Related papers: Automated Complexity Analysis of Integer Programs …
Loop invariants play a central role in the verification of imperative programs. However, finding these invariants is often a difficult and time-consuming task for the programmer. We have previously shown how program transformation can be…
The automatic generation of loop invariants is a fundamental challenge in software verification. While this task is undecidable in general, it is decidable for certain restricted classes of programs. This work focuses on invariant…
ASP(Q) extends Answer Set Programming (ASP) with Quantifiers over answer sets. In this paper we focus on the class of ASP(Q) programs with two quantifiers and weak constraints, denoted as 2-ASP(Q)^w. 2-ASP(Q)^w is a practically relevant…
We consider a non-convex constrained optimization problem, where the objective function is weakly convex and the constraint function is either convex or weakly convex. To solve this problem, we consider the classical switching subgradient…
We describe an algorithm for proving termination of programs abstracted to systems of monotonicity constraints in the integer domain. Monotonicity constraints are a non-trivial extension of the well-known size-change termination method.…
We consider practical methods for the problem of finding a minimum-weight triangulation (MWT) of a planar point set, a classic problem of computational geometry with many applications. While Mulzer and Rote proved in 2006 that computing an…
In this paper, we analyze a derivative-free line search method designed for bound-constrained problems. Our analysis demonstrates that this method exhibits a worst-case complexity comparable to other derivative-free methods for…
There has been an increasing interest in using neural networks in closed-loop control systems to improve performance and reduce computational costs for on-line implementation. However, providing safety and stability guarantees for these…
The well known concept, to reduce the spatio-temporal dynamics beyond instabilities of trivial states to amplitude modulated patterns, is reviewed from the point of view of a formal perturbation expansion for general dissipative partial…
One of the major limitations for the employment of model-based planning and scheduling in practical applications is the need of costly re-planning when an incongruence between the observed reality and the formal model is encountered during…
In probabilistic program analysis, quantitative analysis aims at deriving tight numerical bounds for probabilistic properties such as expectation and assertion probability. Most previous works consider numerical bounds over the whole…
In this paper, we identify a fragment of second-order logic with restricted quantification that is expressive enough to capture numerous static analysis problems (e.g. safety proving, bug finding, termination and non-termination proving,…
While loops are present in virtually all imperative programming languages. They are important both for practical reasons (performing a number of iterations not known in advance) and theoretical reasons (achieving Turing completeness). In…
Nonlinear Programs (NLPs) are prevalent in optimization-based control of nonlinear systems. Solving general NLPs is computationally expensive, necessitating the development of fast hardware or tractable suboptimal approximations. This paper…
We define the complexity of a continuous-time linear system to be the minimum number of bits required to describe its forward increments to a desired level of fidelity, and compute this quantity using the rate distortion function of a…
The reformulation-linearization technique (RLT) is a prominent approach to constructing tight linear relaxations of non-convex continuous and mixed-integer optimization problems. The goal of this paper is to extend the applicability and…
Retrograde analysis reads programs from the end to the beginning: treat statements as constraints on prior states, propagate sets of states backward, and compare the reachable inputs with the intended specification. This tutorial condenses…
We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds…
We present an algorithm for synthesizing program loops satisfying a given polynomial loop invariant. The class of loops we consider can be modeled by a system of algebraic recurrence equations with constant coefficients. We turn the task of…
In this paper we initiate the study of the computational complexity of learning linear temporal logic (LTL) formulas from examples. We construct approximation algorithms for fragments of LTL and prove hardness results; in particular we…