The Deduction Theorem for Strong Propositional Proof Systems

This paper focuses on the deduction theorem for propositional logic. We define and investigate different deduction properties and show that the presence of these deduction properties for strong proof systems is powerful enough to characterize the existence of optimal and even polynomially bounded proof systems. We also exhibit a similar, but apparently weaker condition that implies the existence of complete disjoint NPUnknown control sequence '\mathsf' -pairs. In particular, this yields a sufficient condition for the completeness of the canonical pair of Frege systems and provides a general framework for the search for complete NPUnknown control sequence '\mathsf' -pairs

The deduction theorem for strong propositional proof systems

This paper focuses on the deduction theorem for propositional logic. We define and investigate different deduction properties and show that the presence of these deduction properties for strong proof systems is powerful enough to characterize the existence of optimal and even polynomially bounded proof systems. We also exhibit a similar, but apparently weaker condition that implies the existence of complete disjoint NP-pairs. In particular, this yields a sufficient condition for the completeness of the canonical pair of Frege systems and provides a general framework for the search for complete NP-pairs

Disjoint NP-pairs from propositional proof systems

For a proof system P we introduce the complexity class DNPP(P) of all disjoint NP-pairs for which the disjointness of the pair is efficiently provable in the proof system P. We exhibit structural properties of proof systems which make the previously defined canonical NP-pairs of these proof systems hard or complete for DNPP(P). Moreover we demonstrate that non-equivalent proof systems can have equivalent canonical pairs and that depending on the properties of the proof systems different scenarios for DNPP(P) and the reductions between the canonical pairs exist

Parameterized complexity of DPLL search procedures

We study the performance of DPLL algorithms on parameterized problems. In particular, we investigate how difficult it is to decide whether small solutions exist for satisfiability and other combinatorial problems. For this purpose we develop a Prover-Delayer game which models the running time of DPLL procedures and we establish an information-theoretic method to obtain lower bounds to the running time of parameterized DPLL procedures. We illustrate this technique by showing lower bounds to the parameterized pigeonhole principle and to the ordering principle. As our main application we study the DPLL procedure for the problem of deciding whether a graph has a small clique. We show that proving the absence of a k-clique requires n steps for a non-trivial distribution of graphs close to the critical threshold. For the restricted case of tree-like Parameterized Resolution, this result answers a question asked in [11] of understanding the Resolution complexity of this family of formulas

Downregulation of Fzd6 and Cthrc1 and upregulation of olfactory receptors and protocadherins by dietary beta-carotene in lungs of Bcmo1-/- mice.

An ongoing controversy exists on beneficial versus harmful effects of high beta-carotene (BC) intake, especially for the lung. To elucidate potential mechanisms, we studied effects of BC on lung gene expression. We used a beta-carotene 15,15'-monooxygenase 1 (Bcmo1) knockout mouse (Bcmo1-/-) model, unable to convert BC to retinoids, and wild-type mice (Bcmo1+/+) mice to dissect the effects of intact BC from effects of BC metabolites. As expected, BC supplementation resulted in a higher BC accumulation in lungs of Bcmo1-/- mice than in lungs of Bcmo1+/+ mice. Whole mouse genome transcriptome analysis on lung tissue revealed that more genes were regulated in Bcmo1-/- mice than Bcmo1+/+ mice upon BC supplementation. Frizzled homolog 6 (Fzd6) and collagen triple helix repeat containing 1 (Cthrc1) were significantly downregulated (fold changes -2.99 and -2.60, respectively, false discovery rate <0.05) by BC in Bcmo1-/-. Moreover, many olfactory receptors and many members of the protocadherin family were upregulated. Since both olfactory receptors and protocadherins have an important function in sensory nerves and Fzd6 and Cthrc1 are important in stem cell development, we hypothesize that BC might have an effect on the highly innervated pulmonary neuroendocrine cell (PNEC) cluster. PNECs are highly associated with sensory nerves and are important cells in the control of stem cells. A role for BC in the innervated PNEC cluster might be of particular importance in smoke-induced carcinogenesis since PNEC-derived lung cancer is highly associated with tobacco smoke

Downregulation of Fzd6 and Cthrc1 and upregulation of olfactory receptors and protocadherins by dietary beta-carotene in lungs of Bcmo1-/- mice.

