Related papers: Lower Bounds for Possibly Divergent Probabilistic …
We introduce the class of constant probability (CP) programs and show that classical results from probability theory directly yield a simple decision procedure for (positive) almost sure termination of programs in this class. Moreover,…
In this paper, we develop a novel verification technique to reason about programs featuring concurrency, pointers and randomization. While the integration of concurrency and pointers is well studied, little is known about the combination of…
This paper presents a methodology for temporal logic verification of discrete-time stochastic systems. Our goal is to find a lower bound on the probability that a complex temporal property is satisfied by finite traces of the system.…
Lower bounds for some explicit decision problems over the complex numbers are given.
Hypothesis tests and confidence intervals are ubiquitous in empirical research, yet their connection to subsequent decision-making is often unclear. We develop a theory of certified decisions that pairs recommended decisions with…
Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…
While there are many approaches for automatically proving termination of term rewrite systems, up to now there exist only few techniques to disprove their termination automatically. Almost all of these techniques try to find loops, where…
A linear constraint loop is specified by a system of linear inequalities that define the relation between the values of the program variables before and after a single execution of the loop body. In this paper we consider the problem of…
The goal of this work is to prove a new sure upper bound in a setting that can be thought of as a simplified function field analogue. This result is comparable to a recent result of the author concerning almost sure upper bound of random…
A formulation of "Ne\v{c}iporuk's lower bound method" slightly more inclusive than the usual complexity-measure-specific formulation is presented. Using this general formulation, limitations to lower bounds achievable by the method are…
We establish an Ergodic Theorem for lower probabilities, a generalization of standard probabilities widely used in applications. As a by-product, we provide a version for lower probabilities of the Strong Law of Large Numbers.
Probabilistic programming languages (PPLs) are expressive means for creating and reasoning about probabilistic models. Unfortunately hybrid probabilistic programs, involving both continuous and discrete structures, are not well supported by…
Through a straightforward Bayesian approach we show that under some general conditions a maximum running time, namely the number of discrete steps performed by a computer program during its execution, can be defined such that the…
The termination behavior of probabilistic programs depends on the outcomes of random assignments. Almost sure termination (AST) is concerned with the question whether a program terminates with probability one on all possible inputs.…
Recently, there has been an increasing interest in the bottom-up evaluation of the semantics of logic programs with complex terms. The presence of function symbols in the program may render the ground instantiation infinite, and finiteness…
We give a lower bound for the non-collision probability up to a long time T in a system of n independent random walks with fixed obstacles on the two-dimensional lattice. By `collision' we mean collision between the random walks as well as…
The problems of enumerating lattice walks, with an arbitrary finite set of allowed steps, both in one and two dimensions, where one must always stay in the non-negative half-line and quarter-plane respectively, are used, as case studies, to…
A model of computation for which reasonable yet still incomplete lower bounds are known is the read-once branching program. Here variants of complexity measures successful in the study of read-once branching programs are defined and…
We study the design of voting rules in the metric distortion framework. It is known that any deterministic rule suffers distortion of at least $3$, and that randomized rules can achieve distortion strictly less than $3$, often at the cost…
This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many…