233 research outputs found
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 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
Solving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer
We solved a long-outstanding open problem in Ramsey theory, using SAT solving
Local quantum control of Heisenberg spin chains
Motivated by some recent results of quantum control theory, we discuss the
feasibility of local operator control in arrays of interacting qubits modeled
as isotropic Heisenberg spin chains. Acting on one of the end spins, we aim at
finding piecewise-constant control pulses that lead to optimal fidelities for a
chosen set of quantum gates. We analyze the robustness of the obtained results
f or the gate fidelities to random errors in the control fields, finding that
with faster switching between piecewise-constant controls the system is less
susceptible to these errors. The observed behavior falls into a generic class
of physical phenomena that are related to a competition between resonance- and
relaxation-type behavior, exemplified by motional narrowing in NMR experiments.
Finally, we discuss how the obtained optimal gate fidelities are altered when
the corresponding rapidly-varying piecewise-constant control fields are
smoothened through spectral filtering.Comment: final, published versio
Controlling qubit arrays with anisotropic XXZ Heisenberg interaction by acting on a single qubit
We investigate anisotropic Heisenberg spin-1/2 chains with control
fields acting on one of the end spins, with the aim of exploring local quantum
control in arrays of interacting qubits. In this work, which uses a recent
Lie-algebraic result on the local controllability of spin chains with
"always-on" interactions, we determine piecewise-constant control pulses
corresponding to optimal fidelities for quantum gates such as spin-flip (NOT),
controlled-NOT (CNOT), and square-root-of-SWAP (). We
find the minimal times for realizing different gates depending on the
anisotropy parameter of the model, showing that the shortest among
these gate times are achieved for particular values of larger than
unity. To study the influence of possible imperfections in anticipated
experimental realizations of qubit arrays, we analyze the robustness of the
obtained results for the gate fidelities to random variations in the
control-field amplitudes and finite rise time of the pulses. Finally, we
discuss the implications of our study for superconducting charge-qubit arrays.Comment: 6 pages, 4 figure
Entanglement dynamics of two qubits under the influence of external kicks and Gaussian pulses
We have investigated the dynamics of entanglement between two spin-1/2 qubits
that are subject to independent kick and Gaussian pulse type external magnetic
fields analytically as well as numerically. Dyson time ordering effect on the
dynamics is found to be important for the sequence of kicks. We show that
"almost-steady" high entanglement can be created between two initially
unentangled qubits by using carefully designed kick or pulse sequences
Encoding Redundancy for Satisfaction-Driven Clause Learning
Satisfaction-Driven Clause Learning (SDCL) is a recent SAT
solving paradigm that aggressively trims the search space of possible truth assignments. To determine if the SAT solver is currently exploring a dispensable part of the search space, SDCL uses the so-called positive reduct of a formula: The positive reduct is an easily solvable propositional formula that is satisfiable if the current assignment of the solver can be safely pruned from the search space. In this paper, we present two novel variants of the positive reduct that allow for even more aggressive pruning. Using one of these variants allows SDCL to solve harder problems, in particular the well-known Tseitin formulas and mutilated chessboard problems. For the first time, we are able to generate and automatically check clausal proofs for large instances of these problems
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
Maximum Causal Entropy Specification Inference from Demonstrations
In many settings (e.g., robotics) demonstrations provide a natural way to
specify tasks; however, most methods for learning from demonstrations either do
not provide guarantees that the artifacts learned for the tasks, such as
rewards or policies, can be safely composed and/or do not explicitly capture
history dependencies. Motivated by this deficit, recent works have proposed
learning Boolean task specifications, a class of Boolean non-Markovian rewards
which admit well-defined composition and explicitly handle historical
dependencies. This work continues this line of research by adapting maximum
causal entropy inverse reinforcement learning to estimate the posteriori
probability of a specification given a multi-set of demonstrations. The key
algorithmic insight is to leverage the extensive literature and tooling on
reduced ordered binary decision diagrams to efficiently encode a time unrolled
Markov Decision Process. This enables transforming a naive exponential time
algorithm into a polynomial time algorithm.Comment: Computer Aided Verification, 202
- …