Techniques for solving Boolean equation systems

Boolean equation systems are ordered sequences of Boolean equations decorated with least and greatest fixpoint operators. Boolean equation systems provide a useful framework for formal verification because various specification and verification problems, for instance, μ-calculus model checking can be represented as the problem of solving Boolean equation systems. The general problem of solving a Boolean equation system is a computationally hard task, and no polynomial time solution technique for the problem has been discovered so far. In this thesis, techniques for finding solutions to Boolean equation systems are studied and new methods for solving such systems are devised. The thesis presents a general framework that allows for dividing Boolean equation systems into individual blocks and solving these blocks in isolation with special techniques. Three special techniques are presented, namely: (i) new specialized algorithms for disjunctive and conjunctive form Boolean equation systems, (ii) a new encoding of a general form Boolean equation system into answer set programming, and (iii) new encodings of a general form Boolean equation systems into satisfiability problems. The approaches (ii) and (iii) are motivated by the recent success of answer set programming solvers and satisfiability solvers in formal verification. First, the thesis presents especially fast solution algorithms for disjunctive and conjunctive classes of Boolean equation systems. These special algorithms are useful because many practically relevant model checking problems can be represented as Boolean equation systems that are disjunctive or conjunctive. The new algorithms have been implemented and the performance of the algorithms has been compared experimentally on communication protocol verification examples. Second, the thesis gives a translation of the problem of solving a general form Boolean equation system into the problem of finding a stable model of a logic program. The translation allows to use implementations of answer set programming solvers to solve Boolean equation systems. Experimental tests have been performed using the presented approach and these experiments indicate the usefulness of answer set programming in this problem domain. Third, the thesis presents reductions from the problem of solving general form Boolean equation systems to the satisfiability problems of difference logic and propositional logic. The reductions allow to use implementations of satisfiability solvers to solve Boolean equation systems. The presented reductions have been implemented and it is shown via experiments that the new approach leads to practically efficient methods to solve general Boolean equation systems.Boolen yhtälöryhmät ovat kiintopisteoperaattoreilla varustettuja Boolen yhtälöitä. Boolen yhtälöryhmät luovat hyödyllisen viitekehyksen tietokoneavusteiselle verifioinnille, sillä monet määrittely- ja verifiointiongelmat voidaan kuvata tällaisten kiintopisteyhtälöiden avulla. Työssä kehitetään uusia menetelmiä Boolen yhtälöryhmien ratkaisemiseen. Työssä esitetään yleinen viitekehys Boolen yhtälöryhmien ratkaisemiseen, joka yksinkertaistaa ratkaisun laskemista jakamalla yhtälöryhmät yksinkertaisempiin aliongelmiin. Työssä esitetään kolme uutta mentelmää Boolen yhtälöryhmien ratkaisemiseen. Konjunktiivisten ja disjunktiivisten Boolen yhtälöryhmien ratkaisemiseen kehitetään uusia algoritmeja, sekä esitetään näiden toteutukset ja suorituskykyjä koskevia koetuloksia. Työssä kehitetään käännös Boolen yhtälöryhmän ratkaisemisesta logiikkaohjelman stabiilin mallin löytämiseen sekä menetelmän toimivuutta koskevia koetuloksia. Käännös mahdollistaa logiikkaohjelmointiympäristöjen toteutusten käytön Boolen yhtälöryhmien ratkaisemiseen. Koetulokset osoittavat rajoitepohjaisen logiikkaohjelmointiympäristön tehokkuuden Boolen yhtälöryhmien ratkaisemisessa. Työssä kehitetään myös käännökset Boolen yhtälöryhmän ratkaisemisesta differenssilogiikan sekä lauselogiikan toteutuvuusongelmiin. Käännökset mahdollistavat toteutuvuustarkastimien käytön Boolen yhtälöryhmien ratkaisemiseen. Koetulokset osoittavat esitettyjen menetelmien tehokkuuden Boolen yhtälöryhmien ratkaisemisessa.reviewe

Liquid Clocks - Refinement Types for Time-Dependent Stream Functions

The concept of liquid clocks introduced in this paper is a significant step towards a more precise compile-time framework for the analysis of synchronous and polychromous languages. Compiling languages such as Lustre or SIGNAL indeed involves a number of static analyses of programs before they can be synthesized into executable code, e.g., synchronicity class characterization, clock assignment, static scheduling or causality analysis. These analyses are often equivalent to undecidable problems, necessitating abstracting such programs to provide sound yet incomplete analyses. Such abstractions unfortunately often lead to the rejection of programs that could very well be synthesized into deterministic code, provided abstraction refinement steps could be applied for more accurate analysis. To reduce the false negatives occurring during the compilation process, we leverage recent advances in type theory -- with the definition of decidable classes of value-dependent type systems -- and formal verification, linked to the development of efficient SAT/SMT solvers, to provide a type-theoretic approach that considers all the above analyses as type inference problems. In order to simplify the exposition of our new approach in this paper, we define a refinement type system for a minimalistic, synchronous, stream-processing language to concisely represent, analyse, and verify logical and quantitative properties of programs expressed as stream-processing data-flow networks. Our type system provides a new framework to represent logical time (clocks) and scheduling properties, and to describe their relations with stream values and, possibly, other quantas. We show how to analyze synchronous stream processing programs (à la Lustre, Signal) to enable previously described analyzes involved in compiling such programs. We also prove the soundness of our type system and elaborate on the adaptability of this core framework by outlining its extensibility to specific models of computations and other quantas

