A SAT Solver and Computer Algebra Attack on the Minimum Kochen-Specker Problem

One of the foundational results in quantum mechanics is the Kochen-Specker (KS) theorem, which states that any theory whose predictions agree with quantum mechanics must be contextual, i.e., a quantum observation cannot be understood as revealing a pre-existing value. The theorem hinges on the existence of a mathematical object called a KS vector system. While many KS vector systems are known to exist, the problem of finding the minimum KS vector system has remained stubbornly open for over 55 years, despite significant attempts by leading scientists and mathematicians. In this paper, we present a new method based on a combination of a SAT solver and a computer algebra system (CAS) to address this problem. Our approach improves the lower bound on the minimum number of vectors in a KS system from 22 to 24, and is about 35,000 times more efficient compared to the previous best computational methods. The increase in efficiency derives from the fact we are able to exploit the powerful combinatorial search-with-learning capabilities of a SAT solver together with the isomorph-free exhaustive generation methods of a CAS. The quest for the minimum KS vector system is motivated by myriad applications such as simplifying experimental tests of contextuality, zero-error classical communication, dimension witnessing, and the security of certain quantum cryptographic protocols. To the best of our knowledge, this is the first application of a novel SAT+CAS system to a problem in the realm of quantum foundations

A Time Leap Challenge for SAT Solving

We compare the impact of hardware advancement and algorithm advancement for SAT solving over the last two decades. In particular, we compare 20-year-old SAT-solvers on new computer hardware with modern SAT-solvers on 20-year-old hardware. Our findings show that the progress on the algorithmic side has at least as much impact as the progress on the hardware side.Comment: Authors' version of a paper which is to appear in the proceedings of CP'202

Goal reasoning for autonomous agents using automated planning

Mención Internacional en el título de doctorAutomated planning deals with the task of finding a sequence of actions, namely a plan, which achieves a goal from a given initial state. Most planning research consider goals are provided by a external user, and agents just have to find a plan to achieve them. However, there exist many real world domains where agents should not only reason about their actions but also about their goals, generating new ones or changing them according to the perceived environment. In this thesis we aim at broadening the goal reasoning capabilities of planningbased agents, both when acting in isolation and when operating in the same environment as other agents. In single-agent settings, we firstly explore a special type of planning tasks where we aim at discovering states that fulfill certain cost-based requirements with respect to a given set of goals. By computing these states, agents are able to solve interesting tasks such as find escape plans that move agents in to safe places, hide their true goal to a potential observer, or anticipate dynamically arriving goals. We also show how learning the environment’s dynamics may help agents to solve some of these tasks. Experimental results show that these states can be quickly found in practice, making agents able to solve new planning tasks and helping them in solving some existing ones. In multi-agent settings, we study the automated generation of goals based on other agents’ behavior. We focus on competitive scenarios, where we are interested in computing counterplans that prevent opponents from achieving their goals. We frame these tasks as counterplanning, providing theoretical properties of the counterplans that solve them. We also show how agents can benefit from computing some of the states we propose in the single-agent setting to anticipate their opponent’s movements, thus increasing the odds of blocking them. Experimental results show how counterplans can be found in different environments ranging from competitive planning domains to real-time strategy games.Programa de Doctorado en Ciencia y Tecnología Informática por la Universidad Carlos III de MadridPresidenta: Eva Onaindía de la Rivaherrera.- Secretario: Ángel García Olaya.- Vocal: Mark Robert

Proceedings of SAT Competition 2018 : Solver and Benchmark Descriptions

Non peer reviewe

Activity, context, and plan recognition with computational causal behavior models

Objective of this thesis is to answer the question "how to achieve efficient sensor-based reconstruction of causal structures of human behaviour in order to provide assistance?". To answer this question, the concept of Computational Causal Behaviour Models (CCBMs) is introduced. CCBM allows the specification of human behaviour by means of preconditions and effects and employs Bayesian filtering techniques to reconstruct action sequences from noisy and ambiguous sensor data. Furthermore, a novel approximative inference algorithm – the Marginal Filter – is introduced

