Related papers: Uniform generation of large traces
Replication is a key technique in the design of efficient and reliable distributed systems. As information grows, it becomes difficult or even impossible to store all information at every replica. A common approach to deal with this problem…
We consider random instances of non-convex perceptron problems in the high-dimensional limit of a large number of examples $M$ and weights $N$, with finite load $\alpha = M/N$. We develop a formalism based on replica theory to predict the…
The network inference problem consists of reconstructing the edge set of a network given traces representing the chronology of infection times as epidemics spread through the network. This problem is a paradigmatic representative of…
A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
We propose trace logic, an instance of many-sorted first-order logic, to automate the partial correctness verification of programs containing loops. Trace logic generalizes semantics of program locations and captures loop semantics by…
This article introduces an algorithm to draw random discrete uniform variables within a given range of size n from a source of random bits. The algorithm aims to be simple to implement and optimal both with regards to the amount of random…
A natural approach to software quality assurance consists in writing unit tests securing programmer-declared code invariants. Throughout the literature a great body of work has been devoted to tools and techniques automating this…
We present a nearly-linear time algorithm for counting and randomly generating simple graphs with a given degree sequence in a certain range. For degree sequence $(d_i)_{i=1}^n$ with maximum degree $d_{\max}=O(m^{1/4-\tau})$, our algorithm…
This paper studies trace-based equivalences for systems combining nondeterministic and probabilistic choices. We show how trace semantics for such processes can be recovered by instantiating a coalgebraic construction known as the…
Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…
We study a class of finite state machines, called \defi{$w$-matching machines}, which yield to simulate the behavior of pattern matching algorithms while searching for a pattern $w$. They can be used to compute the asymptotic speed, i.e.…
Large Language Models achieve next-token prediction by transporting a vectorized piece of text (prompt) across an accompanying embedding space under the action of successive transformer layers. The resulting high-dimensional trajectories…
We propose a method to exponentially speed up computation of various fingerprints, such as the ones used to compute similarity and rarity in massive data sets. Rather then maintaining the full stream of $b$ items of a universe $[u]$, such…
Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data…
In this paper, we derive an expression for the expected number of runs in a trace of a binary sequence $x \in \{0,1\}^n$ obtained by passing $x$ through a deletion channel that independently deletes each bit with probability $q$. We use…
We consider an \emph{approximate} version of the trace reconstruction problem, where the goal is to recover an unknown string $s\in\{0,1\}^n$ from $m$ traces (each trace is generated independently by passing $s$ through a probabilistic…
Consider the situation where a word is chosen probabilistically from a finite list. If an attacker knows the list and can inquire about each word in turn, then selecting the word via the uniform distribution maximizes the attacker's…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
We study the problem of generating interesting integer sequences with a combinatorial interpretation. For this we introduce a two-step approach. In the first step, we generate first-order logic sentences which define some combinatorial…