Online Detection of Repetitions with Backtracking

In this paper we present two algorithms for the following problem: given a string and a rational $e > 1$, detect in the online fashion the earliest occurrence of a repetition of exponent $\ge e$ in the string. 1. The first algorithm supports the backtrack operation removing the last letter of the input string. This solution runs in $O(n\log m)$ time and $O(m)$ space, where $m$ is the maximal length of a string generated during the execution of a given sequence of $n$ read and backtrack operations. 2. The second algorithm works in $O(n\log\sigma)$ time and $O(n)$ space, where $n$ is the length of the input string and $\sigma$ is the number of distinct letters. This algorithm is relatively simple and requires much less memory than the previously known solution with the same working time and space. a string generated during the execution of a given sequence of $n$ read and backtrack operations.Comment: 12 pages, 5 figures, accepted to CPM 201

Proceedings of the 1968 Summer Institute on Symbolic Mathematical Computation

Investigating symbolic mathematical computation using PL/1 FORMAC batch system and Scope FORMAC interactive syste

Hybrid Differential Software Testing

Differentielles Testen ist ein wichtiger Bestandteil der Qualitätssicherung von Software, mit dem Ziel Testeingaben zu generieren, die Unterschiede im Verhalten der Software deutlich machen. Solche Unterschiede können zwischen zwei Ausführungspfaden (1) in unterschiedlichen Programmversionen, aber auch (2) im selben Programm auftreten. In dem ersten Fall werden unterschiedliche Programmversionen mit der gleichen Eingabe untersucht, während bei dem zweiten Fall das gleiche Programm mit unterschiedlichen Eingaben analysiert wird. Die Regressionsanalyse, die Side-Channel Analyse, das Maximieren der Ausführungskosten eines Programms und die Robustheitsanalyse von Neuralen Netzwerken sind typische Beispiele für differentielle Softwareanalysen. Eine besondere Herausforderung liegt in der effizienten Analyse von mehreren Programmpfaden (auch über mehrere Programmvarianten hinweg). Die existierenden Ansätze sind dabei meist nicht (spezifisch) dafür konstruiert, unterschiedliches Verhalten präzise hervorzurufen oder sind auf einen Teil des Suchraums limitiert. Diese Arbeit führt das Konzept des hybriden differentiellen Software Testens (HyDiff) ein: eine hybride Analysetechnik für die Generierung von Eingaben zur Erkennung von semantischen Unterschieden in Software. HyDiff besteht aus zwei parallel laufenden Komponenten: (1) einem such-basierten Ansatz, der effizient Eingaben generiert und (2) einer systematischen Analyse, die auch komplexes Programmverhalten erreichen kann. Die such-basierte Komponente verwendet Fuzzing geleitet durch differentielle Heuristiken. Die systematische Analyse basiert auf Dynamic Symbolic Execution, das konkrete Eingaben bei der Analyse integrieren kann. HyDiff wird anhand mehrerer Experimente evaluiert, die in spezifischen Anwendungen im Bereich des differentiellen Testens ausgeführt werden. Die Resultate zeigen eine effektive Generierung von Testeingaben durch HyDiff, wobei es sich signifikant besser als die einzelnen Komponenten verhält.Differential software testing is important for software quality assurance as it aims to automatically generate test inputs that reveal behavioral differences in software. The concrete analysis procedure depends on the targeted result: differential testing can reveal divergences between two execution paths (1) of different program versions or (2) within the same program. The first analysis type would execute different program versions with the same input, while the second type would execute the same program with different inputs. Therefore, detecting regression bugs in software evolution, analyzing side-channels in programs, maximizing the execution cost of a program over multiple executions, and evaluating the robustness of neural networks are instances of differential software analysis with the goal to generate diverging executions of program paths. The key challenge of differential software testing is to simultaneously reason about multiple program paths, often across program variants, in an efficient way. Existing work in differential testing is often not (specifically) directed to reveal a different behavior or is limited to a subset of the search space. This PhD thesis proposes the concept of Hybrid Differential Software Testing (HyDiff) as a hybrid analysis technique to generate difference revealing inputs. HyDiff consists of two components that operate in a parallel setup: (1) a search-based technique that inexpensively generates inputs and (2) a systematic exploration technique to also exercise deeper program behaviors. HyDiff’s search-based component uses differential fuzzing directed by differential heuristics. HyDiff’s systematic exploration component is based on differential dynamic symbolic execution that allows to incorporate concrete inputs in its analysis. HyDiff is evaluated experimentally with applications specific for differential testing. The results show that HyDiff is effective in all considered categories and outperforms its components in isolation

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

Systems of difference equations as a model for the Lorenz system

We consider systems of difference equations as a model for the Lorenz system of differential equations. Using the power series whose coefficients are the solutions of these systems, we define three real functions, that are approximation for the solutions of the Lorenz system