Low complexity and large interactions are possible in Strategy logic

Abstract

Strategy logic is an expressive multi-agent logic which extends ATL* (the multi-agent version of CTL*). It allows for powerful and interdependent branching (making it possible to express the existence of a dominant strategy, or a qualitative Nash equilibrium). However its model-checking is Non-Elementary. In their paper, Mogavero and al. conjectured that restricting the information strategies have of one another would bring the complexity back to 2-EXPTIME, the same as LTL or ATL* on games. This spurs a bunch of papers ranging over different semantics and fragments of Strategy Logic. As of this instant all papers supported the conjecture. However, so far a 2-EXPTIME model-checking is always obtained by restricting the interactions between the different goals (the interdependent branches in a formula); for example only using a single goal or a conjunction of goals. This severely limits the properties one can create, for example neither admissible strategies nor Nash equilibria can be expressed in these restrictions. In this paper, we prove that a 2-EXPTIME model-checking can be obtained for the fragment SL[BG] in the timeline semantic without restricting the interactions between the goals, greatly improving the expressiveness over other known fragments with 2-EXPTIME model-checking. This places SL[BG] in the timeline semantic as the largest extension of ATL* with similar complexity, yet capable of expressing global properties.