Related papers: Multiphase-Linear Ranking Functions and their Rela…
Multiphase ranking functions ($\mathit{M{\Phi}RFs}$) were proposed as a means to prove the termination of a loop in which the computation progresses through a number of "phases", and the progress of each phase is described by a different…
In this paper we study the complexity of the problems: given a loop, described by linear constraints over a finite set of variables, is there a linear or lexicographical-linear ranking function for this loop? While existence of such…
The scope of this work is the constraint-based synthesis of termination arguments for the restricted class of programs called linear lasso programs. A termination argument consists of a ranking function as well as a set of supporting…
We present a new method for the constraint-based synthesis of termination arguments for linear loop programs based on linear ranking templates. Linear ranking templates are parametrized, well-founded relations such that an assignment to the…
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 present a new method for the constraint-based synthesis of termination arguments for linear loop programs based on linear ranking templates. Linear ranking templates are parameterized, well-founded relations such that an assignment to…
Programs with multiphase control-flow are programs where the execution passes through several (possibly implicit) phases. Proving termination of such programs (or inferring corresponding runtime bounds) is often challenging since it…
In this paper we turn the spotlight on a class of lexicographic ranking functions introduced by Bradley, Manna and Sipma in a seminal CAV 2005 paper, and establish for the first time the complexity of some problems involving the inference…
This paper studies the problem of synthesizing (lexicographic) polynomial ranking functions for loops that can be described in polynomial arithmetic over integers and reals. While the analogous ranking function synthesis problem for linear…
Hierarchical multi-label classification (HMC) has gained considerable attention in recent decades. A seminal line of HMC research addresses the problem in two stages: first, training individual classifiers for each class, then integrating…
Maximizing submodular functions have been studied extensively for a wide range of subset-selection problems. However, much less attention has been given to the role of submodularity in sequence-selection and ranking problems. A…
We study the problem of synthesizing polyhedral Lyapunov functions for hybrid linear systems. Such functions are defined as convex piecewise linear functions, with a finite number of pieces. We first prove that deciding whether there exists…
Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often…
Program termination is a hot research topic in program analysis. The last few years have witnessed the development of termination analyzers for programming languages such as C and Java with remarkable precision and performance. These…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
The problem of ranking is a multi-billion dollar problem. In this paper we present an overview of several production quality ranking systems. We show that due to conflicting goals of employing the most effective machine learning models and…
The constrained linear representability problem (CLRP) for polymatroids determines whether there exists a polymatroid that is linear over a specified field while satisfying a collection of constraints on the rank function. Using a computer…
The primary goal of this paper is to give a precise definition and prove existence and uniqueness of multiphase quadrature domains for subharmonic functions, ensuring that the prescribed measures are supported in the interior of the…
The Probability Ranking Principle (PRP) has been considered as the foundational standard in the design of information retrieval (IR) systems. The principle requires an IR module's returned list of results to be ranked with respect to the…
In Multi-Criteria Decision Analysis, Rank Reversals are a serious problem that can greatly affect the results of a Multi-Criteria Decision Method against a particular set of alternatives. It is therefore useful to have a mechanism that…