Resolution proof transformation for compression and interpolation

Verification methods based on SAT, SMT, and theorem proving often rely on proofs of unsatisfiability as a powerful tool to extract information in order to reduce the overall effort. For example a proof may be traversed to identify a minimal reason that led to unsatisfiability, for computing abstractions, or for deriving Craig interpolants. In this paper we focus on two important aspects that concern efficient handling of proofs of unsatisfiability: compression and manipulation. First of all, since the proof size can be very large in general (exponential in the size of the input problem), it is indeed beneficial to adopt techniques to compress it for further processing. Secondly, proofs can be manipulated as a flexible preprocessing step in preparation for interpolant computation. Both these techniques are implemented in a framework that makes use of local rewriting rules to transform the proofs. We show that a careful use of the rules, combined with existing algorithms, can result in an effective simplification of the original proofs. We have evaluated several heuristics on a wide range of unsatisfiable problems deriving from SAT and SMT test cases

Controlled and effective interpolation

Model checking is a well established technique to verify systems, exhaustively and automatically. The state space explosion, known as the main difficulty in model checking scalability, has been successfully approached by symbolic model checking which represents programs using logic, usually at the propositional or first order theories level. Craig interpolation is one of the most successful abstraction techniques used in symbolic methods. Interpolants can be efficiently generated from proofs of unsatisfiability, and have been used as means of over-approximation to generate inductive invariants, refinement predicates, and function summaries. However, interpolation is still not fully understood. For several theories it is only possible to generate one interpolant, giving the interpolation-based application no chance of further optimization via interpolation. For the theories that have interpolation systems that are able to generate different interpolants, it is not understood what makes one interpolant better than another, and how to generate the most suitable ones for a particular verification task. The goal of this thesis is to address the problems of how to generate multiple interpolants for theories that still lack this flexibility in their interpolation algorithms, and how to aim at good interpolants. This thesis extends the state-of-the-art by introducing novel interpolation frameworks for different theories. For propositional logic, this work provides a thorough theoretical analysis showing which properties are desirable in a labeling function for the Labeled Interpolation Systems framework (LIS). The Proof-Sensitive labeling function is presented, and we prove that it generates interpolants with the smallest number of Boolean connectives in the entire LIS framework. Two variants that aim at controlling the logical strength of propositional interpolants while maintaining a small size are given. The new interpolation algorithms are compared to previous ones from the literature in different model checking settings, showing that they consistently lead to a better overall verification performance. The Equalities and Uninterpreted Functions (EUF)-interpolation system, presented in this thesis, is a duality-based interpolation framework capable of generating multiple interpolants for a single proof of unsatisfiability, and provides control over the logical strength of the interpolants it generates using labeling functions. The labeling functions can be theoretically compared with respect to their strength, and we prove that two of them generate the interpolants with the smallest number of equalities. Our experiments follow the theory, showing that the generated interpolants indeed have different logical strength. We combine propositional and EUF interpolation in a model checking setting, and show that the strength of the interpolation algorithms for different theories has to be aligned in order to generate smaller interpolants. This work also introduces the Linear Real Arithmetic (LRA)-interpolation system, an interpolation framework for LRA. The framework is able to generate infinitely many interpolants of different logical strength using the duality of interpolants. The strength of the LRA interpolants can be controlled by a normalized strength factor, which makes it straightforward for an interpolationbased application to choose the level of strength it wants for the interpolants. Our experiments with the LRA-interpolation system and a model checker show that it is very important for the application to be able to fine tune the strength of the LRA interpolants in order to achieve optimal performance. The interpolation frameworks were implemented and form the interpolation module in OpenSMT2, an open source efficient SMT solver. OpenSMT2 has been integrated to the propositional interpolation-based model checkers FunFrog and eVolCheck, and to the first order interpolation-based model checkerHiFrog. This thesis presents real life model checking experiments using the novel interpolation frameworks and the tools aforementioned, showing the viability and strengths of the techniques

