SUNNY-CP and the MiniZinc Challenge

In Constraint Programming (CP) a portfolio solver combines a variety of different constraint solvers for solving a given problem. This fairly recent approach enables to significantly boost the performance of single solvers, especially when multicore architectures are exploited. In this work we give a brief overview of the portfolio solver sunny-cp, and we discuss its performance in the MiniZinc Challenge---the annual international competition for CP solvers---where it won two gold medals in 2015 and 2016. Under consideration in Theory and Practice of Logic Programming (TPLP)Comment: Under consideration in Theory and Practice of Logic Programming (TPLP

A Comparison of SAT Encodings for Acyclicity of Directed Graphs

Many practical applications require synthesizing directed graphs that satisfy the acyclic constraint along with some side constraints. Several methods have been devised for encoding acyclicity of directed graphs into SAT, each of which is based on a cycle-detecting algorithm. The leaf-elimination encoding (LEE) repeatedly eliminates leaves from the graph, and judges the graph to be acyclic if the graph becomes empty at a certain time. The vertex-elimination encoding (VEE) exploits the property that the cyclicity of the resulting graph produced by the vertex-elimination operation entails the cyclicity of the original graph. While VEE is significantly smaller than the transitive-closure encoding for sparse graphs, it generates prohibitively large encodings for large dense graphs. This paper reports on a comparison study of four SAT encodings for acyclicity of directed graphs, namely, LEE using unary encoding for time variables (LEE-u), LEE using binary encoding for time variables (LEE-b), VEE, and a hybrid encoding which combines LEE-b and VEE. The results show that the hybrid encoding significantly outperforms the others

Automatic Detection of At-Most-One and Exactly-One Relations for Improved SAT Encodings of Pseudo-Boolean Constraints

Pseudo-Boolean (PB) constraints often have a critical role in constraint satisfaction and optimisation problems. Encoding PB constraints to SAT has proven to be an efficient approach in many applications, however care must be taken to encode them compactly and with good propagation properties. It has been shown that at-most-one (AMO) and exactly-one (EO) relations over subsets of the variables can be exploited in various encodings of PB constraints, improving their compactness and solving performance. In this paper we detect AMO and EO relations completely automatically and exploit them to improve SAT encodings that are based on Multi-Valued Decision Diagrams (MDDs). Our experiments show substantial reductions in encoding size and dramatic improvements in solving time thanks to automatic AMO and EO detection

Boosting Answer Set Optimization with Weighted Comparator Networks

Answer set programming (ASP) is a paradigm for modeling knowledge intensive domains and solving challenging reasoning problems. In ASP solving, a typical strategy is to preprocess problem instances by rewriting complex rules into simpler ones. Normalization is a rewriting process that removes extended rule types altogether in favor of normal rules. Recently, such techniques led to optimization rewriting in ASP, where the goal is to boost answer set optimization by refactoring the optimization criteria of interest. In this paper, we present a novel, general, and effective technique for optimization rewriting based on comparator networks, which are specific kinds of circuits for reordering the elements of vectors. The idea is to connect an ASP encoding of a comparator network to the literals being optimized and to redistribute the weights of these literals over the structure of the network. The encoding captures information about the weight of an answer set in auxiliary atoms in a structured way that is proven to yield exponential improvements during branch-and-bound optimization on an infinite family of example programs. The used comparator network can be tuned freely, e.g., to find the best size for a given benchmark class. Experiments show accelerated optimization performance on several benchmark problems.Comment: 36 page

Related-Key Differential Analysis of the AES

The Advanced Encryption Standard (AES) is considered to be the most important and widely deployed symmetric primitive. While the cipher was designed to be immune against differential and other classical attacks, this immunity does not hold in the related-key setting, and various related-key attacks have appeared over time. This work presents tools and algorithms to search for related-key distinguishers and attacks of differential nature against the AES. First, we propose two entirely different approaches to find optimal truncated differential characteristics and bounds on the minimum number of active S-boxes for all variants of the AES. In the first approach, we propose a simple MILP model that handles better linear inconsistencies with respect to the AES system of equations and that compares particularly well to previous tool-based approaches to solve this problem. The main advantage of this tool is that it can easily be used as the core algorithm to search for any attack on AES exploiting related-key differentials. Then, we design a fast and low-memory algorithm based on dynamic programming that has a very simple to understand complexity analysis and does not depend on any generic solver. This second algorithm provides us useful insight on the related-key differential search problem for AES and shows that the search space is not as big as one would expect. Finally, we build on the top of our MILP model a fully automated tool to search for the best differential MITM attacks against the AES. We apply our tool on AES-256 and find an attack on 13 rounds with only two related keys. This attack can be seen as the best known cryptanalysis against this variant if only 2 related keys are permitted

Algorithms for the restricted linear coloring arrangement problem

The aim of this project is to develop efficient algorithms for solving or approximating the Minimum Restricted Linear Coloring Arrangement Problem. It is the first approach to its algorithms, and we will face the problem from different perspectives: constraint programming, backtracking, greedy, and genetic algorithms. As a second goal we are interested in providing theoretical results for particular graphs

Learning SAT Encodings for Constraint Satisfaction Problems

Constraint programming addresses many interesting and challenging problems in our world, including recent applications to contexts as diverse as allocating refugee relief funds, short-term mine planning and hardware circuit design. Users define their problems in high-level modelling languages which include descriptive global constraints. One of the most effective ways to solve constraint satisfaction problems (CSPs) is by translating them into instances of the Boolean Satisfiability Problem (SAT). For some global constraints in CSPs there exist many algorithms which encode the constraint into SAT; choosing an appropriate SAT encoding can alter the ultimate solving time dramatically. We investigate the problem of selecting the best SAT encoding for pseudo-Boolean and linear integer constraints. Many machine learning techniques are explored, applied and evaluated to aid this selection. The result is a significant improvement in performance compared to the default choice and to the single best choice from a training set. The approach is successful even for previously unseen problem classes and it greatly outperforms a sophisticated general algorithm selection and configuration tool. This work provides a thorough empirical study and detailed analysis of each stage in the machine learning process as applied to choosing SAT encodings. It does this in three phases: firstly by using generic CSP instance features to select an encoding per constraint type for each instance, then by introducing new features which focus on the constraint types in question, and finally by learning to select encodings for individual constraints. We find that even generic instance features can produce good predictions, but that the specialised features introduced give more robust performance especially when predicting for unseen problem classes. Training to predict per constraint shows potential and leads to better performance for some problem classes, but per-instance selection is still competitive across the corpus of problems as a whole