Related papers: Automated Complexity Analysis of Integer Programs …
We are concerned with the average case runtime complexity analysis of a prototypical imperative language endowed with primitives for sampling and probabilistic choice. Taking inspiration from known approaches from to the modular resource…
A well studied problem in algebraic complexity theory is the determination of the complexity of problems relying on evaluations of bilinear maps. One measure of the complexity of a bilinear map (or 3-tensor) is the optimal number of…
Estimating the Worst-Case Execution Time (WCET) of an application is an essential task in the context of developing real-time or safety-critical software, but it is also a complex and error-prone process. Conventional approaches require at…
Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable.…
Difference constraints have been used for termination analysis in the literature, where they denote relational inequalities of the form x' <= y + c, and describe that the value of x in the current state is at most the value of y in the…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
We present an efficient approach to prove termination of monotone programs with integer variables, an expressive class of loops that is often encountered in computer programs. Our approach is based on a lightweight static analysis method…
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…
Parametric Worst-case execution time (WCET) analysis of a sequential program produces a formula that represents the worst-case execution time of the program, where parameters of the formula are user-defined parameters of the program (as…
This paper analyzes the computational complexity of validated interval methods for uncertain nonlinear systems and steady-state enclosure. Interval analysis produces guaranteed enclosures that account for uncertainty and round-off, but its…
We introduce a particular optimization problem that minimizes the sum of a non-convex quadratic function and logarithmic barrier-functions in a $\ell_\infty$-trust-region (i.e. cube). Our paper covers three topics. We explain the relevance…
The complexity of round robin method of intraprocedural data flow analysis is measured in number of iterations over the control flow graph. Existing complexity bounds realistically explain the complexity of only Bit-vector frameworks which…
A while loop tests a termination condition on every iteration. On a quantum computer, such measurements perturb the evolution of the algorithm. We define a while loop primitive using weak measurements, offering a trade-off between the…
Since many real-world problems arising in the fields of compiler optimisation, automated software engineering, formal proof systems, and so forth are equivalent to the Halting Problem--the most notorious undecidable problem--there is a…
We present the first scalable bound analysis that achieves amortized complexity analysis. In contrast to earlier work, our bound analysis is not based on general purpose reasoners such as abstract interpreters, software model checkers or…
Inspired by classical sensitivity results for nonlinear optimization, we derive and discuss new quantitative bounds to characterize the solution map and dual variables of a parametrized nonlinear program. In particular, we derive explicit…
Neural Networks (NNs) can provide major empirical performance improvements for robotic systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating the…
In 2008, Ben-Amram, Jones and Kristiansen showed that for a simple programming language - representing non-deterministic imperative programs with bounded loops, and arithmetics limited to addition and multiplication - it is possible to…
Integer octagonal constraints (a.k.a. ``Unit Two Variables Per Inequality'' or ``UTVPI integer constraints'') constitute an interesting class of constraints for the representation and solution of integer problems in the fields of constraint…
Auto-active program verification rests on the ability to effectively the translation from annotated programs into verification conditions that are then discharged by automated theorem provers in the background. Characteristic such tools,…