An ongoing controversy exists on beneficial versus harmful effects of high beta-carotene (BC) intake, especially for the lung. To elucidate potential mechanisms, we studied effects of BC on lung gene expression. We used a beta-carotene 15,15'-monooxygenase 1 (Bcmo1) knockout mouse (Bcmo1-/-) model, unable to convert BC to retinoids, and wild-type mice (Bcmo1+/+) mice to dissect the effects of intact BC from effects of BC metabolites. As expected, BC supplementation resulted in a higher BC accumulation in lungs of Bcmo1-/- mice than in lungs of Bcmo1+/+ mice. Whole mouse genome transcriptome analysis on lung tissue revealed that more genes were regulated in Bcmo1-/- mice than Bcmo1+/+ mice upon BC supplementation. Frizzled homolog 6 (Fzd6) and collagen triple helix repeat containing 1 (Cthrc1) were significantly downregulated (fold changes -2.99 and -2.60, respectively, false discovery rate <0.05) by BC in Bcmo1-/-. Moreover, many olfactory receptors and many members of the protocadherin family were upregulated. Since both olfactory receptors and protocadherins have an important function in sensory nerves and Fzd6 and Cthrc1 are important in stem cell development, we hypothesize that BC might have an effect on the highly innervated pulmonary neuroendocrine cell (PNEC) cluster. PNECs are highly associated with sensory nerves and are important cells in the control of stem cells. A role for BC in the innervated PNEC cluster might be of particular importance in smoke-induced carcinogenesis since PNEC-derived lung cancer is highly associated with tobacco smoke

Sparser Random 3SAT Refutation Algorithms and the Interpolation Problem:Extended Abstract

We formalize a combinatorial principle, called the 3XOR principle, due to Feige, Kim and Ofek [12], as a family of unsatisfiable propositional formulas for which refutations of small size in any propo-sitional proof system that possesses the feasible interpolation property imply an efficient deterministic refutation algorithm for random 3SAT with n variables and Ω(n1.4) clauses. Such small size refutations would improve the state of the art (with respect to the clause density) efficient refutation algorithm, which works only for Ω(n1.5) many clauses [13]. We demonstrate polynomial-size refutations of the 3XOR principle in resolution operating with disjunctions of quadratic equations with small integer coefficients, denoted R(quad); this is a weak extension of cutting planes with small coefficients. We show that R(quad) is weakly autom-atizable iff R(lin) is weakly automatizable, where R(lin) is similar to R(quad) but with linear instead of quadratic equations (introduced in [25]). This reduces the problem of refuting random 3CNF with n vari-ables and Ω(n1.4) clauses to the interpolation problem of R(quad) and to the weak automatizability of R(lin)

Effective flexural stiffness of slender reinforced concrete columns under axial forces and biaxial bending

Most of the design codes (ACI-318-2008 and Euro Code-2-2004) propose the moment magnifier method in order to take into account the second order effect to design slender reinforced concrete columns. The accuracy of this method depends on the effective flexural stiffness of the column. This paper proposes a new equation to obtain the effective stiffness EI of slender reinforced concrete columns. The expression is valid for any shape of cross-section, subjected to combined axial loads and biaxial bending, both for short-time and sustained loads, normal and high strength concretes, but it is only suitable for columns with equal effective buckling lengths in the two principal bending planes. The new equation extends the proposed EI equation in the "Biaxial bending moment magnifier method" by Bonet et al. (2004) [6], which is valid only for rectangular sections. The method was compared with 613 experimental tests from the literature and a good degree of accuracy was obtained. It was also compared with the design codes ACI-318 (08) and EC-2 (2004) improving the precision. The method is capable to verify and design with sufficient accuracy slender reinforced concrete columns in practical engineering design applications. © 2010 Elsevier Ltd.The authors wish to express their sincere gratitude to the Spanish "Ministerio de Ciencia e Innovacion" for help provided through projects BIA2008-03734 and BIA2009-10207 and to the European Community with the Feder funds.Bonet Senach, JL.; Romero, ML.; Miguel Sosa, P. (2011). Effective flexural stiffness of slender reinforced concrete columns under axial forces and biaxial bending. Engineering Structures. 33:881-893. doi:10.1016/j.engstruct.2010.12.009S8818933

Parameterized bounded-depth Frege is not optimal

A general framework for parameterized proof complexity was introduced by Dantchev, Martin, and Szeider [9]. There the authors concentrate on tree-like Parameterized Resolution-a parameterized version of classical Resolution-and their gap complexity theorem implies lower bounds for that system. The main result of the present paper significantly improves upon this by showing optimal lower bounds for a parameterized version of bounded-depth Frege. More precisely, we prove that the pigeonhole principle requires proofs of size n in parameterized bounded-depth Frege, and, as a special case, in dag-like Parameterized Resolution. This answers an open question posed in [9]. In the opposite direction, we interpret a well-known technique for FPT algorithms as a DPLL procedure for Parameterized Resolution. Its generalization leads to a proof search algorithm for Parameterized Resolution that in particular shows that tree-like Parameterized Resolution allows short refutations of all parameterized contradictions given as bounded-width CNF's