Logic Meets Algebra: the Case of Regular Languages

The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical formalism required to define them. The algebraic point of view on automata is an essential complement of this classification: by providing alternative, algebraic characterizations for the classes, it often yields the only opportunity for the design of algorithms that decide expressibility in some logical fragment. We survey the existing results relating the expressibility of regular languages in logical fragments of MSO[S] with algebraic properties of their minimal automata. In particular, we show that many of the best known results in this area share the same underlying mechanics and rely on a very strong relation between logical substitutions and block-products of pseudovarieties of monoid. We also explain the impact of these connections on circuit complexity theory.Comment: 37 page

Languages and models for hybrid automata: A coalgebraic perspective

article in pressWe study hybrid automata from a coalgebraic point of view. We show that such a perspective supports a generic theory of hybrid automata with a rich palette of definitions and results. This includes, among other things, notions of bisimulation and behaviour, state minimisation techniques, and regular expression languages.POCI-01-0145-FEDER-016692. RDF — European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation — COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT — Fundação para a Ciência e a Tecnologia within project POCI-01-0145-FEDER-016692 and by the PT-FLAD Chair on Smart Cities & Smart Governance at Universidade do Minh

An extensive English language bibliography on graph theory and its applications, supplement 1

Graph theory and its applications - bibliography, supplement

A Recipe for State-and-Effect Triangles

In the semantics of programming languages one can view programs as state transformers, or as predicate transformers. Recently the author has introduced state-and-effect triangles which capture this situation categorically, involving an adjunction between state- and predicate-transformers. The current paper exploits a classical result in category theory, part of Jon Beck's monadicity theorem, to systematically construct such a state-and-effect triangle from an adjunction. The power of this construction is illustrated in many examples, covering many monads occurring in program semantics, including (probabilistic) power domains

A lattice-theoretic framework for circular assume-guarantee reasoning

We develop an abstract lattice-theoretic framework within which we study soundness and other properties of circular assume-guarantee (A-G) rules constrained by side conditions. We identify a particular side condition, non-blockingness, which admits an intelligible inductive proof of the soundness of circular A-G reasoning. Besides, conditional circular rules based on non-blockingness turn out to be complete in various senses and stronger than a large class of sound conditional A-G rules. In this respect, our framework enlightens the foundations of circular A-G reasoning. Due to its abstractness, the framework can be instantiated to many concrete settings. We show several known circular A-G rules for compositional verification to be instances of our generic rules. Thus, we do the circularity-breaking inductive argument once to establish soundness of our generic rules, which then implies soundness of all the instances without resorting to technically complicated circularity-breaking arguments for each single rule. In this respect, our framework unifies many approaches to circular A-G reasoning and provides a starting point for the systematic development of new circular A-G rules.Wir entwickeln einen abstrakten verbandstheoretischen Rahmen in dem wir die Korrektheit und andere Eigenschaften bedingter zirkulaerer Assume-Guarantee- Regeln (A-G-Regeln) untersuchen. Wir isolieren eine besondere Nebenbedingung, non-blockingness, die zu einem verstaendlichen induktiven Beweis der Korrektheit zirkulaerer A-G-Regeln fuehrt. Ausserdem sind durch non-blockingness eingeschr aenkte zirkulaere Regeln vollstaendig und staerker als eine grosse Klasse von korrekten bedingten A-G-Regeln. So gesehen erhellt unsere Arbeit die Grundlagen des zirkulaeren A-G-Paradigmas.Aufgrund seiner Abstraktheit kann unser Rahmen zu vielen konkreten Formalismen instanziiert werden. Wir zeigen, dass mehrere bekannte A-G-Regeln zur kompositionalen Verifikation Instanzen unserer generischen Regeln sind. So ist der zirkularitaetsaufloesende Beweis der Korrektheit nur einmal fuer unsere generische Regeln zu fuehren, dann erben alle Instanzen Korrektheit, ohne dass noch einmal ein zirkularitaets-aufloesender Beweis noetig ist. In dieser Hinsicht stellt unser Rahmen eine einheitliche Plattform dar, die verschiedene Ausformungen des zirkulaeren A-G-Paradigmas umfasst und von der ausgehend systematisch neue zirkulaere A-G-Regeln entwickelt werden koennen

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems