Incremental LTLf Synthesis
arXiv:2603.01201v1 Announce Type: new Abstract: 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 exponent
arXiv:2603.01201v1 Announce Type: new Abstract: 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.
Executive Summary
The article 'Incremental LTLf Synthesis' introduces a novel approach to reactive synthesis, where goals are provided incrementally during execution. The authors propose two solution techniques: one leveraging auxiliary data structures from automata-based synthesis and another based on LTLf formula progression. The study demonstrates the efficiency of the first approach and the limitations of the second due to exponential formula growth. Experimental results show that naive implementation of the formula progression technique is not competitive, highlighting the need for optimized solutions in incremental synthesis.
Key Points
- ▸ Introduction of incremental LTLf synthesis as a form of reactive synthesis
- ▸ Proposal of two solution techniques: auxiliary data structure approach and LTLf formula progression
- ▸ Exponential growth of formulas in the progression technique and its implications
Merits
Efficient Synthesis
The proposed technique leveraging auxiliary data structures efficiently performs incremental synthesis for multiple LTLf goals.
Demerits
Exponential Formula Growth
The LTLf formula progression technique generates formulas that are exponentially larger than the original ones, leading to potential computational inefficiencies.
Expert Commentary
The article contributes significantly to the field of reactive synthesis by addressing the challenge of incremental goal updates. The proposed techniques, particularly the one leveraging auxiliary data structures, demonstrate potential for efficient synthesis. However, the exponential growth of formulas in the progression technique highlights the need for further optimization to make this approach viable. Future research should focus on developing more efficient algorithms and exploring applications in autonomous systems and real-time control, where dynamic goal updates are common.
Recommendations
- ✓ Further optimization of the LTLf formula progression technique to mitigate exponential formula growth
- ✓ Exploration of applications in autonomous systems and real-time control to demonstrate the practicality of incremental LTLf synthesis