Contribution à la commande sûre des Systèmes à Événements Discrets

Les activités de recherche rentrent dans le spectre de la section 61 du CNU et ont pour domaine l’Automatique des Systèmes à Événements Discrets (SED). Elles sont conduites en vue d’accroître la sûreté de fonctionnement des systèmes automatisés comme ceux qu’il est possible de trouver dans le cadre de la production manufacturière, de la production d'énergie ou du transport. Une grande partie de ces recherches a concerné la conception sûre des systèmes de contrôle-commande à base d’Automates Programmables Industriels (API) et plus particulièrement les thématiques suivantes :- la vérification formelle de programmes de contrôle-commande,- la synthèse algébrique de programmes de contrôle-commande à partir de spécifications informelles,- le test de conformité d’un contrôleur logique vis-à-vis de sa spécification.D'autres recherches ont porté sur la formalisation des outils pour l’analyse de sûreté, utilisés dans le cadre de l’analyse prévisionnelle des risques d’un équipement ou d’une installation industrielle. Cette formalisation des outils utilisés en sûreté a été faite en examinant avec un point de vue SED une problématique qui ne l’était pas à son origine. Il a été étudié :- la modélisation algébrique des arbres de défaillances dynamiques,- l’analyse prévisionnelle des risques d’un point de vue qualitatif pour les systèmes réparables à partir de Boolean logic Driven Markov Processes (BDMPs),- l’analyse prévisionnelle des risques d’un point de vue quantitatif pour les systèmes réparables à l’aide de chaînes de Markov.D'une manière générale, ces activités de recherche ont pour objectif de proposer des apports formels ou méthodologiques à des outils de modélisation généralement issus de l’industrie tout en répondant à des besoins industriels déjà présents ou sur le point de le devenir

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications

A methodology for producing reliable software, volume 1

An investigation into the areas having an impact on producing reliable software including automated verification tools, software modeling, testing techniques, structured programming, and management techniques is presented. This final report contains the results of this investigation, analysis of each technique, and the definition of a methodology for producing reliable software

A Dempster-Shafer theory inspired logic.

Issues of formalising and interpreting epistemic uncertainty have always played a prominent role in Artificial Intelligence. The Dempster-Shafer (DS) theory of partial beliefs is one of the most-well known formalisms to address the partial knowledge. Similarly to the DS theory, which is a generalisation of the classical probability theory, fuzzy logic provides an alternative reasoning apparatus as compared to Boolean logic. Both theories are featured prominently within the Artificial Intelligence domain, but the unified framework accounting for all the aspects of imprecise knowledge is yet to be developed. Fuzzy logic apparatus is often used for reasoning based on vague information, and the beliefs are often processed with the aid of Boolean logic. The situation clearly calls for the development of a logic formalism targeted specifically for the needs of the theory of beliefs. Several frameworks exist based on interpreting epistemic uncertainty through an appropriately defined modal operator. There is an epistemic problem with this kind of frameworks: while addressing uncertain information, they also allow for non-constructive proofs, and in this sense the number of true statements within these frameworks is too large. In this work, it is argued that an inferential apparatus for the theory of beliefs should follow premises of Brouwer's intuitionism. A logic refuting tertium non daturìs constructed by defining a correspondence between the support functions representing beliefs in the DS theory and semantic models based on intuitionistic Kripke models with weighted nodes. Without addional constraints on the semantic models and without modal operators, the constructed logic is equivalent to the minimal intuitionistic logic. A number of possible constraints is considered resulting in additional axioms and making the proposed logic intermediate. Further analysis of the properties of the created framework shows that the approach preserves the Dempster-Shafer belief assignments and thus expresses modality through the belief assignments of the formulae within the developed logic

Liquid Clocks - Refinement Types for Time-Dependent Stream Functions

The concept of liquid clocks introduced in this paper is a significant step towards a more precise compile-time framework for the analysis of synchronous and polychromous languages. Compiling languages such as Lustre or SIGNAL indeed involves a number of static analyses of programs before they can be synthesized into executable code, e.g., synchronicity class characterization, clock assignment, static scheduling or causality analysis. These analyses are often equivalent to undecidable problems, necessitating abstracting such programs to provide sound yet incomplete analyses. Such abstractions unfortunately often lead to the rejection of programs that could very well be synthesized into deterministic code, provided abstraction refinement steps could be applied for more accurate analysis. To reduce the false negatives occurring during the compilation process, we leverage recent advances in type theory -- with the definition of decidable classes of value-dependent type systems -- and formal verification, linked to the development of efficient SAT/SMT solvers, to provide a type-theoretic approach that considers all the above analyses as type inference problems. In order to simplify the exposition of our new approach in this paper, we define a refinement type system for a minimalistic, synchronous, stream-processing language to concisely represent, analyse, and verify logical and quantitative properties of programs expressed as stream-processing data-flow networks. Our type system provides a new framework to represent logical time (clocks) and scheduling properties, and to describe their relations with stream values and, possibly, other quantas. We show how to analyze synchronous stream processing programs (à la Lustre, Signal) to enable previously described analyzes involved in compiling such programs. We also prove the soundness of our type system and elaborate on the adaptability of this core framework by outlining its extensibility to specific models of computations and other quantas