Providing Automated Verification in HOL Using MDGs

While model checking suffers from the state space explosion problem, theorem proving is quite tedious and impractical for verifying complex designs. In this work, we present a verification framework in which we attempt to strike the balance between the expressiveness of theorem proving and the efficiency and automation of state exploration techniques. To this end, we propose to integrate a layer of checking algorithms based on Multiway Decision Graphs (MDG) in the HOL theorem prover. We deeply embedded the MDG underlying logic in HOL and implemented a platform that provides a set of algorithms allowing the user to develop his/her own state-exploration based application inside HOL. While the verification problem is specified in HOL, the proof is derived by tightly combining the MDG based computations and the theorem prover facilities. We have been able to implement and experiment with different state exploration techniques within HOL such as MDG reachability analysis, equivalence and model checking

LCF-style Platform based on Multiway Decision Graphs

AbstractThe combination of state exploration approach (mainly model checking) and deductive reasoning approach (theorem proving) promises to overcome the limitation and to enhance the capabilities of each. In this paper, we are interested in defining a platform for Multiway Decision Graphs (MDGs) in LCF-style theorem prover. We define a platform to represent the MDG operations: conjunction, disjunction, relational product and prune-by-subsumption as a set of inference rules. Based on this platform, the reachability analysis is implemented as a conversion that uses the MDG theory within the HOL theorem prover. Finally, we present some experimental results to show the performance of the MDG operations of our platform

The verification of MDG algorithms in the HOL theorem prover

Formal verification of digital systems is achieved, today, using one of two main approaches: states exploration (mainly model checking and equivalence checking) or deductive reasoning (theorem proving). Indeed, the combination of the two approaches, states exploration and deductive reasoning promises to overcome the limitation and to enhance the capabilities of each. Our research is motivated by this goal. In this thesis, we provide the entire necessary infrastructure (data structure + algorithms) to define high level states exploration in the HOL theorem prover named as MDG-HOL platform. While related work has tackled the same problem by representing primitive Binary Decision Diagram (BDD) operations as inference rules added to the core of the theorem prover, we have based our approach on the Multiway Decision Graphs (MDGs). MDG generalizes ROBDD to represent and manipulate a subset of first-order logic formulae. With MDGs, a data value is represented by a single variable of an abstract type and operations on data are represented in terms of uninterpreted function. Considering MDGs instead of BDDs will raise the abstraction level of what can be verified using a state exploration within a theorem prover. The MDGs embedding is based on the logical formulation of an MDG as a Directed Formulae (DF). The DF syntax is defined as HOL built-in data types. We formalize the basic MDG operations using this syntax within HOL following a deep embedding approach. Such approach ensures the consistency of our embedding. Then, we derive the correctness proof for each MDG basic operator. Based on this platform, the MDG reachability analysis is defined in HOL as a conversion that uses the MDG theory within HOL. Then, we demonstrate the effectiveness of our platform by considering four case studies. Our obtained results show that this verification framework offers a considerable gain in terms of automation without sacrificing CPU time and memory usage compared to automatic model checker tools. Finally, we propose a reduction technique to improve MDGs model checking based on the MDG-HOL platform. The idea is to prune the transition relation of the circuits using pre-proved theorems and lemmas from the specification given at system level. We also use the consistency of the specifications to verify if the reduced model is faithful to the original one. We provide two case studies, the first one is the reduction using SAT-MDG of an Island Tunnel Controller and the second one is the MDG-HOL assume-guarantee reduction of the Look-Aside Interface. The obtained results of our approach offers a considerable gain in terms of heuristics and reduction techniques correctness as to commercial model checking; however a small penalty is paid in terms of CPU time and memory usag

Emerging trends proceedings of the 17th International Conference on Theorem Proving in Higher Order Logics: TPHOLs 2004

technical reportThis volume constitutes the proceedings of the Emerging Trends track of the 17th International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2004) held September 14-17, 2004 in Park City, Utah, USA. The TPHOLs conference covers all aspects of theorem proving in higher order logics as well as related topics in theorem proving and verification. There were 42 papers submitted to TPHOLs 2004 in the full research cate- gory, each of which was refereed by at least 3 reviewers selected by the program committee. Of these submissions, 21 were accepted for presentation at the con- ference and publication in volume 3223 of Springer?s Lecture Notes in Computer Science series. In keeping with longstanding tradition, TPHOLs 2004 also offered a venue for the presentation of work in progress, where researchers invite discussion by means of a brief introductory talk and then discuss their work at a poster session. The work-in-progress papers are held in this volume, which is published as a 2004 technical report of the School of Computing at the University of Utah

Providing a formal linkage between MDG and HOL based on a verified MDG system.

Formal verification techniques can be classified into two categories: deductive theorem proving and symbolic state enumeration. Each method has complementary advantages and disadvantages. In general, theorem provers are high reliability systems. They can be applied to the expressive formalisms that are capable of modelling complex designs such as processors. However, theorem provers use a glass-box approach. To complete a verification, it is necessary to understand the internal structure in detail. The learning curve is very steep and modeling and verifying a system is very time-consuming. In contrast, symbolic state enumeration tools use a black-box approach. When verifying a design, the user does not need to understand its internal structure. Their advantages are their speed and ease of use. But they can only be used to prove relatively simple designs and the system security is much lower than the theorem proving system. Many hybrid tools have been developed to reap the benefits of both theorem proving Systems and symbolic state enumeration Systems. Normally, the verification results from one system are translated to another system. In other words, there is a linkage between the two Systems. However, how can we ensure that this linkage can be trusted? How can we ensure the verification system itself is correct? The contribution of this thesis is that we have produced a methodology which can provide a formal linkage between a symbolic state enumeration system and a theorem proving system based on a verified symbolic state enumeration system. The methodology has been partly realized in two simplified versions of the MDG system (a symbolic state enumeration system) and the HOL system (a theorem proving system) which involves the following three steps. First, we have verified aspects of correctness of two simplified versions of the MDG system. We have made certain that the semantics of a program is preserved in those of its translated form. Secondly, we have provided a formal linkage between the MDG system and the HOL system based on importing theorems. The MDG verification results can be formally imported into HOL to form the HOL theorems. Thirdly, we have combined the translator correctness theorems with the importing theorems. This combination allows the low level MDG verification results to be imported into HOL in terms of the semantics of a high level language (MDG-HDL). We have also summarized a general method which is used to prove the existential theorem for the specification and implementation of the design. The feasibility of this approach has been demonstrated in a case study: the verification of the correctness and usability theorems of a vending machine