Related papers: Small Depth Proof Systems
Optical neural network (ONN) is emerging as an attractive proposal for machine-learning applications, enabling high-speed computation with low-energy consumption. However, there are several challenges in applying ONN for industrial…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
The depth of quantum circuits is a critical factor when running them on state-of-the-art quantum devices due to their limited coherence times. Reducing circuit depth decreases noise in near-term quantum computations and reduces overall…
Large language models are increasingly capable at closed-world mathematical reasoning, but research assistance also requires source-grounded use of the literature. When a proof reaches a non-trivial step, a useful assistant should determine…
The subject logic in computer science should entail proof theoretic applications. So the question arises whether open problems in computational complexity can be solved by advanced proof theoretic techniques. In particular, consider the…
While implementing a quantum algorithm it is crucial to reduce the quantum resources, in order to obtain the desired computational advantage. For most fault-tolerant quantum error-correcting codes the cost of implementing the non-Clifford…
{log} (read 'setlog') was born as a Constraint Logic Programming (CLP) language where sets and binary relations are first-class citizens, thus fostering set programming. Internally, {log} is a constraint satisfiability solver implementing…
We show a tight lower bound of $\Omega(N \log\log N)$ on the number of transmissions required to compute the parity of $N$ input bits with constant error in a noisy communication network of $N$ randomly placed sensors, each having one input…
Automated theorem proving is essential for the formal verification of safety-critical systems. As the corpus of formal proofs grows, a natural paradigm is to learn from existing proofs. However, current learning-based approaches…
In the article ''On the (Non) NP-Hardness of Computing Circuit Complexity'', Murray and Williams imply the PARTITION decision problem is not known to be NP-hard via $2^{n^{o(1)}}$-size AC0 reductions. In this note, we show PARTITION is…
We consider a model of computation motivated by possible limitations on quantum computers. We have a linear array of n wires, and we may perform operations only on pairs of adjacent wires. Our goal is to build a circuits that perform…
The ability of Large Language Models (LLMs) to perform reasoning tasks such as deduction has been widely investigated in recent years. Yet, their capacity to generate proofs-faithful, human-readable explanations of why conclusions…
We observe today a large diversity of proof systems. This diversity has the negative consequence that a lot of theorems are proved many times. Unlike programming languages, it is difficult for these systems to co-operate because they do not…
Language models have become increasingly powerful tools for formal mathematical reasoning. However, most existing approaches rely exclusively on either large general-purpose models or smaller specialized models, each with distinct…
Chain of thought is a natural inference-time method for increasing the computational power of transformer-based large language models (LLMs), but comes at the cost of sequential decoding. Are there more efficient alternatives to expand a…
Reversible computation is one of the most promising emerging technologies of the future. The usage of reversible circuits in computing devices can lead to a significantly lower power consumption. In this paper we study reversible logic…
Generalizations of numeration systems in which N is recognizable by a finite automaton are obtained by describing a lexicographically ordered infinite regular language L over a finite alphabet A. For these systems, we obtain a…
We study lower bounds on adaptive sensing algorithms for recovering low rank matrices using linear measurements. Given an $n \times n$ matrix $A$, a general linear measurement $S(A)$, for an $n \times n$ matrix $S$, is just the inner…
One of the major open problems in complexity theory is to demonstrate an explicit function which requires super logarithmic depth, a.k.a, the $\mathbf{P}$ versus $\mathbf{NC^1}$ problem. The current best depth lower bound is $(3-o(1))\cdot…
We establish a generic form of hardness amplification for the approximability of constant-depth Boolean circuits by polynomials. Specifically, we show that if a Boolean circuit cannot be pointwise approximated by low-degree polynomials to…