Normalized Rewriting: an Alternative to Rewriting modulo a Set of Equations

AbstractIn the first part of this paper, we introducenormalized rewriting, a new rewrite relation. It generalizes former notions of rewriting modulo a set of equationsE, dropping some conditions onE. For example,Ecan now be the theory of identity, idempotence, the theory of Abelian groups or the theory of commutative rings. We give a new completion algorithm for normalized rewriting. It contains as an instance the usual AC completion algorithm, but also the well-known Buchberger algorithm for computing Gröbner bases of polynomial ideals. In the second part, we investigate the particular case of completion of ground equations. In this case we prove by a uniform method that completion moduloEterminates, for some interesting theoriesE. As a consequence, we obtain the decidability of the word problem for some classes of equational theories, including the AC-ground case (a result known since 1991), the ACUI-ground case (a new result to our knowledge), and the cases of ground equations modulo the theory of Abelian groups and commutative rings, which is already known when the signature contains only constants, but is new otherwise. Finally, we give implementation results which show the efficiency of normalized completion with respect to completion modulo AC

Reversible Computation: Extending Horizons of Computing

This open access State-of-the-Art Survey presents the main recent scientific outcomes in the area of reversible computation, focusing on those that have emerged during COST Action IC1405 "Reversible Computation - Extending Horizons of Computing", a European research network that operated from May 2015 to April 2019. Reversible computation is a new paradigm that extends the traditional forwards-only mode of computation with the ability to execute in reverse, so that computation can run backwards as easily and naturally as forwards. It aims to deliver novel computing devices and software, and to enhance existing systems by equipping them with reversibility. There are many potential applications of reversible computation, including languages and software tools for reliable and recovery-oriented distributed systems and revolutionary reversible logic gates and circuits, but they can only be realized and have lasting effect if conceptual and firm theoretical foundations are established first

Reversible Computation: Extending Horizons of Computing

This open access State-of-the-Art Survey presents the main recent scientific outcomes in the area of reversible computation, focusing on those that have emerged during COST Action IC1405 "Reversible Computation - Extending Horizons of Computing", a European research network that operated from May 2015 to April 2019. Reversible computation is a new paradigm that extends the traditional forwards-only mode of computation with the ability to execute in reverse, so that computation can run backwards as easily and naturally as forwards. It aims to deliver novel computing devices and software, and to enhance existing systems by equipping them with reversibility. There are many potential applications of reversible computation, including languages and software tools for reliable and recovery-oriented distributed systems and revolutionary reversible logic gates and circuits, but they can only be realized and have lasting effect if conceptual and firm theoretical foundations are established first

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Tree Automata Techniques and Applications

International audienc

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Representing and Querying Incomplete Information: a Data Interoperability Perspective

This habilitation thesis presents some of my most recent work, which has been done in collaboration with several other people. In particular this thesis concentrates on our contributions to the study of incomplete information in the context of data interoperability. In this scenario data is heterogenous and decentralized, needs to be integrated from several sources and exchanged between different applications. Incompleteness, i.e. the presence of “missing” or “unknown” portions of data, is naturally generated in data exchange and integration, due to data heterogeneity. The management of incomplete information poses new challenges in this context.The focus of our study is the development of models of incomplete information suitable to data interoperability tasks, and the study of techniques for efficiently querying several forms of incompleteness