Paper: Memoryful Branching-Time Logic (at LICS 2006)

Authors: Orna Kupferman Moshe Y. Vardi

Abstract

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, Eø holds at a node s of a computation tree if there is a path ð starting at the root of the tree and going through s such that ð satisfies the linear-time formula ø. 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 AGEø, 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.

BibTeX

  @InProceedings{KupfermanVardi-MemoryfulBranchingT,
    author = 	 {Orna Kupferman and Moshe Y. Vardi},
    title = 	 {Memoryful Branching-Time Logic},
    booktitle =  {Proceedings of the Twenty-First Annual IEEE Symposium on Logic in Computer Science (LICS 2006)},
    year =	 {2006},
    month =	 {August}, 
    pages =      {265--274},
    location =   {Seattle, Washington, USA}, 
    publisher =	 {IEEE Computer Society Press}
  }