Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2112.02152

A reliable Turing machine

Ilir Çapuni·Peter Gács
View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider computations of a Turing machine subjected to noise. In every step, the action (the new state and the new content of the observed cell, the direction of the head movement) can differ from that prescribed by the transition function with a small probability (independently of previous such events). We construct a universal 1-tape Turing machine that for a low enough (constant) noise probability performs arbitrarily large computations. For this unavoidably, the input needs to be encoded -- by a simple code depending on its size. The work uses a technique familiar from reliable cellular automata, complemented by some new ones.

Explore related subjects

cs.CCmath.PR

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ilir Çapuni, Peter Gács. 2021-12-03. A reliable Turing machine. https://arxiv.org/abs/2112.02152

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Graph Homomorphisms and Universal Algebra

Constraint satisfaction problems are computational problems that naturally appear in many areas of theoretical computer science. One of the central themes is their computational complexity, and in particular the border between polynomial-time tractability and NP-hardness. In this course we introduce the universal-algebraic approach to study the computational complexity of finite-domain CSPs. The course covers in particular the cyclic terms and bounded width theorems. To keep the presentation accessible, we start the course in the tangible setting of directed graphs and graph homomorphism problems.

cs.CC↗
arXiv2026

The Exact Growth Rate of Space-Optimal Reversible Pebbling on Chains

We determine the exact time exponent of space-optimal reversible pebbling on chains as $1.331742379256310\ldots$. The growth rate of space-optimal reach exists as a limit and admits a variational formula. The same exponent governs complete computations at minimal space, uniformly in the chain length.

cs.CC↗
arXiv2026

Randomized query complexity can beat certificate complexity

A long-standing open question in query complexity asks whether there is a total Boolean function f with R(f) << C(f), where R(f) and C(f) denote its bounded-error randomized query complexity and certificate complexity, respectively. We construct a function with R(f) = O~(sqrt{C(f)}), which is optimal up to log factors. The same function also has $Q(f) = O~(C(f)^{1/4}), where Q(f) is the bounded-error quantum query complexity of f, which is also nearly optimal.

cs.CC↗