Related papers: The Fundamental Theorem of Perfect Simulation
We introduce and study the computational problem of determining statistical similarity between probability distributions. For distributions $P$ and $Q$ over a finite sample space, their statistical similarity is defined as…
We develop the first two heap logics that have implicit heaplets and that admit FO-complete program verification. The notion of FO-completeness is a theoretical guarantee that all theorems that are valid when recursive definitions are…
We prove two universal approximation theorems for a range of dropout neural networks. These are feed-forward neural networks in which each edge is given a random $\{0,1\}$-valued filter, that have two modes of operation: in the first each…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
Societies often rely on human experts to take a wide variety of decisions affecting their members, from jail-or-release decisions taken by judges and stop-and-frisk decisions taken by police officers to accept-or-reject decisions taken by…
We introduce an automata-theoretic method for the verification of distributed algorithms running on ring networks. In a distributed algorithm, an arbitrary number of processes cooperate to achieve a common goal (e.g., elect a leader).…
In Model-Based Design of Cyber-Physical Systems (CPS), it is often desirable to develop several models of varying fidelity. Models of different fidelity levels can enable mathematical analysis of the model, control synthesis, faster…
We study the problem of determining whether a given temporal specification can be implemented by a symmetric system, i.e., a system composed from identical components. Symmetry is an important goal in the design of distributed systems,…
The notion of Las Vegas algorithms was introduced by Babai (1979) and can be defined in two ways: * In Babai's original definition, a randomized algorithm is called Las Vegas if it has a finitely bounded running time and certifiable random…
We introduce the notion of a reproducible algorithm in the context of learning. A reproducible learning algorithm is resilient to variations in its samples -- with high probability, it returns the exact same output when run on two samples…
In the paper the problem of verification of functional programs (FPs) over strings is considered, where specifications of properties of FPs are defined by other FPs, and a FP S1 meets a specification defined by another FP S2 iff a…
Bisimulation is crucial for verifying process equivalence in probabilistic systems. This paper presents a novel logical framework for analyzing bisimulation in probabilistic parameterized systems, namely, infinite families of finite-state…
This paper considers the problem of completing a rating matrix based on sub-sampled matrix entries as well as observed social graphs and hypergraphs. We show that there exists a \emph{sharp threshold} on the sample probability for the task…
A large part of modern machine learning theory often involves computing the high-dimensional expected trace of a rational expression of large rectangular random matrices. To symbolically compute such quantities using free probability…
This paper is concerned with a recently developed paradigm for population-based optimization, termed particle filter optimization (PFO). This paradigm is attractive in terms of coherence in theory and easiness in mathematical analysis and…
A construction is given for simulating any deterministic finite state machine (FSM) on a quantum computer in a space-efficient manner. By constructing a superposition of input strings of lengths K or less, questions can be asked about the…
One of the theoretical pillars that sustain certain machine learning models are universal approximation theorems, which prove that they can approximate all functions from a function class to arbitrary precision. Independently, classical…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
A formulation of the density functional theory is constructed on the foundations of entropic inference. The theory is introduced as an application of maximum entropy for inhomogeneous fluids in thermal equilibrium. It is shown that entropic…
The overall problem addressed in this paper is the long-standing problem of program correctness, and in particular programs that describe systems of parallel executing processes. We propose a new method for proving correctness of parallel…