Finite Linear Temporal Logic Research Articles

Reinforcement learning under temporal logic constraints as a sequence modeling problem

Reinforcement learning (RL) under temporal logic typically suffers from slow propagation for credit assignment. Inspired by recent advancements called trajectory transformer in machine learning, the reinforcement learning under Temporal Logic (TL) is modeled as a sequence modeling problem in this paper, where an agent utilizes the transformer to fit the optimal policy satisfying the Finite Linear Temporal Logic (LTLf) tasks. To combat the sparse reward issue, dense reward functions for LTLf are designed. For the sake of reducing the computational complexity, a sparse transformer with local and global attention is constructed to automatically conduct credit assignment, which removes the time-consuming value iteration process. The optimal action is found by the beam search performed in transformers. The proposed method generates a series of policies fitted by sparse transformers, which has sustainably high accuracy in fitting the demonstrations. At last, the effectiveness of the proposed method is demonstrated by simulations in Mini-Grid environments.

Hierarchical multi-robot strategies synthesis and optimization under individual and collaborative temporal logic specifications

This paper presents a hierarchical framework for multi-robot temporal logic task planning. We assume that each robot has its individual task specification and the robots have to jointly satisfy a global collaborative task specification, both described in finite linear temporal logic. To reduce the overall computational complexity, a central server firstly extracts and decomposes a collaborative task sequence from the automaton corresponding to the collaborative task specification, and allocates the subtasks in the sequence to robots. The robots then synthesize their initial execution strategies based on locally constructed product automatons, which integrate task requirements of the assigned collaborative tasks and their individual task specifications. Further, to reduce robots’ wait time in collaborations, we propose a distributed execution strategy adjusting mechanism to iteratively improve the time efficiency of robots. Finally, we prove the completeness of the proposed framework under assumptions, and analyze its time complexity and optimality. Extensive simulation results verify the scalability and optimization efficiency of the proposed method.

Finite LTL Synthesis as Planning

LTL synthesis is the task of generating a strategy that satisfies a Linear Temporal Logic (LTL) specification interpreted over infinite traces. In this paper we examine the problem of LTLf synthesis, a variant of LTL synthesis where the specification of the behaviour of the strategy we generate is interpreted over finite traces -- similar to the assumption we make in many planning problems, and important for the synthesis of business processes and other system interactions of finite duration. Existing approaches to LTLf synthesis transform LTLf into deterministic finite-state automata (DFA) and reduce the synthesis problem to a DFA game. Unfortunately, the DFA transformation is worst-case double-exponential in the size of the formula, presenting a computational bottleneck. In contrast, our approach exploits non-deterministic automata, and we reduce the synthesis problem to a non-deterministic planning problem. We leverage our approach not only for strategy generation but also to generate certificates of unrealizability -- the first such method for LTLf. We employ a battery of techniques that exploit the structure of the LTLf specification to improve the efficiency of our transformation to automata. We combine these techniques with lazy determinization of automata and on-the-fly state abstraction. We illustrate the effectiveness of our approach on a set of established LTL synthesis benchmarks adapted to finite LTL.

Applications of Finite Linear Temporal Logic to Piecewise Linear Aggregates

In this paper, we consider piecewise linear aggregates (PLA) and a possibility to use a linear temporal logic for analysis of their performance over finite structures (finite linear temporal logic (LTL)). We describe a calculus where the search is performed with respect to a context of the formula. An important aspect of finite LTL is the simplicity of its model of time and actions. PLA is used for description of numerous complex systems. The answers about the behavior of the aggregate are got by finding an interpretation in which all the formulas describing the work of the aggregate are true. This is illustrated by formalizing alternative bit protocol (ABP) task. We describe the ABP by putting it in the form of a planning problem. From the obtained model, we can find a finite sequence of actions to be executed in order to achieve the goal. In addition, an alternative bit protocol problem is described using the planning domain description language (PDDL). We report the results of experiments conducted using the LPG-TD planner.