Targeting Completeness: Using Closed Forms for Size Bounds of Integer Programs

We present a new procedure to infer size bounds for integer programs automatically. Size bounds are important for the deduction of bounds on the runtime complexity or in general, for the resource analysis of programs. We show that our technique is complete (i.e., it always computes finite size bounds) for a subclass of loops, possibly with non-linear arithmetic. Moreover, we present a novel approach to combine and integrate this complete technique into an incomplete approach to infer size and runtime bounds of general integer programs. We prove completeness of our integration for an important subclass of integer programs. We implemented our new algorithm in the automated complexity analysis tool KoAT to evaluate its power, in particular on programs with non-linear arithmetic

ADCL: Acceleration Driven Clause Learning for Constrained Horn Clauses

Constrained Horn Clauses (CHCs) are often used in automated program verification. Thus, techniques for (dis-)proving satisfiability of CHCs are a very active field of research. On the other hand, acceleration techniques for computing formulas that characterize the N-fold closure of loops have successfully been used for static program analysis. We show how to use acceleration to avoid repeated derivations with recursive CHCs in resolution proofs, which reduces the length of the proofs drastically. This idea gives rise to a novel calculus for (dis)proving satisfiability of CHCs, called Acceleration Driven Clause Learning (ADCL). We implemented this new calculus in our tool LoAT and evaluate it empirically in comparison to other state-of-the-art tools

Automated Termination Proofs for C Programs with Lists (Short WST Version)

There are many techniques and tools for termination of C programs, but up to now they were not very powerful for termination proofs of programs whose termination depends on recursive data structures like lists. We present the first approach that extends powerful techniques for termination analysis of C programs (with memory allocation and explicit pointer arithmetic) to lists.Comment: Presented at WST 2023, short version of arXiv:2305.1215

The semantics of rational contractions

This paper is concerned with the revision of beliefs in the face of new and possibly contradicting information. In the Logic of Theory Change developed by Alchourron, Gärdenfors and Makinson this nonmonotonic process consists of a contraction and an expansion of a set of formulas. to achieve minimal change they formulated widely accepted postulates that rational contractions have to fulfill. Contractions as defined by Alchourron, Gärdenfors and Makinson only operate on deductively closed sets of Formulas. Therefore they cannot be used in practical applications, eg. knowledge representation, where only finitely representable sets can be handled. We present a semantical characterization of rational finite contractions (the class of rational contractions maintaining finite representability) which provides an insight into the true nature of these operations. This characterization shows all possibilities to define concrete functions possessing these properties. When regarding concrete contractions known from literature in the light of our characterization we have found that they are all defined according to the same semantical strategy of minimal semantical change. As this strategy does not correspond to the goal of keeping as many important fotmulas as possible in the contracted set, we suggest a finite contraction defined according to the new strategy of maximal maintenance

Proving Termination of C Programs with Lists

There are many techniques and tools to prove termination of C programs, but up to now these tools were not very powerful for fully automated termination proofs of programs whose termination depends on recursive data structures like lists. We present the first approach that extends powerful techniques for termination analysis of C programs (with memory allocation and explicit pointer arithmetic) to lists.Comment: Full version of a paper which appeared in the Proceedings of CADE 202

Proving Non-Termination by Acceleration Driven Clause Learning

We recently proposed Acceleration Driven Clause Learning (ADCL), a novel calculus to analyze satisfiability of Constrained Horn Clauses (CHCs). Here, we adapt ADCL to transition systems and introduce ADCL-NT, a variant for disproving termination. We implemented ADCL-NT in our tool LoAT and evaluate it against the state of the art

Improving Dependency Tuples for Almost-Sure Innermost Termination of Probabilistic Term Rewriting

Recently, we adapted the well-known dependency pair (DP) framework to a dependency tuple (DT) framework in order to prove almost-sure innermost termination (iAST) of probabilistic term rewriting systems. In this paper, we improve this approach into a complete criterion for iAST by considering positions of subterms. Based on this, we extend the probabilistic DT framework by new transformations. Our implementation in the tool AProVE shows that they increase its power substantially

Automated Termination Analysis for Logic Programs with Cut

Termination is an important and well-studied property for logic programs. However, almost all approaches for automated termination analysis focus on definite logic programs, whereas real-world Prolog programs typically use the cut operator. We introduce a novel pre-processing method which automatically transforms Prolog programs into logic programs without cuts, where termination of the cut-free program implies termination of the original program. Hence after this pre-processing, any technique for proving termination of definite logic programs can be applied. We implemented this pre-processing in our termination prover AProVE and evaluated it successfully with extensive experiments

Профессиональная подготовка студентов технического вуза на иностранном языке: методическая готовность преподавателей: сборник материалов III Всероссийского научно-методологического семинара-конференции, 21–23 апреля 2016 г., Томск

Сборник посвящён вопросам языковой подготовки студентов и сотрудников университета, разработке профессиональных дисциплин на английском языке, новым образовательным технологиям и внедрению электронного обучения. Представлены кейсы из опыта работы университетов по актуальным вопросам образования. Предназначен для научных работников, преподавателей, руководителей подразделений высших учебных заведений, отвечающих за международное образование, языковую подготовку и повышение квалификации в данной области