Formal verification of the Island Tunnel Controller using Multiway Decision Graphs

Zhou, Zijian; Song, Xiaoyu; Tahar, Sofiène; Cerny, Eduard; Corella, Francisco; Langevin, M.

doi:10.1007/bfb0031811

Cited by 23 publications

(12 citation statements)

References 16 publications

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“…The case studies cover two small benchmarks: MIN-MAX and Abstract Counter, one intermediate benchmark: the Look-Aside Interface (LA-1) [44] , and one large benchmark: the Island Tunnel Controller (ITC) [45] . The performance is measured in terms of full reachability analysis for these models.…”

Section: Resultsmentioning

confidence: 99%

An Abstract Reachability Approach by Combining HOL Induction and Multiway Decision Graphs

Abed

Mohamed

Al-Sammane

2009

J. Comput. Sci. Technol.

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In this paper, we provide a necessary infrastructure to define an abstract state exploration in the HOL theorem prover. Our infrastructure is based on a deep embedding of the Multiway Decision Graphs (MDGs) theory in HOL. MDGs generalize Reduced Ordered Binary Decision Diagrams (ROBDDs) to represent and manipulate a subset of first-order logic formulae. The MDGs embedding is based on the logical formulation of an MDG as Directed Formulae (DF). Then, the MDGs operations are defined and the correctness proof of each operation is provided. The MDG reachability algorithm is then defined as a conversion that uses our MDG theory within HOL. Finally, a set of experimentations over benchmark circuits has been conducted to ensure the applicability and to measure the performance of our approach.

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Section: Resultsmentioning

confidence: 99%

An Abstract Reachability Approach by Combining HOL Induction and Multiway Decision Graphs

Abed

Mohamed

Al-Sammane

2009

J. Comput. Sci. Technol.

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“…The non-termination problem was first addressed in [28], where a method was based on the generalization of the state variable that causes divergence. This technique is applicable only to processor-like-loop circuit and if the entrance of the loop does not start in the initial state then this generalization approach may not work.…”

Section: Discussionmentioning

confidence: 99%

NuMDG: A New Tool for Multiway Decision Graphs Construction

Abed

Mokhtari

Ait-Mohamed

et al. 2011

J. Comput. Sci. Technol.

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Multiway Decision Graphs (MDGs) are a canonical representation of a subset of many-sorted first-order logic. This subset generalizes the logic of equality with abstract types and uninterpreted function symbols. The distinction between abstract and concrete sorts mirrors the hardware distinction between data path and control. Here we consider ways to improve MDGs construction. Efficiency is achieved through the use of the Generalized-If-Then-Else (GITE) commonly operator in Binary Decision Diagram packages. Consequently, we review the main algorithms used for MDGs verification techniques. In particular, Relational Product and Pruning by Subsumption are algorithms defined uniformly through this single GITE operator which will lead to a more efficient implementation. Moreover, we provide their correctness proof. This work can be viewed as a way to accommodate the ROBBD algorithms to the realm of abstract sorts and uninterpreted functions. The new tool, called NuMDG, accepts an extended SMV language, supporting abstract data sorts. Finally, we present experimental results demonstrating the efficiency of the NuMDG tool and evaluating its performance using a set of benchmarks from the SMV package.

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“…The star operator is handled by merging the results of simulating the starred expression a small number of times, to find a symbolic state that subsumes the symbolic states that would be computed by exactly simulating all possible numbers of iterations. This approach is similar to that used with MDGs by Zhou et al [26].…”

Section: (S"pap a Ap ß )mentioning

confidence: 97%

Formally Verifying Data and Control with Weak Reachability Invariants

Dill

Skakkebæk

1998

Formal Methods in Computer-Aided Design

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Existing formal verification methods do not handle systems that combine state machines and data paths very well. Model checking deals with finitestate machines efficiently, but model checking full designs is infeasible because of the large amount of state in the data path. Theorem-proving methods may be effective for verifying data path operations, but verifying the control requires finding and proving inductive invariants that characterize the reachable states of the system. We present a new approach to verification of systems that combine control FSMs and data path operations. Invariants are specified only for a small set of control states, called clean states, where the invariants are especially simple. We avoid the need to specify the invariants for the unclean states by symbolically simulating over all paths to find the possible next clean states. The set of all paths from one clean state to the next is represented by a regular expression, which is extracted from the control FSMs. The number of paths is infinite only if the regular expression contains stars. The method uses a heuristic to generalize the symbolic state to cover all of the paths of the starred expression. We have implemented a prototype tool for guiding an existing symbolic simulator and verification tool and used it successfully to prove properties of the Instruction Fetch Unit of TORCH, a superscalar microprocessor designed at Stanford. With much less effort, we were able to find all the bugs in the unit that were found earlier by manually strengthening the invariants.

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Formal verification of the Island Tunnel Controller using Multiway Decision Graphs

Cited by 23 publications

References 16 publications

An Abstract Reachability Approach by Combining HOL Induction and Multiway Decision Graphs

An Abstract Reachability Approach by Combining HOL Induction and Multiway Decision Graphs

NuMDG: A New Tool for Multiway Decision Graphs Construction

Formally Verifying Data and Control with Weak Reachability Invariants

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