Evaluating QBF Solvers: Quantifier Alternations Matter

We present an experimental study of the effects of quantifier alternations on the evaluation of quantified Boolean formula (QBF) solvers. The number of quantifier alternations in a QBF in prenex conjunctive normal form (PCNF) is directly related to the theoretical hardness of the respective QBF satisfiability problem in the polynomial hierarchy. We show empirically that the performance of solvers based on different solving paradigms substantially varies depending on the numbers of alternations in PCNFs. In related theoretical work, quantifier alternations have become the focus of understanding the strengths and weaknesses of various QBF proof systems implemented in solvers. Our results motivate the development of methods to evaluate orthogonal solving paradigms by taking quantifier alternations into account. This is necessary to showcase the broad range of existing QBF solving paradigms for practical QBF applications. Moreover, we highlight the potential of combining different approaches and QBF proof systems in solvers.Comment: preprint of a paper to be published at CP 2018, LNCS, Springer, including appendi

Natural Killer Cell Mediated Cytotoxic Responses in the Tasmanian Devil

The Tasmanian devil (Sarcophilus harrisii), the world's largest marsupial carnivore, is under threat of extinction following the emergence of an infectious cancer. Devil facial tumour disease (DFTD) is spread between Tasmanian devils during biting. The disease is consistently fatal and devils succumb without developing a protective immune response. The aim of this study was to determine if Tasmanian devils were capable of forming cytotoxic antitumour responses and develop antibodies against DFTD cells and foreign tumour cells. The two Tasmanian devils immunised with irradiated DFTD cells did not form cytotoxic or humoral responses against DFTD cells, even after multiple immunisations. However, following immunisation with xenogenic K562 cells, devils did produce cytotoxic responses and antibodies against this foreign tumour cell line. The cytotoxicity appeared to occur through the activity of natural killer (NK) cells in an antibody dependent manner. Classical NK cell responses, such as innate killing of DFTD and foreign cancer cells, were not observed. Cells with an NK-like phenotype comprised approximately 4 percent of peripheral blood mononuclear cells. The results of this study suggest that Tasmanian devils have NK cells with functional cytotoxic pathways. Although devil NK cells do not directly recognise DFTD cancer cells, the development of antibody dependent cell-mediated cytotoxicity presents a potential pathway to induce cytotoxic responses against the disease. These findings have positive implications for future DFTD vaccine research

Bounded arithmetic and propositional proof complexity

This is a survey of basic facts about bounded arithmetic and about the relationships between bounded arithmetic and propositional proof complexity. We introduce the theories S i 2 and T i 2 of bounded arithmetic and characterize their proof theoretic strength and their provably total functions in terms of the polynomial time hierarchy. We discuss other axiomatizations of bounded arithmetic, such as minimization axioms. It is shown that the bounded arithmetic hierarchy collapses if and only if bounded arithmetic proves that the polynomial hierarchy collapses. We discuss Frege and extended Frege proof length, and the two translations from bounded arithmetic proofs into propositional proofs. We present some theorems on bounding the lengths of propositional interpolants in terms of cut-free proof length and in terms of the lengths of resolution refutations. We then define the Razborov-Rudich notion of natural proofs of P � = NP and discuss Razborov’s theorem that certain fragments of bounded arithmetic cannot prove superpolynomial lower bounds on circuit size, assuming a strong cryptographic conjecture. Finally, a complete presentation of a proof of the theorem of Razborov is given

Tableau Methods for Classical Propositional Logic

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