Numerical stability of mass transfer driven by Roche lobe overflow in close binaries

Numerical computation of the time evolution of the mass transfer rate in a close binary can be and, in particular, has been a computational challenge. Using a simple physical model to calculate the mass transfer rate, we show that for a simple explicit iteration scheme the mass transfer rate is numerically unstable unless the time steps are sufficiently small. In general, more sophisticated explicit algorithms do not provide any significant improvement since this instability is a direct result of time discretization. For a typical binary evolution, computation of the mass transfer rate as a smooth function of time limits the maximum tolerable time step and thereby sets the minimum total computational effort required for an evolutionary computation. By methods of ``Controlling Chaos'' it can be shown that a specific implicit iteration scheme, based on Newton's method, is the most promising solution for the problem.Comment: 6 pages, LaTeX, two eps figures, Astronomy and Astrophysics, accepte

Minimal unsatisfiable formulas with bounded clause-variable difference are fixed-parameter tractable

Recognition of minimal unsatisfiable CNF formulas (unsatisfiable CNF formulas which become satisfiable if any clause is removed) is a classical DP-complete problem. It was shown recently that minimal unsatisfiable formulas with n variables and n+k clauses can be recognized in time . We improve this result and present an algorithm with time complexity ; hence the problem turns out to be fixed-parameter tractable (FTP) in the sense of Downey and Fellows (Parameterized Complexity, 1999). Our algorithm gives rise to a fixed-parameter tractable parameterization of the satisfiability problem: If for a given set of clauses F, the number of clauses in each of its subsets exceeds the number of variables occurring in the subset at most by k, then we can decide in time whether F is satisfiable; k is called the maximum deficiency of F and can be efficiently computed by means of graph matching algorithms. Known parameters for fixed-parameter tractable satisfiability decision are tree-width or related to tree-width. Tree-width and maximum deficiency are incomparable in the sense that we can find formulas with constant maximum deficiency and arbitrarily high tree-width, and formulas where the converse prevails

Anti-alignments in conformance checking: the dark side of process models

Conformance checking techniques asses the suitability of a process model in representing an underlying process, observed through a collection of real executions. These techniques suffer from the wellknown state space explosion problem, hence handling process models exhibiting large or even infinite state spaces remains a challenge. One important metric in conformance checking is to asses the precision of the model with respect to the observed executions, i.e., characterize the ability of the model to produce behavior unrelated to the one observed. By avoiding the computation of the full state space of a model, current techniques only provide estimations of the precision metric, which in some situations tend to be very optimistic, thus hiding real problems a process model may have. In this paper we present the notion of antialignment as a concept to help unveiling traces in the model that may deviate significantly from the observed behavior. Using anti-alignments, current estimations can be improved, e.g., in precision checking. We show how to express the problem of finding anti-alignments as the satisfiability of a Boolean formula, and provide a tool which can deal with large models efficiently.Peer ReviewedPostprint (author's final draft

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

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

Incremental QBF Solving

We consider the problem of incrementally solving a sequence of quantified Boolean formulae (QBF). Incremental solving aims at using information learned from one formula in the process of solving the next formulae in the sequence. Based on a general overview of the problem and related challenges, we present an approach to incremental QBF solving which is application-independent and hence applicable to QBF encodings of arbitrary problems. We implemented this approach in our incremental search-based QBF solver DepQBF and report on implementation details. Experimental results illustrate the potential benefits of incremental solving in QBF-based workflows.Comment: revision (camera-ready, to appear in the proceedings of CP 2014, LNCS, Springer

Is irradiation important for the secular evolution of low-mass X-ray binaries?

It is argued that irradiation in low-mass X-ray binaries (LMXBs) caused by accretion-generated X-rays can not only change the optical appearance of LMXBs but also their outburst properties and possibly also their long-term evolution. Irradiation during an outburst of the outer parts of the accretion disc in a transient LMXB leads to drastic changes in the outburst properties. As far as the secular evolution of such systems is concerned, these changes can result in enhanced loss of mass and angular momentum from the system and, most important, in neutron star LMXBs in a much less efficient use of the transferred matter to spin up the neutron star to a ms-pulsar. Irradiation of the donor star can destabilize mass transfer and lead to irradiation-driven mass transfer cycles, i.e. to a secular evolution which differs drastically from an evolution in which irradiation is ignored. It is argued that irradiation-driven mass transfer cycles cannot occur in systems which are transient because of disc instabilities, i.e. in particular in long-period LMXBs with a giant donor. It is furthermore shown that for irradiating either the disc or the donor star, direct irradiation alone is insufficient. Rather, indirect irradiation via scattered accretion luminosity must play an important role in transient LMXBs and is, in fact, necessary to destabilize mass transfer in short-period systems by irradiating the donor star. Whether and to what extent irradiation in LMXBs does change their secular evolution depends on a number of unsolved problems which are briefly discussed at the end of this article.Comment: 11 pages, 4 postscript figures, to appear in New Astronomy Reviews, Proceedings of "Jean-Pierre Lasota, X-ray binaries, accretion disks and compact stars" (October 2007); Ed. M. Abramowicz; small changes in the acknowledgements

Incrementally Computing Minimal Unsatisfiable Cores of QBFs via a Clause Group Solver API

We consider the incremental computation of minimal unsatisfiable cores (MUCs) of QBFs. To this end, we equipped our incremental QBF solver DepQBF with a novel API to allow for incremental solving based on clause groups. A clause group is a set of clauses which is incrementally added to or removed from a previously solved QBF. Our implementation of the novel API is related to incremental SAT solving based on selector variables and assumptions. However, the API entirely hides selector variables and assumptions from the user, which facilitates the integration of DepQBF in other tools. We present implementation details and, for the first time, report on experiments related to the computation of MUCs of QBFs using DepQBF's novel clause group API.Comment: (fixed typo), camera-ready version, 6-page tool paper, to appear in proceedings of SAT 2015, LNCS, Springe