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Our motivation for this work is the remarkable discovery that many large-scale real-world graphs ranging from Internet and World Wide Web to social and biological networks exhibit a power-law distribution: the number of nodes yi of a given degree i is proportional to i −β where β > 0 is a constant that depends on the application domain. There is practical… (More)

The model checking problem for open systems has been widely studied in the literature, for both finite–state (module checking) and infinite–state (pushdown module checking) systems, with respect to CTL and CTL *. In this paper, we further investigate this problem with respect to the µ-calculus enriched with nominals and graded modalities (hybrid graded… (More)

The use of the universal and existential quantifiers with the capability to express the concept of at least k or all but k, for a non-negative integer k, has been thoroughly studied in various kinds of logics. In classical logic there are counting quantifiers, in modal logics graded modalities, in description logics number restrictions. Recently, the… (More)

In this paper we study optimization problems with verifiable one-parameter selfish agents introduced by Auletta et al. [ICALP 2004]. Our goal is to allocate load among the agents, provided that the secret data of each agent is a single positive real number: the cost they incur per unit load. In such a setting the payment is given after the load completion,… (More)

The model checking problem for open systems (called module checking) has been intensively studied in the literature, both for finite–state and infinite–state systems. In this paper, we focus on push-down module checking with respect to decidable fragments of the fully enriched µ–calculus. We recall that finite–state module checking with respect to fully… (More)

The use of the universal and existential quantifiers with the capability to express the concept of at least k or all but k, for a non-negative integer k, has been thoroughly studied in various kinds of logics. In classical logic there are counting quantifiers, in modal logics graded modalities, in description logics number restrictions. Recently, the… (More)

Recently, complexity issues related to the decidability of the µ-calculus, when the universal and existential quantifiers are augmented with graded modalities, have been investigated by Kupfermann, Sattler and Vardi ([19]). Graded modalities refer to the use of the universal and exis-tential quantifiers with the added capability to express the concept of at… (More)

The problem of routing traffic through a congested network is studied. The framework is that introduced by Koutsoupias and Pa-padimitriou where the network is constituted by m parallel links, each having a finite capacity, and there are n selfish (noncooperative) agents wishing to route their traffic through one of these links: thus the problem sets… (More)