Mladen Nikolić

Instance-Based Selection of Policies for SAT Solvers

Execution of most of the modern DPLL-based SAT solvers is guided by a number of heuristics. Decisions made during the search process are usually driven by some fixed heuristic policies. Despite the outstanding progress in SAT solving in recent years, there is still an appealing lack of techniques for selecting policies appropriate for solving specific input formulae. In this paper we present a methodology for instance-based selection of solvers policies that uses a data-mining classification technique. The methodology also relies on analysis of relationships between formulae, their families, and their suitable solving strategies. The evaluation results are very good, demonstrate practical usability of the methodology, and encourage further efforts in this direction.

Measuring similarity of graph nodes by neighbor matching

The problem of measuring similarity of graph nodes is important in a range of practical problems. There is a number of proposed measures, usually based on iterative calculation of similarity and the principle that two nodes are as similar as their neighbors are. In our work, we propose one novel method of that sort, with a refined concept of similarity of nodes that involves matching their neighbors. We prove convergence of the proposed method and show that it has some additional desirable properties that, to our knowledge, the existing methods lack. In addition, we construct a measure of similarity of whole graphs based on the similarities of nodes. We illustrate the proposed method on several specific problems and empirically compare it to other methods.

Statistical methodology for comparison of SAT solvers

Evaluating improvements to modern SAT solvers and comparison of two arbitrary solvers is a challenging and important task. Relative performance of two solvers is usually assessed by running them on a set of SAT instances and comparing the number of solved instances and their running time in a straightforward manner. In this paper we point to shortcomings of this approach and advocate more reliable, statistically founded methodologies that could discriminate better between good and bad ideas. We present one such methodology and illustrate its application.

Simple algorithm portfolio for SAT

The importance of algorithm portfolio techniques for SAT has long been noted, and a number of very successful systems have been devised, including the most successful one—SATzilla. However, all these systems are quite complex (to understand, reimplement, or modify). In this paper we present an algorithm portfolio for SAT that is extremely simple, but in the same time so efficient that it outperforms SATzilla. For a new SAT instance to be solved, our portfolio finds its k-nearest neighbors from the training set and invokes a solver that performs the best for those instances. The main distinguishing feature of our algorithm portfolio is the locality of the selection procedure—the selection of a SAT solver is based only on few instances similar to the input one. An open source tool that implements our approach is publicly available.

Sparse regression interaction models for spatial prediction of soil properties in 3D

Abstract An approach for using lasso (Least Absolute Shrinkage and Selection Operator) regression in creating sparse 3D models of soil properties for spatial prediction at multiple depths is presented. Modeling soil properties in 3D benefits from interactions of spatial predictors with soil depth and its polynomial expansion, which yields a large number of model variables (and corresponding model parameters). Lasso is able to perform variable selection, hence reducing the number of model parameters and making the model more easily interpretable. This also prevents overfitting, which makes the model more accurate. The presented approach was tested using four variable selection approaches – none, stepwise, lasso and hierarchical lasso, on four kinds of models – standard linear model, linear model with polynomial expansion of depth, linear model with interactions of covariates with depth and linear model with interactions of covariates with depth and its polynomial expansion. This framework was used to predict Soil Organic Carbon (SOC) in three contrasting study areas: Bor (Serbia), Edgeroi (Australia) and the Netherlands. Results show that lasso yields substantial improvements in accuracy over standard and stepwise regression — up to 50 % of total variance. It yields models which contain up to five times less nonzero parameters than the full models and that are usually more sparse than models obtained by stepwise regression, up to three times. Extension of the standard linear model by including interactions typically improves the accuracy of models produced by lasso, but is detrimental to standard and stepwise regression. Regarding computation time, it was demonstrated that lasso is several orders of magnitude more efficient than stepwise regression for models with tens or hundreds of variables (including interactions). Proper model evaluation is emphasized. Considering the fact that lasso requires meta-parameter tuning, standard cross-validation does not suffice for adequate model evaluation, hence a nested cross-validation was employed. The presented approach is implemented as publicly available sparsereg3D R package.

Portfolio theorem proving and prover runtime prediction for geometry

In recent years, portfolio problem solving found many applications in automated reasoning, primarily in SAT solving and in automated and interactive theorem proving. Portfolio problem solving is an approach in which for an individual instance of a specific problem, one particular, hopefully most appropriate, solving technique is automatically selected among several available ones and used. The selection usually employs machine learning methods. To our knowledge, this approach has not been used in automated theorem proving in geometry so far and it poses a number of new challenges. In this paper we propose a set of features which characterize a specific geometric theorem, so that machine learning techniques can be used in geometry. Relying on these features and using different machine learning techniques, we constructed several portfolios for theorem proving in geometry and also runtime prediction models for provers involved. The evaluation was performed on two corpora of geometric theorems: one coming from geometric construction problems and one from a benchmark set of the GeoGebra tool. The obtained results show that machine learning techniques can be useful in automated theorem proving in geometry, while there is still room for further progress.

CDCL-based abstract state transition system for coherent logic

We present a new, CDCL-based approach for automated theorem proving in coherent logic -- an expressive semi-decidable fragment of first-order logic that provides potential for obtaining human readable and machine verifiable proofs. The approach is described by means of an abstract state transition system, inspired by existing transition systems for SAT and represents its faithful lifting to coherent logic. The presented transition system includes techniques from which CDCL SAT solvers benefited the most (backjumping and lemma learning), but also allows generation of human readable proofs. In contrast to other approaches to theorem proving in coherent logic, reasoning involved need not to be ground. We prove key properties of the system, primarily that the system yields a semidecision procedure for coherent logic. As a consequence, the semidecidability of another fragment of first order logic which is a proper superset of coherent logic is also proven.