QRAT+: Generalizing QRAT by a More Powerful QBF Redundancy Property

The QRAT (quantified resolution asymmetric tautology) proof system simulates virtually all inference rules applied in state of the art quantified Boolean formula (QBF) reasoning tools. It consists of rules to rewrite a QBF by adding and deleting clauses and universal literals that have a certain redundancy property. To check for this redundancy property in QRAT, propositional unit propagation (UP) is applied to the quantifier free, i.e., propositional part of the QBF. We generalize the redundancy property in the QRAT system by QBF specific UP (QUP). QUP extends UP by the universal reduction operation to eliminate universal literals from clauses. We apply QUP to an abstraction of the QBF where certain universal quantifiers are converted into existential ones. This way, we obtain a generalization of QRAT we call QRAT+. The redundancy property in QRAT+ based on QUP is more powerful than the one in QRAT based on UP. We report on proof theoretical improvements and experimental results to illustrate the benefits of QRAT+ for QBF preprocessing.Comment: preprint of a paper to be published at IJCAR 2018, LNCS, Springer, including appendi

Efficient Certified RAT Verification

Clausal proofs have become a popular approach to validate the results of SAT solvers. However, validating clausal proofs in the most widely supported format (DRAT) is expensive even in highly optimized implementations. We present a new format, called LRAT, which extends the DRAT format with hints that facilitate a simple and fast validation algorithm. Checking validity of LRAT proofs can be implemented using trusted systems such as the languages supported by theorem provers. We demonstrate this by implementing two certified LRAT checkers, one in Coq and one in ACL2

Efficient Certified Resolution Proof Checking

We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms a state-of-the-art checker by two orders of magnitude. We then formalize the theory underlying propositional proof checking in Coq, and extract a correct-by-construction proof checker for our format from the formalization. An empirical evaluation using 280 unsatisfiable instances from the 2015 and 2016 SAT competitions shows that this certified checker usually performs comparably to a state-of-the-art non-certified proof checker. Using this format, we formally verify the recent 200 TB proof of the Boolean Pythagorean Triples conjecture

Cyclosporin A in psoriasis

Although a large therapeutic arsenal of conventional drugs is available to treat patients with psoriasis, a group of patients still exists that fulfill the inherent exclusion criteria or present with subjective or objective side-effects. This necessitates the need for controlled studies with potential new antipsoriatic drugs like cyclosporin A. In this thesis patientoriented studies on the treatment of severe psoriasis vulgaris with systemic low-dose and topical cyclosporin A are presented in an attempt to answer the following questions. A - What is the efficacy of short-term low-dose cyclosporin A in patients with severe, recalcitrant psoriasis ? (Chapters 3 and 4) B - Is there a preferential dose regimen for long-term treatment, either continous or intermittent ? Can the combination with a conventional drug like etretinate produce an additive positive effect ? (Chapter 5) C- Can topically applied cyclosporin A be effective in dermatologic disorders such as psoriasis ? (Chapter 6) D - What are the side-effects of orally administered cyclosporin A ? How can nephrotoxocity be monitored ? What are the recommended guidelines for the practicing dermatologist for using cyclosporin A ? (Chapters 7 and 8

DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL

We present the latest major release version 6.0 of the quantified Boolean formula (QBF) solver DepQBF, which is based on QCDCL. QCDCL is an extension of the conflict-driven clause learning (CDCL) paradigm implemented in state of the art propositional satisfiability (SAT) solvers. The Q-resolution calculus (QRES) is a QBF proof system which underlies QCDCL. QCDCL solvers can produce QRES proofs of QBFs in prenex conjunctive normal form (PCNF) as a byproduct of the solving process. In contrast to traditional QCDCL based on QRES, DepQBF 6.0 implements a variant of QCDCL which is based on a generalization of QRES. This generalization is due to a set of additional axioms and leaves the original Q-resolution rules unchanged. The generalization of QRES enables QCDCL to potentially produce exponentially shorter proofs than the traditional variant. We present an overview of the features implemented in DepQBF and report on experimental results which demonstrate the effectiveness of generalized QRES in QCDCL.Comment: 12 pages + appendix; to appear in the proceedings of CADE-26, LNCS, Springer, 201

