Certifying Correctness for Combinatorial Algorithms : by Using Pseudo-Boolean Reasoning

Over the last decades, dramatic improvements in combinatorialoptimisation algorithms have significantly impacted artificialintelligence, operations research, and other areas. These advances,however, are achieved through highly sophisticated algorithms that aredifficult to verify and prone to implementation errors that can causeincorrect results. A promising approach to detect wrong results is touse certifying algorithms that produce not only the desired output butalso a certificate or proof of correctness of the output. An externaltool can then verify the proof to determine that the given answer isvalid. In the Boolean satisfiability (SAT) community, this concept iswell established in the form of proof logging, which has become thestandard solution for generating trustworthy outputs. The problem isthat there are still some SAT solving techniques for which prooflogging is challenging and not yet used in practice. Additionally,there are many formalisms more expressive than SAT, such as constraintprogramming, various graph problems and maximum satisfiability(MaxSAT), for which efficient proof logging is out of reach forstate-of-the-art techniques.This work develops a new proof system building on the cutting planesproof system and operating on pseudo-Boolean constraints (0-1 linearinequalities). We explain how such machine-verifiable proofs can becreated for various problems, including parity reasoning, symmetry anddominance breaking, constraint programming, subgraph isomorphism andmaximum common subgraph problems, and pseudo-Boolean problems. Weimplement and evaluate the resulting algorithms and a verifier for theproof format, demonstrating that the approach is practical for a widerange of problems. We are optimistic that the proposed proof system issuitable for designing certifying variants of algorithms inpseudo-Boolean optimisation, MaxSAT and beyond

Generalizing Boolean Satisfiability III: Implementation

This is the third of three papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high-performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal has been to define a representation in which this structure is apparent and can be exploited to improve computational performance. The first paper surveyed existing work that (knowingly or not) exploited problem structure to improve the performance of satisfiability engines, and the second paper showed that this structure could be understood in terms of groups of permutations acting on individual clauses in any particular Boolean theory. We conclude the series by discussing the techniques needed to implement our ideas, and by reporting on their performance on a variety of problem instances

Solving hard industrial combinatorial problems with SAT

The topic of this thesis is the development of SAT-based techniques and tools for solving industrial combinatorial problems. First, it describes the architecture of state-of-the-art SAT and SMT Solvers based on the classical DPLL procedure. These systems can be used as black boxes for solving combinatorial problems. However, sometimes we can increase their efficiency with slight modifications of the basic algorithm. Therefore, the study and development of techniques for adjusting SAT Solvers to specific combinatorial problems is the first goal of this thesis. Namely, SAT Solvers can only deal with propositional logic. For solving general combinatorial problems, two different approaches are possible: - Reducing the complex constraints into propositional clauses. - Enriching the SAT Solver language. The first approach corresponds to encoding the constraint into SAT. The second one corresponds to using propagators, the basis for SMT Solvers. Regarding the first approach, in this document we improve the encoding of two of the most important combinatorial constraints: cardinality constraints and pseudo-Boolean constraints. After that, we present a new mixed approach, called lazy decomposition, which combines the advantages of encodings and propagators. The other part of the thesis uses these theoretical improvements in industrial combinatorial problems. We give a method for efficiently scheduling some professional sport leagues with SAT. The results are promising and show that a SAT approach is valid for these problems. However, the chaotical behavior of CDCL-based SAT Solvers due to VSIDS heuristics makes it difficult to obtain a similar solution for two similar problems. This may be inconvenient in real-world problems, since a user expects similar solutions when it makes slight modifications to the problem specification. In order to overcome this limitation, we have studied and solved the close solution problem, i.e., the problem of quickly finding a close solution when a similar problem is considered

Efficient local search for Pseudo Boolean Optimization

Algorithms and the Foundations of Software technolog

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Integrating protein structural information

Dissertação apresentada para obtenção de Grau de Doutor em Bioquímica,Bioquímica Estrutural, pela Universidade Nova de Lisboa, Faculdade de Ciências e TecnologiaThe central theme of this work is the application of constraint programming and other artificial intelligence techniques to protein structure problems, with the goal of better combining experimental data with structure prediction methods. Part one of the dissertation introduces the main subjects of protein structure and constraint programming, summarises the state of the art in the modelling of protein structures and complexes, sets the context for the techniques described later on, and outlines the main points of the thesis: the integration of experimental data in modelling. The first chapter, Protein Structure, introduces the reader to the basic notions of amino acid structure, protein chains, and protein folding and interaction. These are important concepts to understand the work described in parts two and three. Chapter two, Protein Modelling, gives a brief overview of experimental and theoretical techniques to model protein structures. The information in this chapter provides the context of the investigations described in parts two and three, but is not essential to understanding the methods developed. Chapter three, Constraint Programming, outlines the main concepts of this programming technique. Understanding variable modelling, the notions of consistency and propagation, and search methods should greatly help the reader interested in the details of the algorithms, as described in part two of this book. The fourth chapter, Integrating Structural Information, is a summary of the thesis proposed here. This chapter is an overview of the objectives of this work, and gives an idea of how the algorithms developed here could help in modelling protein structures. The main goal is to provide a flexible and continuously evolving framework for the integration of structural information from a diversity of experimental techniques and theoretical predictions. Part two describes the algorithms developed, which make up the main original contribution of this work. This part is aimed especially at developers interested in the details of the algorithms, in replicating the results, in improving the method or in integrating them in other applications. Biochemical aspects are dealt with briefly and as necessary, and the emphasis is on the algorithms and the code

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Enhanced online programming for industrial robots

The use of robots and automation levels in the industrial sector is expected to grow, and is driven by the on-going need for lower costs and enhanced productivity. The manufacturing industry continues to seek ways of realizing enhanced production, and the programming of articulated production robots has been identified as a major area for improvement. However, realizing this automation level increase requires capable programming and control technologies. Many industries employ offline-programming which operates within a manually controlled and specific work environment. This is especially true within the high-volume automotive industry, particularly in high-speed assembly and component handling. For small-batch manufacturing and small to medium-sized enterprises, online programming continues to play an important role, but the complexity of programming remains a major obstacle for automation using industrial robots. Scenarios that rely on manual data input based on real world obstructions require that entire production systems cease for significant time periods while data is being manipulated, leading to financial losses. The application of simulation tools generate discrete portions of the total robot trajectories, while requiring manual inputs to link paths associated with different activities. Human input is also required to correct inaccuracies and errors resulting from unknowns and falsehoods in the environment. This study developed a new supported online robot programming approach, which is implemented as a robot control program. By applying online and offline programming in addition to appropriate manual robot control techniques, disadvantages such as manual pre-processing times and production downtimes have been either reduced or completely eliminated. The industrial requirements were evaluated considering modern manufacturing aspects. A cell-based Voronoi generation algorithm within a probabilistic world model has been introduced, together with a trajectory planner and an appropriate human machine interface. The robot programs so achieved are comparable to manually programmed robot programs and the results for a Mitsubishi RV-2AJ five-axis industrial robot are presented. Automated workspace analysis techniques and trajectory smoothing are used to accomplish this. The new robot control program considers the working production environment as a single and complete workspace. Non-productive time is required, but unlike previously reported approaches, this is achieved automatically and in a timely manner. As such, the actual cell-learning time is minimal

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing