Related papers: Targeting Completeness: Automated Complexity Analy…
Recent work has shown that the computations of Transformers can be simulated in the RASP family of programming languages. These findings have enabled improved understanding of the expressive capacity and generalization abilities of…
This paper addresses the problem of improving response times of robots implemented in the Robotic Operating System (ROS) using formal verification of computational-time feasibility. In order to verify the real time behaviour of a robot…
A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound andcomplete characterization of the set of polynomial time computable functions is obtained. As a consequence,…
We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…
We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
Given the complexity of modern software systems, it is of great importance that such systems be able to autonomously modify themselves, i.e., self-adapt, with minimal human supervision. It is critical that this adaptation both results in…
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…
Implicit computational complexity, which aims at characterizing complexity classes by machine-independent means, has traditionally been based, on the one hand, on programs and deductive formalisms for free algebras, and on the other hand on…
While reachability analysis is one of the most promising approaches for formal verification of dynamic systems, a major disadvantage preventing a more widespread application is the requirement to manually tune algorithm parameters such as…
This manuscript explores novel complexity results for the feasibility problem over $p$-order cones, extending the foundational work of Porkolab and Khachiyan. By leveraging the intrinsic structure of $p$-order cones, we derive refined…
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 consider the class of packing integer programs (PIPs) that are column sparse, i.e. there is a specified upper bound k on the number of constraints that each variable appears in. We give an (ek+o(k))-approximation algorithm for k-column…
Branch-and-cut is the most widely used algorithm for solving integer programs, employed by commercial solvers like CPLEX and Gurobi. Branch-and-cut has a wide variety of tunable parameters that have a huge impact on the size of the search…
This paper takes an empirical look at asymptotic runtime growth rates for the most widely used algorithms for solving linear programming (LP) problems across a set of six optimization application areas that are known to produce large and…
We show how the complexity of higher-order functional programs can be analysed automatically by applying program transformations to a defunctionalized versions of them, and feeding the result to existing tools for the complexity analysis of…
Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for…
Powerful results from the theory of integer programming have recently led to substantial advances in parameterized complexity. However, our perception is that, except for Lenstra's algorithm for solving integer linear programming in fixed…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows overcoming these…
We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…