A Decidable Temporal Logic of Repeating Values
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CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
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ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
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Theoretical Computer Science
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FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
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FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
On the complexity of branching-time logics
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Graded computation tree logic with binary coding
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Relentful strategic reasoning in alternating-time temporal logic
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
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Journal of Computer and System Sciences
Journal of Computer and System Sciences
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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Journal of the ACM (JACM)
ACM Transactions on Computational Logic (TOCL)
Information Processing Letters
Reasoning about Data Repetitions with Counter Systems
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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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 冒 starting at the root of the tree and going through s such that 冒 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.