**7. Complexities of Model Checking**

In this section, we analyse the computational complexities of the model checking problems for these strategic logics. Firstly, we present the definition about the model checking problem. Secondly, we study the model-checking complexities for ADL∗, LDL-SL[1G], and LDL-SL. Then we apply expressivity results to infer other logics' modelchecking complexities. Due to space restriction, we omit the introduction about automaton theory; please refer to, e.g., [31].

Let |G| (resp. |*ϕ*|) denote the number of transitions in G (resp. the length of *ϕ*).

**Problem 1** ( Model-Checking Problem (MCP) for Strategic Logic))**.** *given a concurrent game structure CGS* G*, a sentence ϕ in strategic logic* L*, and a state w, decide whether* G, *w* |= *ϕ.*
