TY - GEN

T1 - Memoryful branching-time logic

AU - Kupferman, Orna

AU - Vardi, Moshe Y.

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34547378491&partnerID=8YFLogxK

U2 - 10.1109/LICS.2006.34

DO - 10.1109/LICS.2006.34

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AN - SCOPUS:34547378491

SN - 0769526314

SN - 9780769526317

T3 - Proceedings - Symposium on Logic in Computer Science

SP - 265

EP - 274

BT - Proceedings - 21st Annual IEEE Symposium on Logic in Computer Science, LICS 2006

T2 - 21st Annual IEEE Symposium on Logic in Computer Science, LICS 2006

Y2 - 12 August 2006 through 15 August 2006

ER -