An automata-based automatic verification environment

With the continuing growth of computer systems including safety-critical computer control systems, the need for reliable tools to help construct, analyze, and verify such systems also continues to grow. The basic motivation of this work is to build such a formal verification environment for computer-based systems. An example of such a tool is the Design Oriented Verification and Evaluation (DOVE) created by Australian Defense Science and Technology Organization. One of the advantages of DOVE is that it combines ease of use provided by a graphical user interface for describing specifications in the form of extended state machines with the rigor of proving linear temporal logic properties in a robust theorem prover, Isabelle which was developed at Cambridge University, UK, and TU Munich, Germany. A different class of examples is that of model checkers, such as SPIN and SMV. In this work, we describe our technique to increase the utility of DOVE by extending it with the capability to build systems by specifying components. This added utility is demonstrated with a concrete example from a real project to study aspects of the control unit for an infusion pump being built at the Walter Reid Army Institute of Research. Secondly, we provide a formulation of linear temporal logic (LTL) in the theorem prover Isabelle. Next, we present a formalization of a variation of the algorithm for translating LTL into Büchi automata. The original translation algorithm is presented in Gerth et al and is the basis of model checkers such as SPIN. We also provide a formal proof of the termination and correctness of this algorithm. All definitions and proofs have been done fully formally within the generic theorem prover Isabelle, which guarantees the rigor of our work and the reliability of the results obtained. Finally, we introduce the automata theoretic framework for automatic verification as our future works

Partiality and Recursion in Interactive Theorem Provers - An Overview

To appearInternational audienceThe use of interactive theorem provers to establish the correctness of critical parts of a software development or for formalising mathematics is becoming more common and feasible in practice. However, most mature theorem provers lack a direct treatment of partial and general recursive functions; overcoming this weakness has been the objective of intensive research during the last decades. In this article, we review many techniques that have been proposed in the literature to simplify the formalisation of partial and general recursive functions in interactive theorem provers. Moreover, we classify the techniques according to their theoretical basis and their practical use. This uniform presentation of the different techniques facilitates the comparison and highlights their commonalities and differences, as well as their relative advantages and limitations. We focus on theorem provers based on constructive type theory (in particular, Agda and Coq) and higher-order logic (in particular Isabelle/HOL). Other systems and logics are covered to a certain extent, but not exhaustively. In addition to the description of the techniques, we also demonstrate tools which facilitate working with the problematic functions in particular theorem provers

Inductive invariants for nested recursion

Abstract. We show that certain input-output relations, termed inductive invariants are of central importance for termination proofs of algorithms defined by nested recursion. Inductive invariants can be used to enhance recursive function definition packages in higher-order logic mechanizations. We demonstrate the usefulness of inductive invariants on a large example of the BDD algorithm Apply. Finally, we introduce a related concept of inductive fixpoints with the property that for every functional in higher-order logic there exists a largest partial function that is such a fixpoint.