Module Checking for Uncertain Agents

Abstract

Abstract. Module checking is a decision problem proposed in late 1990s to formalize verification of open systems, i.e., systems that must adapt their behavior to the input they receive from the environment. It was recently shown that module checking offers a distinctly different perspective from the better-known problem of model checking. Module checking has been studied in several variants. Syntactically, specifications in temporal logic CTL and strategic logic ATL have been used. Semantically, the environment was assumed to have either perfect or imperfect information about the global state of the interaction. In this work, we rectify our approach to imperfect information module checking from the previous paper. Moreover, we study the variant of module checking where also the system acts under uncertainty. More precisely, we assume that the system consists of one or more agents whose decision making is constrained by their observational capabilities. We propose an automatabased verification procedure for the new problem, and establish its computational complexity.

On the Complexity of ATL and ATL* Module Checking

“…In this paper, we demonstrate that the claim made in [16] is not correct for ATL * . While ATL module checking has the same complexity as CTL module checking, ATL * module checking turns out to be exponentially harder than CTL * module checking, and precisely, 3EXPTIME-complete with a PTIMEcomplete complexity for a fixed-size formula 1 .…”

“…Because of that, active research on module checking subsided shortly after its conception. The belief has been recently refuted in [15]. There, it was proved that module checking includes two features inherently absent in the semantics of ATL/ATL * , namely irrevocability and nondeterminism of strategies.…”

“…This result has brought back the interests in module checking as an interesting formalism for the verification of open systems. In particular, in [15], several scenarios were discussed to show the usefulness of considering the features of both settings combined together. This has led to an extension of the module-checking framework to ATL/ATL * specifications [15,16].…”

“…In particular, in [15], several scenarios were discussed to show the usefulness of considering the features of both settings combined together. This has led to an extension of the module-checking framework to ATL/ATL * specifications [15,16]. Notably, it has been showed that ATL/ATL * module checking is strictly more expressive than both CTL/CTL * module checking and ATL/ATL * model checking [15,16].…”

“…This has led to an extension of the module-checking framework to ATL/ATL * specifications [15,16]. Notably, it has been showed that ATL/ATL * module checking is strictly more expressive than both CTL/CTL * module checking and ATL/ATL * model checking [15,16]. The computational complexity aspects have been shortly discussed in [16], where it is claimed that the complexity of ATL/ATL * module checking is not worse than that of CTL/CTL * module checking.…”