Related papers: Uniform generation of large traces
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
Many large language models (LLMs) use reasoning to generate responses but do not reveal their full reasoning traces (a.k.a. chains of thought), instead outputting only final answers and brief reasoning summaries. To demonstrate that hiding…
Consider infinite random words over a finite alphabet where the letters occur as an i.i.d. sequence according to some arbitrary distribution on the alphabet. The expectation and the variance of the waiting time for the first completed…
This paper proposes a model, the linear model, for randomly generating logic programs with low density of rules and investigates statistical properties of such random logic programs. It is mathematically shown that the average number of…
Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…
In classical asynchronous distributed systems composed of a fixed number n of processes where some proportion may fail by crashing, many objects do not have a wait-free linearizable implementation (e.g. stacks, queues, etc.). It has been…
We revisit a fundamental problem in string matching: given a pattern of length m and a text of length n, both over an alphabet of size $\sigma$, compute the Hamming distance between the pattern and the text at every location. Several…
In the realm of motion generation, the creation of long-duration, high-quality motion sequences remains a significant challenge. This paper presents our groundbreaking work on "Infinite Motion", a novel approach that leverages long text to…
We consider filtering for a continuous-time, or asynchronous, stochastic system where the full distribution over states is too large to be stored or calculated. We assume that the rate matrix of the system can be compactly represented and…
Recently, a plethora of works have proposed inference-time algorithms (e.g. best-of-n), which incorporate verifiers to assist the generation process. Their quality-efficiency trade-offs have been empirically benchmarked on a variety of…
In this article we describe an algorithm that can be applied for the generation of various classes of maps on orientable surfaces. It uses existing generators for abstract graphs and combines them with an efficient embedding and isomorphism…
In this paper we introduce a word embedding composition method based on the intuitive idea that a fair embedding representation for a given set of words should satisfy that the new vector will be at the same distance of the vector…
We consider several problems in the field of distributed optimization and hypothesis testing. We show how to obtain convergence times for these problems that scale linearly with the total number of nodes in the network by using a recent…
Let $G$ be a finite group generated by $k$ elements. The well-known product replacement algorithm provides an effective method for sampling generating sets of $G$. We study a refinement of this algorithm that is designed to output…
Machine-translated text plays an important role in modern life by smoothing communication from various communities using different languages. However, unnatural translation may lead to misunderstanding, a detector is thus needed to avoid…
Consider a universal Turing machine that produces a partial or total function (or a binary stream), based on the answers to the binary queries that it makes during the computation. We study the probability that the machine will produce a…
We introduce a novel definition of approximate palindromes in strings, and provide an algorithm to find all maximal approximate palindromes in a string with up to $k$ errors. Our definition is based on the usual edit operations of…
We show that every trace monoid is isomorphic to a sub-monoid of a monoid of word vectors. It provides a concrete representation of the elements of a trace monoid as processes associated with a resource sharing mechanism. We illustrate this…
The completely bounded trace and spectral norms in finite dimensions are shown to be expressible by semidefinite programs. This provides an efficient method by which these norms may be both calculated and verified, and gives alternate…