Related papers: BoolE: Exact Symbolic Reasoning via Boolean Equali…
Reasoning high-level abstractions from bit-blasted Boolean networks (BNs) such as gate-level netlists can significantly benefit functional verification, logic minimization, datapath synthesis, malicious logic identification, etc. Mostly,…
Boolean algebraic manipulation is at the core of logic synthesis in Electronic Design Automation (EDA) design flow. Existing methods struggle to fully exploit optimization opportunities, and often suffer from an explosive search space and…
Boolean equivalence allows Boolean networks with identical functionality to exhibit diverse graph structures. This gives more room for exploration in logic optimization, while also posing a challenge for tasks involving consistency between…
The proliferation of agentic systems has thrust the reasoning capabilities of AI into the forefront of contemporary machine learning. While it is known that there \emph{exist} neural networks which can reason through any Boolean task…
Neural networks have emerged as essential components in safety-critical applications -- these use cases demand complex, yet trustworthy computations. Binarized Neural Networks (BNNs) are a type of neural network where each neuron is…
The construction and analysis of an abstract reachability tree (ART) are the basis for a successful method for software verification. The ART represents unwindings of the control-flow graph of the program. Traditionally, a transition of the…
The rapid growth of the size and complexity in deep neural networks has sharply increased computational demands, challenging their efficient deployment in real-world scenarios. Boolean networks, constructed with logic gates, offer a…
In technology mapping, the quality of the final implementation heavily relies on the circuit structure after technology-independent optimization. Recent studies have introduced equality saturation as a novel optimization approach. However,…
Dense retrieval, which aims to encode the semantic information of arbitrary text into dense vector representations or embeddings, has emerged as an effective and efficient paradigm for text retrieval, consequently becoming an essential…
Automated standard cell library extension is crucial for maximizing Quality of Results (QoR) in modern VLSI design. We introduce CellE, a novel framework that leverages formal methods to achieve exhaustive discovery of functionally…
We study the statistical behaviour of reasoning probes in a stylized model of looped reasoning, given by Boolean circuits whose computational graph is a perfect $\nu$-ary tree ($\nu\ge 2$) and whose output is appended to the input and fed…
One of the main challenges in the verification of software systems is the analysis of unbounded data structures with dynamic memory allocation, such as linked data structures and arrays. We describe Bohne, a new analysis for verifying data…
A main open question in contemporary AI research is quantifying the forms of reasoning neural networks can perform when perfectly trained. This paper answers this by interpreting reasoning tasks as circuit emulation, where the gates define…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
Boolean optimization finds a wide range of application domains, that motivated a number of different organizations of Boolean optimizers since the mid 90s. Some of the most successful approaches are based on iterative calls to an NP oracle,…
This paper proposes a frequent itemset mining algorithm based on the Boolean matrix method, aiming to solve the storage and computational bottlenecks of traditional frequent pattern mining algorithms in high-dimensional and large-scale…
The dramatic improvements in combinatorial optimization algorithms over the last decades have had a major impact in artificial intelligence, operations research, and beyond, but the output of current state-of-the-art solvers is often hard…
Deep learning is computationally intensive, with significant efforts focused on reducing arithmetic complexity, particularly regarding energy consumption dominated by data movement. While existing literature emphasizes inference, training…
Boolean functions and networks are commonly used in the modeling and analysis of complex biological systems, and this paradigm is highly relevant in other important areas in data science and decision making, such as in the medical field and…
Interactive theorem provers, like Isabelle/HOL, Coq and Lean, have expressive languages that allow the formalization of general mathematical objects and proofs. In this context, an important goal is to reduce the time and effort needed to…