11,776 research outputs found

    Immunity and Simplicity for Exact Counting and Other Counting Classes

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    Ko [RAIRO 24, 1990] and Bruschi [TCS 102, 1992] showed that in some relativized world, PSPACE (in fact, ParityP) contains a set that is immune to the polynomial hierarchy (PH). In this paper, we study and settle the question of (relativized) separations with immunity for PH and the counting classes PP, C_{=}P, and ParityP in all possible pairwise combinations. Our main result is that there is an oracle A relative to which C_{=}P contains a set that is immune to BPP^{ParityP}. In particular, this C_{=}P^A set is immune to PH^{A} and ParityP^{A}. Strengthening results of Tor\'{a}n [J.ACM 38, 1991] and Green [IPL 37, 1991], we also show that, in suitable relativizations, NP contains a C_{=}P-immune set, and ParityP contains a PP^{PH}-immune set. This implies the existence of a C_{=}P^{B}-simple set for some oracle B, which extends results of Balc\'{a}zar et al. [SIAM J.Comp. 14, 1985; RAIRO 22, 1988] and provides the first example of a simple set in a class not known to be contained in PH. Our proof technique requires a circuit lower bound for ``exact counting'' that is derived from Razborov's [Mat. Zametki 41, 1987] lower bound for majority.Comment: 20 page

    Give it up for climate change : a defence of the beneficiary pays principle

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    This article focuses on the normative problem of establishing how the burdens associated with implementing policies designed to prevent, or manage, climate change should be shared amongst states involved in ongoing international climate change negotiations. This problem has three key features: identifying the nature and extent of the burdens that need to be borne; identifying the type of agent that should be allocated these burdens; and distributing amongst the particular ‘tokens’ of the relevant ‘agent type’ climatic burdens according to principles that none could reasonably reject. The article defends a key role in climatic burden-sharing policy for the principle that states benefiting most from activities that cause climate change should bear the greatest burden in terms of the costs of preventing dangerous climate change. I outline two versions of this ‘beneficiary pays’ principle; examine the strengths and weakness of each version; and explore how the most plausible version (which I call the ‘unjust enrichment’ account) could be operationalized in the context of global climate governance

    The historiography of the Black Panther party

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    This article examines forty years of historical writing on the Black Panther Party (BPP), arguing that this historiography has now reached maturity. It evaluates key publications on the BPP, splitting the historiography into three periods. The first phase, the article asserts, was dominated by accounts written by participants and observers of the BPP in action. These offered insight into the personalities of the BPP leadership but included relatively little on other BPP members. They were supplemented by a collection of friendly academic studies, a number of which emphasized the role of the FBI in precipitating the BPP's decline. The article identifies the 1994 publication of Hugh Pearson's biographical study of Huey P. Newton as the beginning of a second phase. Pearson's work, which built on a collection of accounts written by observers and right-wing writers during the first phase, precipitated an outpouring of new studies that opposed its conclusions. These works overwhelmingly focussed on individual BPP chapters and the experiences of the BPP rank and file; they were generally friendly towards the party and often appraised the BPP's actions through the 1970s. A second wave of participant accounts also emerged in this period which offered a more personal interpretation of the BPP's decline. A third period emerged in the early 2000s that abandoned the obsession with Pearson's study and focussed instead on the BPP's contribution to African American and American culture beyond its political program and violent image. The article reveals the paradox at the heart of the local approach, one which recent studies addressed in their focus on the BPP's Oakland chapter and their return to a tight chronological approach that focussed on the BPP's peak years. It concludes by noting the remaining omissions in the BPP's historical record and anticipating further studie

    Ant colony optimisation and local search for bin-packing and cutting stock problems

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    The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimization problems. Exact solution methods can only be used for very small instances, so for real-world problems, we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary Programming. In the work presented here, we used an ant colony optimization (ACO) approach to solve both Bin Packing and Cutting Stock Problems. We present a pure ACO approach, as well as an ACO approach augmented with a simple but very effective local search algorithm. It is shown that the pure ACO approach can compete with existing evolutionary methods, whereas the hybrid approach can outperform the best-known hybrid evolutionary solution methods for certain problem classes. The hybrid ACO approach is also shown to require different parameter values from the pure ACO approach and to give a more robust performance across different problems with a single set of parameter values. The local search algorithm is also run with random restarts and shown to perform significantly worse than when combined with ACO
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