相关论文: Rethinking Circuit Completeness in Language Models…

Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…

It is well-known that typical word embedding methods such as Word2Vec and GloVe have the property that the meaning can be composed by adding up the embeddings (additive compositionality). Several theories have been proposed to explain…

Through considerable effort and intuition, several recent works have reverse-engineered nontrivial behaviors of transformer models. This paper systematizes the mechanistic interpretability process they followed. First, researchers choose a…

In literature, NAND and NOR are two logic gates that display functional completeness, hence regarded as Universal gates. So, the present effort is focused on exploring a library of universal gates in binary that are still unexplored in…

The best known size lower bounds against unrestricted circuits have remained around $3n$ for several decades. Moreover, the only known technique for proving lower bounds in this model, gate elimination, is inherently limited to proving…

In modern computers, computation is performed by assembling together sets of logic gates. Popular gates like AND, OR, XOR, processing two logic inputs and yielding one logic output, are often addressed as irreversible logic gates where the…

We perform formal verification of quantum circuits by integrating several techniques specialized to particular classes of circuits. Our verification methodology is based on the new notion of a reversible miter that allows one to leverage…

Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure…

LLMs have demonstrated strong performance in data-rich domains such as programming, yet their reliability in engineering tasks remains limited. Circuit analysis--requiring multimodal understanding and precise mathematical…

We consider the multiplicative complexity of Boolean functions with multiple bits of output, studying how large a multiplicative complexity is necessary and sufficient to provide a desired nonlinearity. For so-called $\Sigma\Pi\Sigma$…

Inaccurate circuits make possible the conservation of limited resources, such as energy. But effective design of such circuits requires an understanding of resulting tradeoffs between accuracy and design parameters, such as voltages and…

The Circuit Satisfiability (CSAT) problem, a variant of the Boolean Satisfiability (SAT) problem, plays a critical role in integrated circuit design and verification. However, existing SAT solvers, optimized for Conjunctive Normal Form…

This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…

Reversible circuits find applications in many areas of Computer Science including Quantum Computation. This paper examines the testability of an important subclass of reversible logic circuits that are composed of k-wire controlled NOT…

Transformers have become the foundational architecture for a broad spectrum of sequence modeling applications, underpinning state-of-the-art systems in natural language processing, vision, and beyond. However, their theoretical limitations…

Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…

We revisit the long-neglected problem of sequential circuit constructions from regular expressions. The class of languages that are recognized by sequential circuits is equivalent to the class of regular languages. This fact is shown in [5]…

There is an increasing interest in applying recent advances in AI to automated reasoning, as it may provide useful heuristics in reasoning over formalisms in first-order, second-order, or even meta-logics. To facilitate this research, we…

In this study, we construct the quantum reversible counterparts of the logical AND, OR, XOR, NOR, and NAND gates. We utilize a quantum Fourier transform (QFT)-based adder circuit that replicates the functionality of a digital half-adder,…

Chain-of-thought (CoT) reasoning improves the problem-solving ability of large language models (LLMs), but generated reasoning traces may not faithfully reflect the model's actual decision process. Existing CoT unfaithfulness detectors…