inability of partitioning to fully exploit state-space minimization, which has a crucial effect on performance. We conclude that more specialized decomposition techniques are needed for LTLf synthesis which take into account the effects of minimization.« less
  9. When humans and robots perform complex tasks together, the robot must have a strategy to choose its actions based on observed human behavior. One well-studied approach for finding such strategies is reactive synthesis. Existing approaches for finite-horizon tasks have used an explicit state approach, which incurs high runtime. In this work, we present a compositional approach to perform synthesis for finite-horizon tasks based on binary decision diagrams. We show that for pick-and-place tasks, the compositional approach achieves orders-of-magnitude speed-ups compared to previous approaches. We demonstrate the synthesized strategy on a UR5 robot.