A Reduction from Unbounded Linear Mixed Arithmetic Problems into Bounded Problems

We present a combination of the Mixed-Echelon-Hermite transformation and the Double-Bounded Reduction for systems of linear mixed arithmetic that preserve satisfiability and can be computed in polynomial time. Together, the two transformations turn any system of linear mixed constraints into a bounded system, i.e., a system for which termination can be achieved easily. Existing approaches for linear mixed arithmetic, e.g., branch-and-bound and cuts from proofs, only explore a finite search space after application of our two transformations. Instead of generating a priori bounds for the variables, e.g., as suggested by Papadimitriou, unbounded variables are eliminated through the two transformations. The transformations orient themselves on the structure of an input system instead of computing a priori (over-)approximations out of the available constants. Experiments provide further evidence to the efficiency of the transformations in practice. We also present a polynomial method for converting certificates of (un)satisfiability from the transformed to the original system

A Reduction from Unbounded Linear Mixed Arithmetic Problems into Bounded Problems

International audienceWe present a combination of the Mixed-Echelon-Hermite transformation and the Double-Bounded Reduction for systems of linear mixed arithmetic that preserve satisfiability and can be computed in polynomial time. Together, the two transformations turn any system of linear mixed constraints into a bounded system, i.e., a system for which termination can be achieved easily. Existing approaches for linear mixed arithmetic, e.g., branch-and-bound and cuts from proofs, only explore a finite search space after application of our two transformations. Instead of generating a priori bounds for the variables, e.g., as suggested by Papadimitriou, unbounded variables are eliminated through the two transformations. The transformations orient themselves on the structure of an input system instead of computing a priori (over- )approximations out of the available constants. Experiments provide further evidence to the efficiency of the transformations in practice. We also present a polynomial method for converting certificates of (un)satisfiability from the transformed to the original system

We Appreciate Power : a multimodal critical discourse analysis of Grimes' Music Video Posted on YouTube

The aim of this dissertation is to produce a multimodal critical discourse analysis of Grimes' video We Appreciate Power. This will serve to explore issues of ideology, identity and multilingualism in both the music video and the YouTube polylogues generated in the same web page. In this work I suggest that Grimes adopts a poststructuralist view that inherits Haraway's cyborg concept (1991) in this piece of multimedia. I claim that Grimes wanted to show the conflictive moral boundaries that the idea of the cyborg and trans-humanism casts upon Western civilization, such as the loss of free will but also the transgression of problematic dichotomies. The fact that the comment section of the video is available to use might signal that Grimes wanted to raise awareness about trans-humanism. By doing virtual ethnography research, examples of discussion about the relationship between the video and the studied polylogues will be examined regarding the notions of the cyborg and multilingualism.El objetivo de esta disertación es producir un análisis de discurso crítico multimodal del vídeo de Grimes We Appreciate Power. Esto servirá para explorar temas de ideología, identidad y multilingüismo dentro, tanto del vídeo musical, como de los polílogos generados en la misma página web de YouTube. En este trabajo sugiero que Grimes adopta un visión post-estructuralista que hereda el concepto ciborg de Haraway (1991) en esta pieza multimedia. Afirmo que Grimes quería mostrar los límites morales conflictivos que la idea del ciborg y el transhumanismo expresan sobre la civilización Occidental, como son la pérdida del libre albedrío pero también la transgresión de las dicotomías problemáticas. El hecho de que la sección de comentarios del vídeo esté disponible para ser utilizada puede significar que Grimes quiere despertar conciencia sobre el transhumanismo. Mediante la investigación etnográfica virtual, se analizarán ejemplos de discusión sobre la relación entre el vídeo y los polílogos estudiados respecto a las nociones de ciborg y multilingüismo.L'objectiu d'aquesta dissertació és produir una anàlisi de discurs crític multimodal del vídeo de Grimes We Appreciate Power. Això servirà per explorar temes d'ideologia, identitat i multilingüisme dins, tant del vídeo musical, com dels polílegs generats a la mateixa pàgina web de YouTube. En aquest treball suggereixo que Grimes adopta un visió post-estructuralista que hereta el concepte ciborg de Haraway (1991) en aquesta peça multimèdia. Afirmo que Grimes volia mostrar els límits morals conflictius que la idea del ciborg i el trans-humanisme expressen sobre la civilització Occidental, com la pèrdua del lliure albir però també la transgressió de les dicotomies problemàtiques. El fet que la secció de comentaris del vídeo estigui disponible per ser utilitzada pot significar que Grimes vol despertar consciència sobre el trans-humanisme. Mitjançant la investigació etnogràfica virtual, s'analitzaran exemples de discussió sobre la relació entre el vídeo i els polílegs estudiats respecte a les nocions de ciborg i multilingüisme

Decision procedures for linear arithmetic

In this thesis, we present new decision procedures for linear arithmetic in the context of SMT solvers and theorem provers: 1) CutSat++, a calculus for linear integer arithmetic that combines techniques from SAT solving and quantifier elimination in order to be sound, terminating, and complete. 2) The largest cube test and the unit cube test, two sound (although incomplete) tests that find integer and mixed solutions in polynomial time. The tests are especially efficient on absolutely unbounded constraint systems, which are difficult to handle for many other decision procedures. 3) Techniques for the investigation of equalities implied by a constraint system. Moreover, we present several applications for these techniques. 4) The Double-Bounded reduction and the Mixed-Echelon-Hermite transformation, two transformations that reduce any constraint system in polynomial time to an equisatisfiable constraint system that is bounded. The transformations are beneficial because they turn branch-and-bound into a complete and efficient decision procedure for unbounded constraint systems. We have implemented the above decision procedures (except for Cut- Sat++) as part of our linear arithmetic theory solver SPASS-IQ and as part of our CDCL(LA) solver SPASS-SATT. We also present various benchmark evaluations that confirm the practical efficiency of our new decision procedures.In dieser Arbeit präsentieren wir neue Entscheidungsprozeduren für lineare Arithmetik im Kontext von SMT-Solvern und Theorembeweisern: 1) CutSat++, ein korrekter und vollständiger Kalkül für ganzzahlige lineare Arithmetik, der Techniken zur Entscheidung von Aussagenlogik mit Techniken aus der Quantorenelimination vereint. 2) Der Größte-Würfeltest und der Einheitswürfeltest, zwei korrekte (wenn auch unvollständige) Tests, die in polynomieller Zeit (gemischt-)ganzzahlige Lösungen finden. Die Tests sind besonders effizient auf vollständig unbegrenzten Systemen, welche für viele andere Entscheidungsprozeduren schwer sind. 3) Techniken zur Ermittlung von Gleichungen, die von einem linearen Ungleichungssystem impliziert werden. Des Weiteren präsentieren wir mehrere Anwendungsmöglichkeiten für diese Techniken. 4) Die Beidseitig-Begrenzte-Reduktion und die Gemischte-Echelon-Hermitesche- Transformation, die ein Ungleichungssystem in polynomieller Zeit auf ein erfüllbarkeitsäquivalentes System reduzieren, das begrenzt ist. Vereint verwandeln die Transformationen Branch-and-Bound in eine vollständige und effiziente Entscheidungsprozedur für unbeschränkte Ungleichungssysteme. Wir haben diese Techniken (ausgenommen CutSat++) in SPASS-IQ (unserem theory solver für lineare Arithmetik) und in SPASS-SATT (unserem CDCL(LA) solver) implementiert. Basierend darauf präsentieren wir Benchmark-Evaluationen, die die Effizienz unserer Entscheidungsprozeduren bestätigen