LTLf Synthesis with Fairness and Stability Assumptions

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 LTL f 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 LTL f goals under infinite-trace assumptions, we could reduce the problem to LTL synthesis. Unfortunately, while synthesis in LTL f and in LTLhave the same worst-case complexity (both 2EXPTIME-complete), the algorithms available for LTLsyn-thesis are much more difficult in practice than those for LTL f synthesis. In this work we show that in interesting cases we can avoid such a detour to LTLsynthesis and keep the simplicity of LTL f 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 LTLsynthesis. Introduction In many situations we are interested in expressing properties over an unbounded but finite sequence of successive states. Linear-time Temporal Logic over finite traces ( LTL f) and its variants have been thoroughly investigated for doing so. There has been broad research for logical reasoning (De Gi-acomo and V ardi 2013; Li et al. 2019), synthesis (De Gi-acomo and V ardi 2015; Camacho et al. 2018), and planning (Camacho et al. 2017; De Giacomo and Rubin 2018). Recently synthesis under assumptions in LTL f has attracted specific interest (De Giacomo and Rubin 2018; Camacho, Bienvenu, and McIlraith 2018). First, planning for LTL f goals can be considered as a form of LTL f synthesis under assumptions, where the assumptions are the dynamics of the environment encoded in the planning domain (Green 1969; Camacho, Bienvenu, and McIlraith 2018; Aminof et al. 2018; Aminof et al. 2019). Synthesis under assumptions has been extensively studied in LTL, where environment assumptions are expressed as LTL formulas (Chatterjee and Henzinger 2007; Chatter-jee, Henzinger, and Jobstmann 2008; D'Ippolito et al. 2013; Bloem, Ehlers, and K onighofer 2015; Brenguier, Raskin, and Sankur 2017). In fact, LTL formulas can be used as assumptions as long as it is guaranteed that the environment is able to behave so as to keep the assumptions true, i.e., assumptions are environment realizable. Under these circumstances, it is possible to reduce synthesis for LTL goal ψ G under assumptions ψ A to standard synthesis for ψ A ψ G. Note that because of the guarantee of ψ A being environment realizable, no agent strategy can win ψ A ψ G by falsifying ψ A. See (Aminof et al. 2019) for a discussion.