On QBF Proofs and Preprocessing

QBFs (quantified boolean formulas), which are a superset of propositional formulas, provide a canonical representation for PSPACE problems. To overcome the inherent complexity of QBF, significant effort has been invested in developing QBF solvers as well as the underlying proof systems. At the same time, formula preprocessing is crucial for the application of QBF solvers. This paper focuses on a missing link in currently-available technology: How to obtain a certificate (e.g. proof) for a formula that had been preprocessed before it was given to a solver? The paper targets a suite of commonly-used preprocessing techniques and shows how to reconstruct certificates for them. On the negative side, the paper discusses certain limitations of the currently-used proof systems in the light of preprocessing. The presented techniques were implemented and evaluated in the state-of-the-art QBF preprocessor bloqqer.Comment: LPAR 201

Cyclosporin in atopic dermatitis: A multicentre placebo-controlled study

The efficacy of cyclosporin (Sandimmun®) given in a daily dose of 5 mg/kg for 6 weeks in severe atopic dermatitis was confirmed in this double-blind, placebo-controlled, short-term study. Of the 46 patients included in the study, 23 were randomized to receive cyclosporin and 23 to receive placebo. Four of the 23 patients (17%) on cyclosporin, and 14 of the 23 patients (61%) who received placebo, discontinued the trial because of inefficacy. All patients who discontinued the trial were assessed following the principle the principle of ‘intention to treat’. Compared with the baseline, the mean scores for disease severity [6-area, total body severity assessment (TBSA)] improved by 55%, and the mean scores for extent of disease [rule-of-nines area assessment (RoNAA)] improved by 40%, in patients treated with cyclosporin. Nine of the patients who received cyclosporin and completed the study (n=14) had an individual reduction of disease severity (TBSA) of 75% or more, and in three patients this reduction was nearly 100%. In the placebo group, a mean worsening of disease severity (4%) and of extent of the disease (25%), compared with the baseline, was observed al week 6. Patients' and investigators' mean scores for the overall efficacy were similar, and showed a statistically significant difference in favour of cyclosporin. Two patients on cyclosporin developed hypertension during therapy, and one of these withdrew from the study. At the end of the trial, no statistically significant differences in the systolic or diastolic blood pressures were observed between the two groups. In the cyclosporin group, the increases in the values of serum creatinine and bilirubin at week 6, compared with the respective values at the baseline, were statistically significantly different from those in the placebo group, but all values normalized in the post-treatment period. Cyclosporin can be a safe and very effective treatment in episodes of severe atopic dermatitis, provided that the recommended guidelines for its administration are strictly observed

Somatostatin receptor scintigraphy in cutaneous malignant lymphomas

Background: Lymphoid cells may express somatostatin receptors (SS-Rs) on their cell surface. Therefore radiolabeled somatostalin analogues may be used to visualize SS-R-positive lymphoid neoplasms in vivo. Exact staging is the basis for treatment decisions in cutaneous malignant lymphoma. We considered the possibility that SS-R scintigraphy might offer a clinically useful method of diagnostic imaging in patients with cutaneous malignant lymphoma. Objective: We evaluated SS-R scintigraphy in comparison with conventional staging methods in the staging of cutaneous malignant lymphoma. Methods: We conducted a prospective study in 14 consecutive patients with histologically proven cutaneous malignant lymphoma. SS-R scintigraphy was compared with physical, radiologic, and bone marrow examinations. Lymph node excisions were performed in patients with palpable lymph nodes. Results: SS-R scintigraphy was positive in the lymph nodes in all four patients with malignant lymph node infiltration and negative in the three patients with dermatopathic lymphadenopathy. In two patients, previously unsuspected lymphoma localizations were visualized by SS-R scintigraphy. In only three patients all skin lesions were visualized by SS-R scintigraphy; these three patients had not been treated with topical corticosteroids. SS-R scintigraphy failed to detect an adrenal mass in one patient and bone marrow infiltration in two patients. Conclusion: SS-R scintigraphy may help distinguish dermatopathic lymphadenopathy from malignant lymph node infiltration in patients with cutaneous malignant lymphoma

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