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

Unsatisfiability proofs for distributed clause-sharing SAT solvers

Distributed clause-sharing SAT solvers can solve problems up to one hundred times faster than sequential SAT solvers by sharing derived information among multiple sequential solvers working on the same problem. Unlike sequential solvers, however, distributed solvers have not been able to produce proofs of unsatisfiability in a scalable manner, which has limited their use in critical applications. In this paper, we present a method to produce unsatisfiability proofs for distributed SAT solvers by combining the partial proofs produced by each sequential solver into a single, linear proof. Our approach is more scalable and general than previous explorations for parallel clause-sharing solvers, allowing use on distributed solvers without shared memory. We propose a simple sequential algorithm as well as a fully distributed algorithm for proof composition. Our empirical evaluation shows that for large-scale distributed solvers (100 nodes of 16 cores each), our distributed approach allows reliable proof composition and checking with reasonable overhead. We analyze the overhead and discuss how and where future efforts may further improve performance

Fiskalische Kosten einer steuerlichen Förderung von Forschung und Entwicklung in Deutschland - Eine empirische Analyse verschiedener Gestaltungsoptionen

Der Beitrag berechnet die Aufkommensausfälle verschiedener Gestaltungsmodelle für eine steuerliche Forschungsförderung in Deutschland auf Basis eines Mikrosimulationsmodells. Die fiskalischen Kosten betragen zwischen 464 Mio. € und 5.701 Mio. €. Eine Erstattungsoption der Steuergutschrift über die Gewerbe- und Körperschaftsteuerschuld hinaus ist unerlässlich, da sonst etwa ein Drittel der Unternehmen nicht oder nur teilweise in den Genuss der Förderung kommen würde und sich dadurch starke Verzerrungen zwischen ertragsstarken und ertragsschwachen Unternehmen ergeben. Eine Differenzierung der Fördersätze für KMU und große Unternehmen kann die Aufkommensausfälle wirksam begrenzen. Eine Kappungsgrenze in Höhe eines absoluten Betrages ist wegen der Verzerrungen innerhalb der Gruppe großer Unternehmen ungünstig. Als besonders pragmatisch erscheint eine Verrechnung der Steuergutschrift mit der abzuführenden Lohnsteuer

Cape York IIIAB iron meteorite: Trace element distribution in mineral and metallic phases

Several mineral and metallic phases in a sample from the Agpalilik mass of the Cape York iron meteorite shower have been analysed for major and trace elements using electron microprobe analysis, rapid instrumental neutron activation analysis, instrumental neutron activation analysis, radiochemical neutron activation analysis, thermochemical methods, and secondary ion mass spectrometry. The phases investigated in this way included kamacite, plessite, taenite, troilite, chromite, and schreibersite. In addition, a rare nickel-rich phase has been found and is described in detail. The genetic implications of the presence of the nickel-rich phase (which may be termed nickel-rich taenite, but does not seem to be related to tetrataenite) are very important. A compositional gradient in Ni and Cu distribution is present, with the largest values near the troilite boundary and the lowest near the kamacite boundary. The phase occurs exclusively at the troilite/kamacite interface and is often associated with rhabdite. It seems as if this was one of the last precipitates from a very Ni-rich troilite-taenite liquid, after schreibersite crystallization purged the system for several siderophile elements. This is supported by the distribution of trace elements between troilite, kamacite, and schreibersite. A fractional crystallization history for the origin of Cape York, starting with dendrites, seems plausible

Migrating Solver State

We present approaches to store and restore the state of a SAT solver, allowing us to migrate the state between different compute resources, or even between different solvers. This can be used in many ways, e.g., to improve the fault tolerance of solvers, to schedule SAT problems on a restricted number of cores, or to use dedicated preprocessing tools for inprocessing. We identify a minimum viable subset of the solver state to migrate such that the loss of performance is small. We then present and implement two different approaches to state migration: one approach stores the state at the end of a solver run whereas the other approach stores the state continuously as part of the proof trace. We show that our approaches enable the generation of correct models and valid unsatisfiability proofs. Experimental results confirm that the overhead is reasonable and that in several cases solver performance actually improves

Trace elements in phases of the Sikhote-Alin iron meteorite

A sample of the IIAB iron meteorite Sikhote-Alin has been studied for trace elements in the metal and troilite phases using electron microprobe analysis, radiochemical neutron activation analysis, and secondary ion mass spectrometry. Comparison with other members of the IIAB iron group shows that this is a typical IIAB meteorite, and fits quite well in the group, which shows a wide variations of the content of some trace elements. The variation and also the distribution coefficients of some trace elements between metal and sulphide is not consistent with a simple fractional crystallization model