Propagators and Solvers for the Algebra of Modular Systems

To appear in the proceedings of LPAR 21. Solving complex problems can involve non-trivial combinations of distinct knowledge bases and problem solvers. The Algebra of Modular Systems is a knowledge representation framework that provides a method for formally specifying such systems in purely semantic terms. Formally, an expression of the algebra defines a class of structures. Many expressive formalism used in practice solve the model expansion task, where a structure is given on the input and an expansion of this structure in the defined class of structures is searched (this practice overcomes the common undecidability problem for expressive logics). In this paper, we construct a solver for the model expansion task for a complex modular systems from an expression in the algebra and black-box propagators or solvers for the primitive modules. To this end, we define a general notion of propagators equipped with an explanation mechanism, an extension of the alge- bra to propagators, and a lazy conflict-driven learning algorithm. The result is a framework for seamlessly combining solving technology from different domains to produce a solver for a combined system.Comment: To appear in the proceedings of LPAR 2

On Computational Small Steps and Big Steps: Refocusing for Outermost Reduction

We study the relationship between small-step semantics, big-step semantics and abstract machines, for programming languages that employ an outermost reduction strategy, i.e., languages where reductions near the root of the abstract syntax tree are performed before reductions near the leaves.In particular, we investigate how Biernacka and Danvy's syntactic correspondence and Reynolds's functional correspondence can be applied to inter-derive semantic specifications for such languages.The main contribution of this dissertation is three-fold:First, we identify that backward overlapping reduction rules in the small-step semantics cause the refocusing step of the syntactic correspondence to be inapplicable.Second, we propose two solutions to overcome this in-applicability: backtracking and rule generalization.Third, we show how these solutions affect the other transformations of the two correspondences.Other contributions include the application of the syntactic and functional correspondences to Boolean normalization.In particular, we show how to systematically derive a spectrum of normalization functions for negational and conjunctive normalization

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

Logical and deep learning methods for temporal reasoning

In this thesis, we study logical and deep learning methods for the temporal reasoning of reactive systems. In Part I, we determine decidability borders for the satisfiability and realizability problem of temporal hyperproperties. Temporal hyperproperties relate multiple computation traces to each other and are expressed in a temporal hyperlogic. In particular, we identify decidable fragments of the highly expressive hyperlogics HyperQPTL and HyperCTL*. As an application, we elaborate on an enforcement mechanism for temporal hyperproperties. We study explicit enforcement algorithms for specifications given as formulas in universally quantified HyperLTL. In Part II, we train a (deep) neural network on the trace generation and realizability problem of linear-time temporal logic (LTL). We consider a method to generate large amounts of additional training data from practical specification patterns. The training data is generated with classical solvers, which provide one of many possible solutions to each formula. We demonstrate that it is sufficient to train on those particular solutions such that the neural network generalizes to the semantics of the logic. The neural network can predict solutions even for formulas from benchmarks from the literature on which the classical solver timed out. Additionally, we show that it solves a significant portion of problems from the annual synthesis competition (SYNTCOMP) and even out-of-distribution examples from a recent case study.Diese Arbeit befasst sich mit logischen Methoden und mehrschichtigen Lernmethoden für das zeitabhängige Argumentieren über reaktive Systeme. In Teil I werden die Grenzen der Entscheidbarkeit des Erfüllbarkeits- und des Realisierbarkeitsproblem von temporalen Hypereigenschaften bestimmt. Temporale Hypereigenschaften setzen mehrere Berechnungsspuren zueinander in Beziehung und werden in einer temporalen Hyperlogik ausgedrückt. Insbesondere werden entscheidbare Fragmente der hochexpressiven Hyperlogiken HyperQPTL und HyperCTL* identifiziert. Als Anwendung wird ein Enforcement-Mechanismus für temporale Hypereigenschaften erarbeitet. Explizite Enforcement-Algorithmen für Spezifikationen, die als Formeln in universell quantifiziertem HyperLTL angegeben werden, werden untersucht. In Teil II wird ein (mehrschichtiges) neuronales Netz auf den Problemen der Spurgenerierung und Realisierbarkeit von Linear-zeit Temporallogik (LTL) trainiert. Es wird eine Methode betrachtet, um aus praktischen Spezifikationsmustern große Mengen zusätzlicher Trainingsdaten zu generieren. Die Trainingsdaten werden mit klassischen Solvern generiert, die zu jeder Formel nur eine von vielen möglichen Lösungen liefern. Es wird gezeigt, dass es ausreichend ist, an diesen speziellen Lösungen zu trainieren, sodass das neuronale Netz zur Semantik der Logik generalisiert. Das neuronale Netz kann Lösungen sogar für Formeln aus Benchmarks aus der Literatur vorhersagen, bei denen der klassische Solver eine Zeitüberschreitung hatte. Zusätzlich wird gezeigt, dass das neuronale Netz einen erheblichen Teil der Probleme aus dem jährlichen Synthesewettbewerb (SYNTCOMP) und sogar Beispiele außerhalb der Distribution aus einer aktuellen Fallstudie lösen kann

