Strategic Issues, Problems and Challenges in Inductive Theorem Proving

Abstract(Automated) Inductive Theorem Proving (ITP) is a challenging field in automated reasoning and theorem proving. Typically, (Automated) Theorem Proving (TP) refers to methods, techniques and tools for automatically proving general (most often first-order) theorems. Nowadays, the field of TP has reached a certain degree of maturity and powerful TP systems are widely available and used. The situation with ITP is strikingly different, in the sense that proving inductive theorems in an essentially automatic way still is a very challenging task, even for the most advanced existing ITP systems. Both in general TP and in ITP, strategies for guiding the proof search process are of fundamental importance, in automated as well as in interactive or mixed settings. In the paper we will analyze and discuss the most important strategic and proof search issues in ITP, compare ITP with TP, and argue why ITP is in a sense much more challenging. More generally, we will systematically isolate, investigate and classify the main problems and challenges in ITP w.r.t. automation, on different levels and from different points of views. Finally, based on this analysis we will present some theses about the state of the art in the field, possible criteria for what could be considered as substantial progress, and promising lines of research for the future, towards (more) automated ITP

MaskD : a tool for measuring masking fault-tolerance

Fil: Putruele, Luciano. Universidad Nacional de Rı́o Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Computación; Argentina.Fil: Putruele, Luciano. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: Demasi, Ramiro Adrián. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.Fil: Demasi, Ramiro Adrián. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: Castro, Pablo Francisco. Universidad Nacional de Rı́o Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Computación; Argentina.Fil: Castro, Pablo Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: D'Argenio, Pedro Ruben. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.Fil: D'Argenio, Pedro Ruben. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: D'Argenio, Pedro Ruben. Saarland University. Saarland Informatics Campus; Germany.We present MaskD, an automated tool designed to measure the level of fault-tolerance provided by software components. The tool focuses on measuring masking fault-tolerance, that is, the kind of fault-tolerance that allows systems to mask faults in such a way that they cannot be observed by the users. The tool takes as input a nominal model (which serves as a specification) and its fault-tolerant implementation, described by means of a guarded-command language, and automatically computes the masking distance between them. This value can be understood as the level of fault-tolerance provided by the implementation. The tool is based on a sound and complete framework we have introduced in previous work. We present the ideas behind the tool by means of a simple example and report experiments realized on more complex case studies.This work was supported by ANPCyT PICT-2017-3894 (RAFTSys), ANPCyT PICT 2019-03134, SeCyT-UNC 33620180100354CB (ARES), and EU Grant agreement ID: 101008233 (MISSION).publishedVersionFil: Putruele, Luciano. Universidad Nacional de Rı́o Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Computación; Argentina.Fil: Putruele, Luciano. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: Demasi, Ramiro Adrián. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.Fil: Demasi, Ramiro Adrián. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: Castro, Pablo Francisco. Universidad Nacional de Rı́o Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Computación; Argentina.Fil: Castro, Pablo Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: D'Argenio, Pedro Ruben. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.Fil: D'Argenio, Pedro Ruben. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: D'Argenio, Pedro Ruben. Saarland University. Saarland Informatics Campus; Germany

On Kleene Algebra vs. Process Algebra

We try to clarify the relationship between Kleene algebra and process algebra, based on the very recent work on Kleene algebra and process algebra. Both for concurrent Kleene algebra (CKA) with communications and truly concurrent process algebra APTC with Kleene star and parallel star, the extended Milner's expansion law $a\parallel b=a\cdot b+b\cdot a+a\parallel b +a\mid b$ holds, with $a,b$ being primitives (atomic actions), $\parallel$ being the parallel composition, $+$ being the alternative composition, $\cdot$ being the sequential composition and the communication merge $\mid$ with the background of computation. CKA and APTC are all the truly concurrent computation models, can have the same syntax (primitives and operators), maybe have the same or different semantics

Twenty years of rewriting logic

AbstractRewriting logic is a simple computational logic that can naturally express both concurrent computation and logical deduction with great generality. This paper provides a gentle, intuitive introduction to its main ideas, as well as a survey of the work that many researchers have carried out over the last twenty years in advancing: (i) its foundations; (ii) its semantic framework and logical framework uses; (iii) its language implementations and its formal tools; and (iv) its many applications to automated deduction, software and hardware specification and verification, security, real-time and cyber-physical systems, probabilistic systems, bioinformatics and chemical systems

Advancing Deductive Program-Level Verification for Real-World Application: Lessons Learned from an Industrial Case Study

This thesis is concerned with practicability of deductive program verification on source code level. As part of a case study for the verification of real-world software, the specification and verification approach to show correctness of the virtualizing kernel PikeOS is presented. Issues within the verification process using current tools and methodologies are discussed and several aspects of these problems are then addressed in detail to improve the verification process and tool usability