Transfer of succinct ATL and ATLS complexity results to concrete symbolic languages

Determine whether the equality of asymptotic model-checking complexities established for objective ATL and ATLS over the abstract Boolean succinct representation transfers to concrete symbolic input languages such as ISPL, and whether this transfer can inform an efficient extension of MCMAS to support ATLS.

Background

The paper establishes that objective ATL and ATLS have the same asymptotic model-checking complexity, namely PTIME with an NEXP oracle, when systems are given using the abstract Boolean succinct representation studied in the paper. This result contrasts with the differing complexities of ATL and ATLS under explicit representations.

The authors leave unresolved whether the coincidence observed for the abstract representation persists for concrete symbolic modeling languages, specifically ISPL, and whether understanding this issue could support an efficient implementation of ATLS in MCMAS, which currently supports ATL rather than ATLS. This is a concrete future-work question concerning the practical transfer of the paper’s complexity classification.