A type-theoretic framework for software component synthesis

A language-agnostic approach for type-based component-oriented software synthesis is developed from the fundamental principles of abstract algebra and Combinatory Logic. It relies on an enumerative type inhabitation algorithm for Finite Combinatory Logic with Intersection Types (FCL) and a universal algebraic construction to translate terms of Combinatory Logic into any given target language. New insights are gained on the combination of semantic domains of discourse with intersection types. Long standing gaps in the algorithmic understanding of the type inhabitation question of FCL are closed. A practical implementation is developed and its applications by the author and other researchers are discussed. They include, but are not limited to, vast improvements in the context of synthesis of software product line members. An interactive theorem prover, Coq, is used to formalize and check all the theoretical results. This makes them more reusable for other developments and enhances confidence in their correctness.Es wird ein sprachunabhängiger Ansatz für die typbasierte und komponentenorientierte Synthese von Software entwickelt. Hierzu werden grundlegende Erkenntnisse über abstrakte Algebra und kombinatorische Logik verwendet. Der Ansatz beruht auf dem enumerativen Typinhabitationsproblem der endlichen kombinatorischen Logik mit Intersektionstypen, sowie einer universellen algebraischen Konstruktion, um Ergebnisterme in jede beliebe Zielsprache übersetzen zu können. Es werden neue Einblicke gewonnen, wie verschiedene semantische Domänen des Diskurses über Softwareeigenschaften miteinander verbunden werden können. Offene Fragestellungen im Zusammenhand mit der Algorithmik des Typinhabitationsproblems für Intersektionstypen werden beantwortet. Eine praktische Implementierung des Ansatzes wird entwickelt und ihre bisherigen Anwendungen durch den Autor und andere Wissenschaftler werden diskutiert. Diese beinhalten starke Verbesserungen im Zusammenhang mit der Synthese von Ausprägungen von Software Produktlinien. Ein interaktiver Theorembeweiser wir genutzt, um alle Ergebnisse der Arbeit zu formalisieren und mechanisch zu überprüfen. Dies trägt zum einen zur Wiederverwendbarkeit der theoretischen Ergebnisse in anderen Kontexten bei, und erhöht zum andern das Vertrauen in ihre Korrektheit

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

Tools and Algorithms for the Construction and Analysis of Systems

This open access two-volume set constitutes the proceedings of the 26th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The total of 60 regular papers presented in these volumes was carefully reviewed and selected from 155 submissions. The papers are organized in topical sections as follows: Part I: Program verification; SAT and SMT; Timed and Dynamical Systems; Verifying Concurrent Systems; Probabilistic Systems; Model Checking and Reachability; and Timed and Probabilistic Systems. Part II: Bisimulation; Verification and Efficiency; Logic and Proof; Tools and Case Studies; Games and Automata; and SV-COMP 2020