Related papers: Approximate NFA Universality and Related Problems …
We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…
Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…
We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.
The problem of compression in standard information theory consists of assigning codes as short as possible to numbers. Here we consider the problem of optimal coding -- under an arbitrary coding scheme -- and show that it predicts Zipf's…
Consider the finite regular language L_n = {w0 : w \in {0,1}^*, |w| \le n}. It was shown by Ambainis, Nayak, Ta-Shma and Vazirani that while this language is accepted by a deterministic finite automaton of size O(n), any one-way quantum…
The classical universal approximation (UA) theorem for neural networks establishes mild conditions under which a feedforward neural network can approximate a continuous function $f$ with arbitrary accuracy. A recent result shows that neural…
We introduce an algorithm for the uniform generation of infinite traces, i.e., infinite words up to commutation of some letters. The algorithm outputs on-the-fly approximations of a theoretical infinite trace, the latter being distributed…
Given an order of the underlying alphabet we can lift it to the states of a finite deterministic automaton: to compare states we use the order of the strings reaching them. When the order on strings is the co-lexicographic one \emph{and}…
The (Non-Preemptive) Throughput Maximization problem is a natural and fundamental scheduling problem. We are given $n$ jobs, where each job $j$ is characterized by a processing time and a time window, contained in a global interval $[0,T)$,…
Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
Optimal mechanism design enjoys a beautiful and well-developed theory, and also a number of killer applications. Rules of thumb produced by the field influence everything from how governments sell wireless spectrum licenses to how the major…
A complete deterministic finite (semi)automaton (DFA) with a set of states $Q$ is \emph{completely reachable} if every nonempty subset of $Q$ is the image of the action of some word applied to $Q$. The concept of completely reachable…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML…
An automaton is universal if it accepts every possible input. We study the notion of u-universality, which asserts that the automaton accepts every input starting with u. Universality and u-universality are both EXPTIME-hard for…
Weighted finite automata (WFA) are often used to represent probabilistic models, such as $n$-gram language models, since they are efficient for recognition tasks in time and space. The probabilistic source to be represented as a WFA,…
A word is called a reset word for a deterministic finite automaton if it maps all the states of the automaton to a unique state. Deciding about the existence of a reset word of a given maximum length for a given automaton is known to be an…
A central question in random matrix theory is universality. When an emergent phenomena is observed from a large collection of chosen random variables it is natural to ask if this behavior is specific to the chosen random variable or if the…
We prove that a random automaton with $n$ states and any fixed non-singleton alphabet is synchronizing with high probability (modulo an unpublished result about unique highest trees of random graphs). Moreover, we also prove that the…