MaxSAT Evaluation 2020 : Solver and Benchmark Descriptions

Non peer reviewe

SAT and CP: Parallelisation and Applications

This thesis is considered with the parallelisation of solvers which search for either an arbitrary, or an optimum, solution to a problem stated in some formal way. We discuss the parallelisation of two solvers, and their application in three chapters.In the first chapter, we consider SAT, the decision problem of propositional logic, and algorithms for showing the satisfiability or unsatisfiability of propositional formulas. We sketch some proof-theoretic foundations which are related to the strength of different algorithmic approaches. Furthermore, we discuss details of the implementations of SAT solvers, and show how to improve upon existing sequential solvers. Lastly, we discuss the parallelisation of these solvers with a focus on clause exchange, the communication of intermediate results within a parallel solver. The second chapter is concerned with Contraint Programing (CP) with learning. Contrary to classical Constraint Programming techniques, this incorporates learning mechanisms as they are used in the field of SAT solving. We present results from parallelising CHUFFED, a learning CP solver. As this is both a kind of CP and SAT solver, it is not clear which parallelisation approaches work best here. In the final chapter, we will discuss Sorting networks, which are data oblivious sorting algorithms, i. e., the comparisons they perform do not depend on the input data. Their independence of the input data lends them to parallel implementation. We consider the question how many parallel sorting steps are needed to sort some inputs, and present both lower and upper bounds for several cases

Generalising weighted model counting

Given a formula in propositional or (finite-domain) first-order logic and some non-negative weights, weighted model counting (WMC) is a function problem that asks to compute the sum of the weights of the models of the formula. Originally used as a flexible way of performing probabilistic inference on graphical models, WMC has found many applications across artificial intelligence (AI), machine learning, and other domains. Areas of AI that rely on WMC include explainable AI, neural-symbolic AI, probabilistic programming, and statistical relational AI. WMC also has applications in bioinformatics, data mining, natural language processing, prognostics, and robotics. In this work, we are interested in revisiting the foundations of WMC and considering generalisations of some of the key definitions in the interest of conceptual clarity and practical efficiency. We begin by developing a measure-theoretic perspective on WMC, which suggests a new and more general way of defining the weights of an instance. This new representation can be as succinct as standard WMC but can also expand as needed to represent less-structured probability distributions. We demonstrate the performance benefits of the new format by developing a novel WMC encoding for Bayesian networks. We then show how existing WMC encodings for Bayesian networks can be transformed into this more general format and what conditions ensure that the transformation is correct (i.e., preserves the answer). Combining the strengths of the more flexible representation with the tricks used in existing encodings yields further efficiency improvements in Bayesian network probabilistic inference. Next, we turn our attention to the first-order setting. Here, we argue that the capabilities of practical model counting algorithms are severely limited by their inability to perform arbitrary recursive computations. To enable arbitrary recursion, we relax the restrictions that typically accompany domain recursion and generalise circuits (used to express a solution to a model counting problem) to graphs that are allowed to have cycles. These improvements enable us to find efficient solutions to counting fundamental structures such as injections and bijections that were previously unsolvable by any available algorithm. The second strand of this work is concerned with synthetic data generation. Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm’s superiority over another. However, benchmarks are often limited and fail to reveal differences among the algorithms. First, we show how random instances of probabilistic logic programs (that typically use WMC algorithms for inference) can be generated using constraint programming. We also introduce a new constraint to control the independence structure of the underlying probability distribution and provide a combinatorial argument for the correctness of the constraint model. This model allows us to, for the first time, experimentally investigate inference algorithms on more than just a handful of instances. Second, we introduce a random model for WMC instances with a parameter that influences primal treewidth—the parameter most commonly used to characterise the difficulty of an instance. We show that the easy-hard-easy pattern with respect to clause density is different for algorithms based on dynamic programming and algebraic decision diagrams than for all other solvers. We also demonstrate that all WMC algorithms scale exponentially with respect to primal treewidth, although at differing rates

Proceedings of SAT Competition 2016 : Solver and Benchmark Descriptions

Peer reviewe