Related papers: On CNF Conversion for SAT and SMT Enumeration
For random CNF formulae with m clauses, n variables and an unrestricted number of literals per clause the transition from high to low satisfiability can be determined exactly for large n. The critical density m/n turns out to be strongly…
Constrained sampling and counting are two fundamental problems in artificial intelligence with a diverse range of applications, spanning probabilistic reasoning and planning to constrained-random verification. While the theory of these…
Incremental SAT and QBF solving potentially yields improvements when sequences of related formulas are solved. An incremental application is usually tailored towards some specific solver and decomposes a problem into incremental solver…
Though early successes of Statistical Machine Translation (SMT) systems are attributed in part to the explicit modelling of the interaction between any two source and target units, e.g., alignment, the recent Neural Machine Translation…
Analyzing a Feature Model (FM) and reasoning on the corresponding configuration space is a central task in Software Product Line (SPL) engineering. Problems such as deciding the satisfiability of the FM and eliminating inconsistent parts of…
Number Theoretic Transform (NTT) is an essential mathematical tool for computing polynomial multiplication in promising lattice-based cryptography. However, costly division operations and complex data dependencies make efficient and…
We analyse the complexity of the satisfiability problem, or similarly feasibility problem, (trSAT) for transformer encoders (TE), which naturally occurs in formal verification or interpretation, collectively referred to as formal reasoning.…
The following paper proposes a new approach to determine whether a logical (CNF) formula is satisfiable or not using probability theory methods. Furthermore, we will introduce an algorithm that speeds up the standard solution for (CNF-SAT)…
Spiking neural networks (SNNs) have shown advantages in computation and energy efficiency over traditional artificial neural networks (ANNs) thanks to their event-driven representations. SNNs also replace weight multiplications in ANNs with…
A class of discrete event synthesis problems can be reduced to solving language equations f . X ⊆ S, where F is the fixed component and S the specification. Sequential synthesis deals with FSMs when the automata for F and S are prefix…
In this paper we introduce the Wastewater Treatment Plant Problem, a real-world scheduling problem, and compare the performance of several tools on it. We show that, for a naive modeling, state-of-the-art SMT solvers outperform other tools…
We explore similarities and differences between widely-used threshold resummation formalisms, employing electroweak boson production as an instructive example. Resummations based on both full QCD and soft-collinear effective theory (SCET)…
We discuss the topic of unsatisfiability proofs in SMT, particularly with reference to quantifier free non-linear real arithmetic. We outline how the methods here do not admit trivial proofs and how past formalisation attempts are not…
SMT solvers have been used successfully as reasoning engines for automated verification and other applications based on automated reasoning. Current techniques for dealing with quantified formulas in SMT are generally incomplete, forcing…
Although Fourier series approximation is ubiquitous in computational physics owing to the Fast Fourier Transform (FFT) algorithm, efficient techniques for the fast evaluation of a three-dimensional truncated Fourier series at a set of…
Time series forecasting is essential for a wide range of real-world applications. Recent studies have shown the superiority of Transformer in dealing with such problems, especially long sequence time series input(LSTI) and long sequence…
By the MAXSAT problem, we are given a set $V$ of $m$ variables and a collection $C$ of $n$ clauses over $V$, i.e., a conjunctive normal form ($\textit{CNF}$) formula. We will seek a truth assignment to maximize the number of satisfied…
Supervised fine-tuning (SFT) on domain-specific data is the dominant approach for adapting foundation models to specialized tasks. However, it has been observed that SFT models tend to forget knowledge acquired during pretraining. In vision…
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…
Despite their practical success, modern seq2seq architectures are unable to generalize systematically on several SCAN tasks. Hence, it is not clear if SCAN-style compositional generalization is useful in realistic NLP tasks. In this work,…