Related papers: Quasi-friendly sup-interpretations

In this paper, we survey the complexity of distinct methods that allow the programmer to synthesize a sup-interpretation, a function providing an upper- bound on the size of the output values computed by a program. It consists in a static…

A sup-interpretation is a tool which provides an upper bound on the size of a value computed by some symbol of a program. Sup-interpretations have shown their interest to deal with the complexity of first order functional programs. For…

Quasi-interpretations are a technique to guarantee complexity bounds on first-order functional programs: with termination orderings they give in particular a sufficient condition for a program to be executable in polynomial time, called…

Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…

We improve and refine a method for certifying that the values' sizes computed by an imperative program will be bounded by polynomials in the program's inputs' sizes. Our work ''tames'' the non-determinism of the original analysis, and…

Some type-based approaches to termination use sized types: an ordinal bound for the size of a data structure is stored in its type. A recursive function over a sized type is accepted if it is visible in the type system that recursive calls…

In a common formulation of semi-infinite programs, the infinite constraint set is a requirement that a function parametrized by the decision variables is nonnegative over an interval. If this function is sufficiently closely approximable by…

We introduce a method for proving lower bounds on the efficacy of semidefinite programming (SDP) relaxations for combinatorial problems. In particular, we show that the cut, TSP, and stable set polytopes on $n$-vertex graphs are not the…

This article provides an original understanding of the behavior of a class of graph-oriented semi-supervised learning algorithms in the limit of large and numerous data. It is demonstrated that the intuition at the root of these methods…

In [arXiv 0811.3913] the authors introduced the notion of quasi-polynomial function as being a mapping f: X^n -> X defined and valued on a bounded chain X and which can be factorized as f(x_1,...,x_n)=p(phi(x_1),...,phi(x_n)), where p is a…

Synthesizing programs from examples requires searching over a vast, combinatorial space of possible programs. In this search process, a key challenge is representing the behavior of a partially written program before it can be executed, to…

Many sequential decision making problems can be formulated as an adaptive submodular maximization problem. However, most of existing studies in this field focus on pool-based setting, where one can pick items in any order, and there have…

An uninterpreted program (UP) is a program whose semantics is defined over the theory of uninterpreted functions. This is a common abstraction used in equivalence checking, compiler optimization, and program verification. While simple, the…

We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summands are defined with respect to different partial orders. We…

We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…

Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…

Our goal is to study the feasibility of porting termination analysis techniques developed for one programming paradigm to another paradigm. In this paper, we show how to adapt termination analysis techniques based on polynomial…

Submodular functions and their optimization have found applications in diverse settings ranging from machine learning and data mining to game theory and economics. In this work, we consider the constrained maximization of a submodular…

A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…

We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order.…