The recent publications in the field of computational logic and mathematics reveal a strong trend towards the development of more efficient algorithms and novel representations for solving complex problems. A significant focus is on enhancing the computational efficiency of algorithms, whether through innovative matrix representations for Boolean Satisfiability (SAT) problems, active learning techniques for pomset recognizers, or novel approaches to computing Collatz sequence stopping times. Additionally, there's a notable interest in the modular counting of solutions in Constraint Satisfaction Problems (CSPs) and the exploration of ordinal ranks in Monadic Second-Order Logic (MSO) over the full binary tree. The application of neural networks to solve nonograms and the development of cube-based isomorph-free finite model finding algorithms represent the integration of machine learning and computational logic. Furthermore, SAT-based techniques for finding lexicographically smallest finite models and the evaluation of SAT and SMT solvers on large-scale Sudoku puzzles underscore the ongoing evolution of logical solvers. Lastly, the verified and optimized implementation of orthologic proof search highlights the importance of formal verification in ensuring the correctness and efficiency of computational methods.

Noteworthy Papers

• Inverse Intersections for Boolean Satisfiability Problems: Introduces a matrix representation for SAT problems and a polynomial-time algorithm for searching through the set of valid assignments.
• Active Learning Techniques for Pomset Recognizers: Enhances learning algorithms for pomset recognizers with a new counter-example analysis procedure and a finite test suite for general equivalence.
• Efficient Computation of Collatz Sequence Stopping Times: Presents a novel algorithm that significantly improves computational efficiency for computing Collatz sequence stopping times.
• Modular Counting CSP: Reductions and Algorithms: Advances the understanding of counting solutions modulo an integer in CSPs, providing a solution algorithm for the case p=2.
• A Dichotomy Theorem for Ordinal Ranks in MSO: Establishes a dichotomy theorem for ordinal ranks in MSO, with potential applications in ordinal-related problems.
• Solving nonograms using Neural Networks: Combines heuristic algorithms with neural networks for solving nonograms, achieving the best results.
• Cube-based Isomorph-free Finite Model Finding: Develops a novel algorithm for isomorphism-free enumeration of finite models, significantly faster than traditional methods.
• SAT-Based Techniques for Lexicographically Smallest Finite Models: Proposes SAT-based techniques for finding lexicographically smallest finite models, facilitating the cataloging of algebraic structures.
• Evaluating SAT and SMT Solvers on Large-Scale Sudoku Puzzles: Demonstrates the superior performance of modern SMT solvers over classical SAT solvers in solving large-scale Sudoku puzzles.
• Verified and Optimized Implementation of Orthologic Proof Search: Reports on the development of an optimized and verified decision procedure for orthologic, with a quadratic runtime.