Verifying agents with memory is harder than it seemed

Game-theoretic semantics for ATL+ with applications to model checking

“…However, the PSPACE upper bound result of [5] is easily confirmed by our algorithm, and we provide a new simple proof of that result. In addition to new methods, we use some ideas from [5].…”

“…As mentioned earlier, the PSPACE upper bound proof for the model checking of ATL + in [5] contains a flaw. Indeed, the claim of Theorem 4 in [5] is incorrect and a counterexample to it can be extracted from our Example 3.3, where M, q 0 |= ϕ for ϕ = {a 2 } (G p 1 ∨ F p 2 ).…”

“…The price for this is the reasonably higher computational complexity of model checking ATL + , viz. PSPACE-completeness [5]. Still, the PSPACE-completeness result alone gives a rather crude estimate of the amount of memory needed for model checking ATL + .…”

“…The approach via GTS enables us, inter alia, to perform a more precise analysis on the memory resources needed in evaluating ATL + -formulae than the algorithm from [5] which employs a mix of a path construction procedure for checking strategic formulae A Φ on one hand, and the standard labelling algorithm on the other hand. Our model checking algorithm for ATL + follows uniformly a procedure directly based on GTS and in fact enables us, inter alia, to identify and correct a flaw in the model checking procedure of [5] and some of the claims on which it is based (see Section 5). However, the PSPACE upper bound result of [5] is easily confirmed by our algorithm, and we provide a new simple proof of that result.…”

“…Our model checking algorithm for ATL + follows uniformly a procedure directly based on GTS and in fact enables us, inter alia, to identify and correct a flaw in the model checking procedure of [5] and some of the claims on which it is based (see Section 5). However, the PSPACE upper bound result of [5] is easily confirmed by our algorithm, and we provide a new simple proof of that result. In addition to new methods, we use some ideas from [5].…”