Related papers: Advances in Symmetry Breaking for SAT Modulo Theor…
Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models…
We present a clear and mathematically simple procedure explaining spontaneous symmetry breaking in quantum mechanical systems. The procedure is applicable to a wide range of models and can be easily used to explain the existence of a…
To enhance the scalability and performance of the traditional finite-difference time-domain (FDTD) methods, a three-dimensional summation-by-parts simultaneous approximation term (SBP-SAT) FDTD method is developed to solve complex…
An overview of current experimental bounds on $CPT$ violation in neutral meson mixing is given. New values for the $CPT$ asymmetry in the $B^0$ and $B_s^0$ systems are deduced from published BaBar, Belle and LHCb results. With dedicated…
This paper introduces a new approach to solving a continuous-time version of the multi-agent path finding problem. The algorithm translates the problem into an extension of the classical Boolean satisfiability problem, satisfiability modulo…
Over the past several decades, CDCL SAT solvers have proven remarkably effective on large industrial formulas, despite SAT being NP-complete and widely believed to be intractable. While considerable empirical research has been done on…
Modern conflict-driven clause-learning (CDCL) Boolean SAT solvers provide efficient automatic analysis of real-world feature models (FM) of systems ranging from cars to operating systems. It is well-known that solver-based analysis of…
In the contexts of automated reasoning and formal verification, important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for several theories…
In nature, symmetry governs regularities, while symmetry breaking brings texture. In artificial neural networks, symmetry has been a central design principle to efficiently capture regularities in the world, but the role of symmetry…
The distribution of overlaps of solutions of a random CSP is an indicator of the overall geometry of its solution space. For random $k$-SAT, nonrigorous methods from Statistical Physics support the validity of the ``one step replica…
Answer set programming (ASP) is a paradigm for declarative problem solving where problems are first formalized as rule sets, i.e., answer-set programs, in a uniform way and then solved by computing answer sets for programs. The…
The pattern of spontaneous chiral symmetry breaking (CSB) in confining background fields is analyzed. It is explicitly demonstrated how to get the inverse square root large proper time asymptotic of the operator product expansion which is…
In the Constraint Satisfaction Problem (CSP for short) the goal is to decide the existence of a homomorphism from a given relational structure $G$ to a given relational structure $H$. If the structure $H$ is fixed and $G$ is the only input,…
Symmetries occur naturally in CSP or SAT problems and are not very difficult to discover, but using them to prune the search space tends to be very challenging. Indeed, this usually requires finding specific elements in a group of…
Symmetry handling inequalities (SHIs) are an appealing and popular tool for handling symmetries in integer programming. Despite their practical application, little is known about their interaction with optimization problems. This article…
In a previous paper, we proposed a unique physically implemented type simulator for combinatorial optimization problems, called the spontaneous symmetry breaking machine (SSBM). In this paper, we first report the results of experimental…
The Boolean satisfiability problem (SAT) is a well-known example of monotonic reasoning, of intense practical interest due to fast solvers, complemented by rigorous fine-grained complexity results. However, for non-monotonic reasoning,…
This paper introduces SATFuL, a SAT solver for fuzzy logics. In contrast to the Boolean case, for which numerous SAT solvers exist, the SAT problem for fuzzy logics has attracted less attention, even though these tools have interesting…
We propose a new type of symmetry breaking mechanism that takes boundaries into account, and show how it can detect surface modes by interpreting them as the order parameter associated with a generalized symmetry breaking. We argue that…
Set constraints provide a highly general way to formulate program analyses. However, solving arbitrary boolean combinations of set constraints is NEXPTIME-hard. Moreover, while theoretical algorithms to solve arbitrary set constraints…