Estimating and understanding motion : from diagnostic to robotic surgery

Estimating and understanding motion from an image sequence is a central topic in computer vision. The high interest in this topic is because we are living in a world where many events that occur in the environment are dynamic. This makes motion estimation and understanding a natural component and a key factor in a widespread of applications including object recognition , 3D shape reconstruction, autonomous navigation and medica! diagnosis. Particularly, we focus on the medical domain in which understanding the human body for clinical purposes requires retrieving the organs' complex motion patterns, which is in general a hard problem when using only image data. In this thesis, we cope with this problem by posing the question - How to achieve a realistic motion estimation to offer a better clinical understanding? We focus this thesis on answering this question by using a variational formulation as a basis to understand one of the most complex motions in the human's body, the heart motion, through three different applications: (i) cardiac motion estimation for diagnostic, (ii) force estimation and (iii) motion prediction, both for robotic surgery. Firstly, we focus on a central topic in cardiac imaging that is the estimation of the cardiac motion. The main aim is to offer objective and understandable measures to physicians for helping them in the diagnostic of cardiovascular diseases. We employ ultrafast ultrasound data and tools for imaging motion drawn from diverse areas such as low-rank analysis and variational deformation to perform a realistic cardiac motion estimation. The significance is that by taking low-rank data with carefully chosen penalization, synergies in this complex variational problem can be created. We demonstrate how our proposed solution deals with complex deformations through careful numerical experiments using realistic and simulated data. We then move from diagnostic to robotic surgeries where surgeons perform delicate procedures remotely through robotic manipulators without directly interacting with the patients. As a result, they lack force feedback, which is an important primary sense for increasing surgeon-patient transparency and avoiding injuries and high mental workload. To solve this problem, we follow the conservation principies of continuum mechanics in which it is clear that the change in shape of an elastic object is directly proportional to the force applied. Thus, we create a variational framework to acquire the deformation that the tissues undergo due to an applied force. Then, this information is used in a learning system to find the nonlinear relationship between the given data and the applied force. We carried out experiments with in-vivo and ex-vivo data and combined statistical, graphical and perceptual analyses to demonstrate the strength of our solution. Finally, we explore robotic cardiac surgery, which allows carrying out complex procedures including Off-Pump Coronary Artery Bypass Grafting (OPCABG). This procedure avoids the associated complications of using Cardiopulmonary Bypass (CPB) since the heart is not arrested while performing the surgery on a beating heart. Thus, surgeons have to deal with a dynamic target that compromisetheir dexterity and the surgery's precision. To compensate the heart motion, we propase a solution composed of three elements: an energy function to estimate the 3D heart motion, a specular highlight detection strategy and a prediction approach for increasing the robustness of the solution. We conduct evaluation of our solution using phantom and realistic datasets. We conclude the thesis by reporting our findings on these three applications and highlight the dependency between motion estimation and motion understanding at any dynamic event, particularly in clinical scenarios.L’estimació i comprensió del moviment dins d’una seqüència d’imatges és un tema central en la visió per ordinador, el que genera un gran interès perquè vivim en un entorn ple d’esdeveniments dinàmics. Per aquest motiu és considerat com un component natural i factor clau dins d’un ampli ventall d’aplicacions, el qual inclou el reconeixement d’objectes, la reconstrucció de formes tridimensionals, la navegació autònoma i el diagnòstic de malalties. En particular, ens situem en l’àmbit mèdic en el qual la comprensió del cos humà, amb finalitats clíniques, requereix l’obtenció de patrons complexos de moviment dels òrgans. Aquesta és, en general, una tasca difícil quan s’utilitzen només dades de tipus visual. En aquesta tesi afrontem el problema plantejant-nos la pregunta - Com es pot aconseguir una estimació realista del moviment amb l’objectiu d’oferir una millor comprensió clínica? La tesi se centra en la resposta mitjançant l’ús d’una formulació variacional com a base per entendre un dels moviments més complexos del cos humà, el del cor, a través de tres aplicacions: (i) estimació del moviment cardíac per al diagnòstic, (ii) estimació de forces i (iii) predicció del moviment, orientant-se les dues últimes en cirurgia robòtica. En primer lloc, ens centrem en un tema principal en la imatge cardíaca, que és l’estimació del moviment cardíac. L’objectiu principal és oferir als metges mesures objectives i comprensibles per ajudar-los en el diagnòstic de les malalties cardiovasculars. Fem servir dades d’ultrasons ultraràpids i eines per al moviment d’imatges procedents de diverses àrees, com ara l’anàlisi de baix rang i la deformació variacional, per fer una estimació realista del moviment cardíac. La importància rau en que, en prendre les dades de baix rang amb una penalització acurada, es poden crear sinergies en aquest problema variacional complex. Mitjançant acurats experiments numèrics, amb dades realístiques i simulades, hem demostrat com les nostres propostes solucionen deformacions complexes. Després passem del diagnòstic a la cirurgia robòtica, on els cirurgians realitzen procediments delicats remotament, a través de manipuladors robòtics, sense interactuar directament amb els pacients. Com a conseqüència, no tenen la percepció de la força com a resposta, que és un sentit primari important per augmentar la transparència entre el cirurgià i el pacient, per evitar lesions i per reduir la càrrega de treball mental. Resolem aquest problema seguint els principis de conservació de la mecànica del medi continu, en els quals està clar que el canvi en la forma d’un objecte elàstic és directament proporcional a la força aplicada. Per això hem creat un marc variacional que adquireix la deformació que pateixen els teixits per l’aplicació d’una força. Aquesta informació s’utilitza en un sistema d’aprenentatge, per trobar la relació no lineal entre les dades donades i la força aplicada. Hem dut a terme experiments amb dades in-vivo i ex-vivo i hem combinat l’anàlisi estadístic, gràfic i de percepció que demostren la robustesa de la nostra solució. Finalment, explorem la cirurgia cardíaca robòtica, la qual cosa permet realitzar procediments complexos, incloent la cirurgia coronària sense bomba (off-pump coronary artery bypass grafting o OPCAB). Aquest procediment evita les complicacions associades a l’ús de circulació extracorpòria (Cardiopulmonary Bypass o CPB), ja que el cor no s’atura mentre es realitza la cirurgia. Això comporta que els cirurgians han de tractar amb un objectiu dinàmic que compromet la seva destresa i la precisió de la cirurgia. Per compensar el moviment del cor, proposem una solució composta de tres elements: un funcional d’energia per estimar el moviment tridimensional del cor, una estratègia de detecció de les reflexions especulars i una aproximació basada en mètodes de predicció, per tal d’augmentar la robustesa de la solució. L’avaluació de la nostra solució s’ha dut a terme mitjançant conjunts de dades sintètiques i realistes. La tesi conclou informant dels nostres resultats en aquestes tres aplicacions i posant de relleu la dependència entre l’estimació i la comprensió del moviment en qualsevol esdeveniment dinàmic, especialment en escenaris clínics.Postprint (published version

Efficient local search for Pseudo Boolean Optimization

Algorithms and the Foundations of Software technolog

Dagstuhl News January - December 2006

"Dagstuhl News" is a publication edited especially for the members of the Foundation "Informatikzentrum Schloss Dagstuhl" to thank them for their support. The News give a summary of the scientific work being done in Dagstuhl. Each Dagstuhl Seminar is presented by a small abstract describing the contents and scientific highlights of the seminar as well as the perspectives or challenges of the research topic