Related papers: On Improving the Backjump Level in PB Solvers
Recent research in areas such as SAT solving and Integer Linear Programming has shown that the performances of a single arbitrarily efficient solver can be significantly outperformed by a portfolio of possibly slower on-average solvers. We…
The past three decades have witnessed notable success in designing efficient SAT solvers, with modern solvers capable of solving industrial benchmarks containing millions of variables in just a few seconds. The success of modern SAT solvers…
In life-testing experiments, it is often of interest to predict unobserved future failure times based on observed early failure times. A point best linear unbiased predictor (BLUP) has been developed in this context by Kaminsky and Nelson…
In various scenarios, a single phase of modelling and solving is either not sufficient or not feasible to solve the problem at hand. A standard approach to solving AI planning problems, for example, is to incrementally extend the planning…
Conflict-Driven Clause Learning (CDCL) is the mainstream framework for solving the Satisfiability problem (SAT), and CDCL solvers typically rely on various heuristics, which have a significant impact on their performance. Modern CDCL…
Automated reasoners, such as SAT/SMT solvers and first-order provers, are becoming the backbones of rigorous systems engineering, being used for example in applications of system verification, program synthesis, and cybersecurity.…
Original and learnt clauses in Conflict-Driven Clause Learning (CDCL) SAT solvers often contain redundant literals. This may have a negative impact on performance because redundant literals may deteriorate both the effectiveness of Boolean…
We propose a new algorithm for Promise Constraint Satisfaction Problems PCSPs). It is a combination of the $\textbf{C}$onstraint Basic $\textbf{L}$P relaxation and the $\textbf{A}$ffine I$\textbf{P}$ relaxation (CLAP). We give a…
Boolean Satisfiability (SAT) is a well-known NP-complete problem. Despite this theoretical hardness, SAT solvers based on Conflict Driven Clause Learning (CDCL) can solve large SAT instances from many important domains. CDCL learns clauses…
A Pseudo-Boolean (PB) constraint is a linear inequality constraint over Boolean literals. One of the popular, efficient ideas used to solve PB-problems (a set of PB-constraints) is to translate them to SAT instances (encodings) via, for…
Finding good branching orders is key to solving SAT problems efficiently, but finding such branching orders is a difficult problem. Using a learning based approach to predict a good branching order before solving, therefore, has potential.…
Efficient implementations of DPLL with the addition of clause learning are the fastest complete Boolean satisfiability solvers and can handle many significant real-world problems, such as verification, planning and design. Despite its…
This thesis investigates the extent to which the optimal value of a constraint satisfaction problem (CSP) can be approximated by some sentence of fixed point logic with counting (FPC). It is known that, assuming $\mathsf{P} \neq…
We investigate the theoretical complexity of branch-and-bound (BB) and cutting plane (CP) algorithms for mixed-integer optimization. In particular, we study the relative efficiency of BB and CP, when both are based on the same family of…
Modern conflict-driven clause learning (CDCL) SAT solvers are very good in solving conjunctive normal form (CNF) formulas. However, some application problems involve lots of parity (xor) constraints which are not necessarily efficiently…
Two essential ingredients of modern mixed-integer programming (MIP) solvers are diving heuristics that simulate a partial depth-first search in a branch-and-bound search tree and conflict analysis of infeasible subproblems to learn valid…
Quantum linear system solvers typically realize the inverse map as a polynomial transformation of the spectrum, so their practical cost hinges on implementing this transformation at a low polynomial degree. We introduce constrained optimal…
The design of efficient and generic algorithms for solving combinatorial optimization problems has been an active field of research for many years. Standard exact solving approaches are based on a clever and complete enumeration of the…
In Verification and in (optimal) AI Planning, a successful method is to formulate the application as boolean satisfiability (SAT), and solve it with state-of-the-art DPLL-based procedures. There is a lack of understanding of why this works…
In this paper we begin by discussing the simple bilevel programming problem (SBP) and its extension the simple mathematical programming problem under equilibrium constraints (SMPEC). Here we first define both these problems and study their…