Alternating-time temporal logic

Abstract

Temporal logic comes in two varieties: linear-time temporal logic assumes implicit universal quantification over d l paths that are generated by system moves; branchingtime temporal logic allows explicit existential and universal quantification over all paths. We introduce a third, more general variety of temporal logic: alternating-time temporal logic offers selective quantification over those paths that are possible outcomes of games, such as the game in which the system and the environment alternate moves. While linear-time and branching-time logics are natural specification languages for closed systems, alternating-time logics are natural specification languages for open systems. For example, by preceding the temporal operator ''eventudly'' with a selective path quantifier, we can specify that in the game between the system and the environment, the system has a strategy to reach a certain state. Also the problems of receptiveness, realizability, and controllability can be formulated as model-checking problems for alternatingtime formulas.Depending on whether we admit arbitrary nesting of selective path quantifiers and temporal operators, we obtain the two alternating-time temporal logics ATL and ATL*. We interpret the formulas of ATL and ATL* with respect to two models of composition for open systems, synchronous and asynchronous. For synchronous systems, the expressive power of ATL beyond CTL comes at no cost: the model-checking complexity of synchronous ATL is linear in the size of the system and the length of the formula. The symbolic model-checking algorithm for CTL extends with few modifications to synchronous ATL, and with some work, also to asynchronous ATL, whose modelchecking complexity is quadratic. This makes ATL an obvious candidate for the automatic verification of open systems. In the case of ATL*, the model-checking problem is closely related to the synthesis problem for linear-time formulas, and requires doubly exponential time for both synchronous and asynchronous systems.'

The Planning Spectrum - One, Two, Three, Infinity

“…In ATL, the path quantifiers in CTL and CTL* are replaced by game quantifiers. Nevertheless, there is no obvious way to expressed formulas of the form α.ϕ, where α is a path quantifier and ϕ is an LTL formula in ATL * , which is the most expressive logic studied by Alur et al (2002). Our conjecture is that our logic and ATL * are of incomparable expressiveness.…”

“…In the field of temporal logics, the work on alternating temporal logic (ATL) (Alur, Henzinger, & Kupferman, 2002) is related to our work. In ATL, the path quantifiers in CTL and CTL* are replaced by game quantifiers.…”

Algorithms for Omega-Regular Games with Imperfect Information

“…For example, in the context of hybrid systems, the controller acquires information about the state of the plant using sensors with finite precision, which return imperfect information about the state. Similarly, if the players represent individual processes, then a process has only access to the public variables of the other processes, not to their private variables [19,2].…”

“…First, decision problems for imperfect-information games usually lie in higher complexity classes than their perfect-information counter-parts [19,14,2]. The algorithmic difference is often exponential, due to a subset construction that, similar to the determinization of finite automata, turns an imperfect-information game into an equivalent perfect-information game.…”

A Lattice Theory for Solving Games of Imperfect Information

“…states using a well-suited monotonic function like the controllable predecessor operator [AHK02,MPS95]. Those algorithms make a strong hypothesis: they consider that the controller that executes the switching strategy has a perfect information about the state of the controlled system.…”