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We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…

We study the complexity of fundamental distributed graph problems in the recently popular setting where information about the input graph is available to the nodes before the start of the computation. We focus on the most common such…

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…

In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…

The main observation of this paper is that some sequential weak compactness arguments in Hilbert space theory can be replaced by Heine/Borel compactness arguments (for the strong topology). Even though the latter form of compactness fails…

Determining whether a program terminates is a core challenge in program analysis with direct implications for correctness, verification, and security. We investigate whether transformer architectures can recognise termination patterns…

The paper studies semi-almost periodic holomorphic functions on a polydisk which have, in a sense, the weakest possible discontinuities on the boundary torus. The basic result used in the proofs is an extension of the classical Bohr…

We give a number of approximation metatheorems for monotone maximization problems expressible in the first-order logic, in substantially more general settings than the previously known. We obtain * constant-factor approximation algorithm in…

We consider a generalization of polynomial programs: algebraic programs, which are optimization or feasibility problems with algebraic objectives or constraints. Algebraic functions are defined as zeros of multivariate polynomials. They are…

This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by…

Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on…

Logical formalisms such as first-order logic (FO) and fixpoint logic (FP) are well suited to express in a declarative manner fundamental graph functionalities required in distributed systems. We show that these logics constitute good…

We present a methodology for proving termination of left-linear term rewriting systems (TRSs) by using Albert Burroni's polygraphs, a kind of rewriting systems on algebraic circuits. We translate the considered TRS into a polygraph of…

Planar functions are mappings from a finite field $\mathbb{F}_q$ to itself with an extremal differential property. Such functions give rise to finite projective planes and other combinatorial objects. There is a subtle difference between…

Typing of lambda-terms in Elementary and Light Affine Logic (EAL, LAL, resp.) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, resp.) proof-nets admits a guaranteed polynomial…

We study the approximation of nonlinear operators between function spaces by transformers. Our approach is to lift functions to measures supported on their graphs and leverage a recently introduced measure-theoretic view of transformers. A…

A Path-Complete Lyapunov Function is an algebraic criterion composed of a finite number of functions, called its pieces, and a directed, labeled graph defining Lyapunov inequalities between these pieces. It provides a stability certificate…

We study the termination of minimal model programs for log canonical pairs in the complex analytic setting. By using the termination, we prove a relation between the minimal model theory for projective log canonical pairs and that for log…

Pull-tabbing is an evaluation approach for functional logic computations, based on a graph transformation recently proposed, which avoids making irrevocable non-deterministic choices that would jeopardize the completeness of computations.…

Many graph problems were first shown to be fixed-parameter tractable using the results of Robertson and Seymour on graph minors. We show that the combination of finite, computable, obstruction sets and efficient order tests is not just one…