Related papers: Supermartingales, Ranking Functions and Probabilis…
We study the problem of enumerating answers of Conjunctive Queries ranked according to a given ranking function. Our main contribution is a novel algorithm with small preprocessing time, logarithmic delay, and non-trivial space usage during…
We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…
We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…
This paper considers the computational hardness of computing expected outcomes and deciding almost-sure termination of probabilistic programs. We show that deciding almost-sure termination and deciding whether the expected outcome of a…
Finding whether a linear-constraint loop has a linear ranking function is an important key to understanding the loop behavior, proving its termination and establishing iteration bounds. If no preconditions are provided, the decision problem…
We describe the Amber tool for proving and refuting the termination of a class of probabilistic while-programs with polynomial arithmetic, in a fully automated manner. Amber combines martingale theory with properties of asymptotic bounding…
In this paper we estimate the rest of the approximation of a stationary process by a martingale in terms of the projections of partial sums. Then, based on this estimate, we obtain almost sure approximation of partial sums by a martingale…
This work provides a novel convergence analysis for stochastic optimization in terms of stopping times, addressing the practical reality that algorithms are often terminated adaptively based on observed progress. Unlike prior approaches,…
Liveness properties are traditionally proven using a ranking function that maps system states to some well-founded set. Carrying out such proofs in first-order logic enables automation by SMT solvers. However, reasoning about many natural…
Rankings are central to decision-making in fields ranging from education to online platforms, yet classical deterministic methods such as the Borda count method or Copeland-type pairwise methods ignore uncertainty due to sampling noise or…
There are many evaluation strategies for term rewrite systems, but automatically proving termination or analyzing complexity is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies…
The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
We use the abstract method of (local) martingale problems in order to give criteria for convergence of stochastic processes. Extending previous notions, the formulation we use is neither restricted to Markov processes (or semimartingales),…
We consider the problem of maximizing an unknown function over a compact and convex set using as few observations as possible. We observe that the optimization of the function essentially relies on learning the induced bipartite ranking…
Ranking populations such as institutions based on certain characteristics is often of interest, and these ranks are typically estimated using samples drawn from the populations. Due to sample randomness, it is important to quantify the…
Many programs allow the user to input data several times during its execution. If the program runs forever the user may input data infinitely often. A program terminates if it terminates no matter what the user does. We discuss various ways…
We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of nonrecursive programs.…
We introduce refutationally complete superposition calculi for intentional and extensional clausal $\lambda$-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a…
This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum…