On the Complexity of ATL and ATL* Module Checking

Abstract

Module checking has been introduced in late 1990s to verify open systems, i.e., systems whose behavior depends on the continuous interaction with the environment. Classically, module checking has been investigated with respect to specifications given as CTL and CTL * formulas. Recently, it has been shown that CTL (resp., CTL * ) module checking offers a distinctly different perspective from the better-known problem of ATL (resp., ATL * ) model checking. In particular, ATL (resp., ATL * ) module checking strictly enhances the expressiveness of both CTL (resp., CTL * ) module checking and ATL (resp. ATL * ) model checking. In this paper, we provide asymptotically optimal bounds on the computational cost of module checking against ATL and ATL * , whose upper bounds are based on an automata-theoretic approach. We show that module-checking for ATL is EXPTIME-complete, which is the same complexity of module checking against CTL. On the other hand, ATL * module checking turns out to be 3EXPTIME-complete, hence exponentially harder than CTL * module checking.

Obstruction Logic: A Strategic Temporal Logic to Reason About Dynamic Game Models

“…Module checking [30,9,8] is another line of work which is related to our logic. Although there is a similarity between module checking and OL model checking for the 1-fragment on unary models, the two approaches are orthogonal.…”