Christoph Zengler

Model Counting in Product Configuration

We describe how to use propositional model counting for a quantitative analysis of product configuration data. Our approach computes valuable meta information such as the total number of valid configurations or the relative frequency of components. Thi s information can be used to assess the severity of documentation errors or to measure documentation quality. As an application example we show how we apply these methods to product documentation formulas of the Mercedes-Benz line of vehicles. In order to process these large formulas we developed and implemented a new model counter for non-CNF formulas. Our model counter can process formulas, whose CNF representations could not be processed up till now.

Extending clause learning of SAT solvers with Boolean Gröbner bases

We extend clause learning as performed by most modern SAT Solvers by integrating the computation of Boolean Grobner bases into the conflict learning process. Instead of learning only one clause per conflict, we compute and learn additional binary clauses from a Grobner basis of the current conflict. We used the Grobner basis engine of the logic package Redlog contained in the computer algebra system Reduce to extend the SAT solver MiniSAT with Grobner basis learning. Our approach shows a significant reduction of conflicts and a reduction of restarts and computation time on many hard problems from the SAT 2009 competition.

Boolean Quantifier Elimination for Automotive Configuration A Case Study

This paper evaluates different algorithms for existential Boolean quantifier elimination in the area of automotive configuration. We compare approaches based on model enumeration, on resolution, on dependency sequents, on substitution, and on knowledge compilation with projection. We describe two real-life applications: model counting on a set of customer-relevant options and projection of BOM (bill of materials) constraints. Our work includes an implementation of the presented techniques on top of state-of-the-art tools. We evaluate the different approaches on real production data from our collaboration with BMW.

Parametric quantified SAT solving

We generalize successful algorithmic ideas for quantified satisfiability solving to the parametric case where there are parameters in the input problem. The output is then not necessarily a truth value but more generally a propositional formula in the parameters of the input. Since one can naturally embed propositional logic into first-order logic over Boolean algebras, our work amounts from a model-theoretic point of view to a quantifier elimination procedure for initial Boolean algebras. Our work is completely and efficiently implemented in the logic package Redlog contained in the open source computer algebra system Reduce. We describe this implementation and discuss computation examples pointing at possible applications of our work to configuration problems in the automotive industry.

New approaches to boolean quantifier elimination

We present four different approaches for existential Boolean quantifier elimination, based on model enumeration, resolution, knowledge compilation with projection, and substitution. We point out possible applications in the area of verification and we present preliminary benchmark results of the different approaches.

Automated Deduction in Geometry : 7th International Workshop, ADG 2008

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Automated Deduction in Geometry

AUTOMATED DEDUCTION IN GEOMETRY 7TH INTERNATIONAL WORKSHOP ADG 2008 SHANGHAI CHINA SEPTEMBER 22 PDF Are you looking for Ebook automated deduction in geometry 7th international workshop adg 2008 shanghai china september 22 PDF? You will be glad to know that right now automated deduction in geometry 7th international workshop adg 2008 shanghai china september 22 PDF is available on our online library. With our online resources, you can find automated deduction in geometry 7th international workshop adg 2008 shanghai china september 22 or just about any type of ebooks, for any type of product.

Boolean Gröbner bases in SAT solving

We want to incorporate the reasoning power of Boolean Gröbner bases into modern SAT solvers. There are many starting points where to plug in the Gröbner bases engine in the SAT solving process. As a first step we chose the learning part where new consequences (lemmas) of the original formula are deduced. This paper shows first promising results, also published at the CASC 2010 in Armenia [1].