Memoryful branching-time logic

Orna Kupferman*, Moshe Y. Vardi

*Corresponding author for this work

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

35 Scopus citations


Traditional branching-time logics such as CTL* are memoryless: once a path in the computation tree is quantified at a given node, the computation that led to that node is forgotten. Recent work in planning suggests that CTL* cannot easily express temporal goals that refer to whole computations. Such goals require memoryful quantification of paths. With such a memoryful quantification, Eψ holds at a node s of a computation tree if there is a path π starting at the root of the tree and going through s such that . satisfies the linear-time formula ψ. We define the memoryful branching-time logic mCTL* and study its expressive power and algorithmic properties. We show that mCTL* is as expressive, but exponentially more succinct, than CTL*, and that the ability of mCTL* to refer to the present is essential for this equivalence. From the algorithmic point of view, while the satisfiability problem for mCTL* is 2EXPTIME-complete - not harder than that of CTL*, its model-checking problem is EXPSPACE-complete - exponentially harder than that of CTL*. The upper bounds are obtained by extending the automata-theoretic approach to handle memoryful quantification, and are much more efficient than these obtained by translating mCTL* to branching logics with past. The EXPSPACE lower bound for the model-checking problem applies already to formulas of restricted form (in particular, to AGEψ, which is useful for specifying possibility properties), and implies that reasoning about a memoryful branching-time logic is harder than reasoning about the linear-time logic of its path formulas.

Original languageAmerican English
Title of host publicationProceedings - 21st Annual IEEE Symposium on Logic in Computer Science, LICS 2006
Number of pages10
StatePublished - 2006
Event21st Annual IEEE Symposium on Logic in Computer Science, LICS 2006 - Seattle, WA, United States
Duration: 12 Aug 200615 Aug 2006

Publication series

NameProceedings - Symposium on Logic in Computer Science
ISSN (Print)1043-6871


Conference21st Annual IEEE Symposium on Logic in Computer Science, LICS 2006
Country/TerritoryUnited States
CitySeattle, WA


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