Alternating-time temporal logic*

Rajeev Alur, Thomas A. Henzinger, Orna Kupferman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

69 Scopus citations


Temporal logic comes in two varieties: linear-time temporal logic assumes implicit universal quantification over all paths that are generated by system moves; branching-time 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 "eventually" 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 alternating-time 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* over alternating transition systems. While in ordinary transition systems, each transition corresponds to a possible step of the system, in alternating transition systems, each transition corresponds to a possible move in the game between the system and the environment. Fair alternating transition systems can capture both synchronous and asynchronous compositions of open systems. 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 model-checking 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.

Original languageAmerican English
Title of host publicationCompositionality
Subtitle of host publicationThe Significant Difference - International Symposium, COMPOS 1997, Revised Lectures
EditorsWillem-Paul de Roever, Langmaack Langmaack, Pnueli Pnueli
PublisherSpringer Verlag
Number of pages38
ISBN (Print)3540654933, 9783540654933
StatePublished - 1998
Externally publishedYes
EventInternational Symposium on Compositionality: The Significant Difference, COMPOS 1997 - Bad Malente, Germany
Duration: 8 Sep 199712 Sep 1997

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceInternational Symposium on Compositionality: The Significant Difference, COMPOS 1997
CityBad Malente

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1998.


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