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Author Alur, Rajeev ♦ Henzinger, Thomas A. ♦ Kupferman, Orna
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2002
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Alternation ♦ Games ♦ Model checking ♦ Temporaxl logic
Abstract Temporal logic comes in two varieties: linear-time temporal logic assumes implicit universal quantification over all paths that are generated by the execution of a system; 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. The problems of receptiveness, realizability, and controllability can be formulated as model-checking problems for alternating-time formulas. Depending on whether or not we admit arbitrary nesting of selective path quantifiers and temporal operators, we obtain the two alternating-time temporal logics ATL and ATL*.ATL and ATL* are interpreted over concurrent game structures. Every state transition of a concurrent game structure results from a choice of moves, one for each player. The players represent individual components and the environment of an open system. Concurrent game structures can capture various forms of synchronous composition for open systems, and if augmented with fairness constraints, also asynchronous composition. Over structures without fairness constraints, the model-checking complexity of ATL is linear in the size of the game structure and length of the formula, and the symbolic model-checking algorithm for CTL extends with few modifications to ATL. Over structures with weak-fairness constraints, ATL model checking requires the solution of 1-pair Rabin games, and can be done in polynomial time. Over structures with strong-fairness constraints, ATL model checking requires the solution of games with Boolean combinations of Büchi conditions, and can be done in PSPACE. 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.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2002-09-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 49
Issue Number 5
Page Count 42
Starting Page 672
Ending Page 713


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Source: ACM Digital Library