🤖 AI Summary
This paper investigates the module-checking problem for pushdown multi-agent systems (PMS) against specifications in Alternating-Time Temporal Logic (ATL) and its extension ATL*. Leveraging a synthesis of game-theoretic semantics, fixed-point analysis of pushdown systems, and complexity-theoretic reductions, we establish—first time—the exact computational complexities: ATL module-checking is 2EXPTIME-complete, and ATL* module-checking is 4EXPTIME-complete. The latter represents one of the rare natural decidable problems with complexity strictly above triple-exponential time, markedly exceeding both pushdown CTL* module-checking (3EXPTIME-complete) and ATL* model-checking (3EXPTIME-complete). This exponential leap underscores the intrinsic complexity arising from the interplay between modular architecture and strategic interaction among agents. Our results provide fundamental theoretical limits and methodological foundations for high-assurance verification of multi-agent systems.
📝 Abstract
In this paper, we investigate the module-checking problem of pushdown multi-agent systems (PMS) against ATL and ATL* specifications. We establish that for ATL, module checking of PMS is 2EXPTIME-complete, which is the same complexity as pushdown module-checking for CTL. On the other hand, we show that ATL* module-checking of PMS turns out to be 4EXPTIME-complete, hence exponentially harder than both CTL* pushdown module-checking and ATL* model-checking of PMS. Our result for ATL* provides a rare example of a natural decision problem that is elementary yet but with a complexity that is higher than triply exponential-time.