The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
Handbook of theoretical computer science (vol. B)
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Conditional nonlinear planning
Proceedings of the first international conference on Artificial intelligence planning systems
Using temporal logics to express search control knowledge for planning
Artificial Intelligence
An automata-theoretic approach to branching-time model checking
Journal of the ACM (JACM)
Alternating-time temporal logic
Journal of the ACM (JACM)
Planning for temporally extended goals
Annals of Mathematics and Artificial Intelligence
TALplanner: A temporal logic based forward chaining planner
Annals of Mathematics and Artificial Intelligence
Bounded Model Search in Linear Temporal Logic and Its Application to Planning
TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Automata-Theoretic Approach to Planning for Temporally Extended Goals
ECP '99 Proceedings of the 5th European Conference on Planning: Recent Advances in AI Planning
Strong Cyclic Planning Revisited
ECP '99 Proceedings of the 5th European Conference on Planning: Recent Advances in AI Planning
Planning with a language for extended goals
Eighteenth national conference on Artificial intelligence
On the Expressive Power of CTL
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
The Planning Spectrum - One, Two, Three, Infinity
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Weak, strong, and strong cyclic planning via symbolic model checking
Artificial Intelligence - special issue on planning with uncertainty and incomplete information
Deterministic generators and games for Ltl fragments
ACM Transactions on Computational Logic (TOCL)
Automated Planning: Theory & Practice
Automated Planning: Theory & Practice
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Memoryful Branching-Time Logic
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
The complexity of tree automata and logics of programs
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Distributed reactive systems are hard to synthesize
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Planning as model checking for extended goals in non-deterministic domains
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
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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Linear Temporal Logic (LTL) is widely used for defining conditions on the execution paths of dynamic systems. In the case of dynamic systems that allow for nondeterministic evolutions, one has to specify, along with an LTL formula ϕ, which are the paths that are required to satisfy the formula. Two extreme cases are the universal interpretation A.ϕ, which requires that the formula be satisfied for all execution paths, and the existential interpretation Ε.ϕ, which requires that the formula be satisfied for some execution path. When LTL is applied to the definition of goals in planning problems on nondeterministic domains, these two extreme cases are too restrictive. It is often impossible to develop plans that achieve the goal in all the nondeterministic evolutions of a system, and it is too weak to require that the goal is satisfied by some execution. In this paper we explore alternative interpretations of an LTL formula that are between these extreme cases. We define a new language that permits an arbitrary combination of the A and Ε quantifiers, thus allowing, for instance, to require that each finite execution can be extended to an execution satisfying an LTL formula (AΕ.ϕ), or that there is some finite execution whose extensions all satisfy an LTL formula (ΕA.ϕ). We show that only eight of these combinations of path quantifiers are relevant, corresponding to an alternation of the quantifiers of length one (A and Ε), two (AΕ and ΕA), three (AΕA and ΕAΕ), and infinity ((AΕ)ω and (ΕA)ω). We also present a planning algorithm for the new language that is based on an automata-theoretic approach, and study its complexity.