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This paper presents a practical decision procedure for Propositional Projection Temporal Logic with infinite models. First, a set Prop l of labels l i , 0 ⩽ i ⩽ n ∈ N 0 , is used to mark nodes of an LNFG of a formula, and a node with l i is treated as an accepting state as in an automaton. Further, the generalized Büchi accepting condition for automata is employed to identify a path (resulting a word) in an LNFG as a model of the formula. In addition, the implementation details of the decision procedure and relevant algorithms including pre-processing, LNFG, circle finding algorithms are presented; as a matter of fact, all algorithms are implemented by C++ programs. [ABSTRACT FROM AUTHOR]

With the fast development of social network services, network marketing of products with externalities has been attracting more and more attention from both academia and business. The extensive study on network marketing mainly concerns with positive externalities. The focus of this paper is on the much less understood counterpart for negative externalities, where a consumer has lower incentive to buy a product as the product is possessed by more social network neighbors. For a seller who markets these products, it is desirable to have a good schedule which specifies an order of consumers he approaches. We design polynomial time algorithms that find marketing schedules for products with negative externalities. The goals are two-fold: maximizing the product sale and ensuring consumer regret-free decisions. We show that the maximization is NP-hard. Our algorithms achieve satisfactory performance guarantees, approximating the maximum within constant factors in most of the cases. Two of these algorithms provide regret-proof schedules, reaching an equilibrium state where no consumers regret their previous decisions. Our work is the first attempt to address these marketing problems from an algorithmic point of view. [ABSTRACT FROM AUTHOR]