The performance of combining multiway decision graphs and HOL theorem prover

Abed, Sa’ed; Mohamed, Otmane Aït; Sammane, Ghiath Al

doi:10.1109/fdl.2008.4641435

Cited by 2 publications

(10 citation statements)

References 14 publications

(17 reference statements)

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“…The both side eq function is used to represent the LHS and RHS of an equation. The HOL definitions of the mapping functions and the well-formedness conditions are included in [40] . This mapping simplifies our implementation and enables us to automate the MDG operations by using the infrastructure of the predefined List Theory in HOL to inherit all the definitions and theorems.…”

Section: Df In Holmentioning

confidence: 99%

“…(Note that there is no need of an equation v = a for every concrete variable v ∈ V .) Please note that all the embedding details can be reached at [40]. …”

Section: Well-formedness Conditionsmentioning

confidence: 99%

“…where Condition2 and Condition3 represent the wellformedness conditions [40] . The STRIP ABS DF function extracts the abstract variables of a DF and STRIP DF extracts the LHS variables of each disjuncts of a DF.…”

Section: Well-formedness Conditionsmentioning

confidence: 99%

“…Finally, axiom WF E3 expresses the equality of concrete term and concrete individual constant. The theorems needed for the inference rule representing this condition are described in [40].…”

Section: Well-formedness Conditionsmentioning

confidence: 99%

“…The assumptions needed for this condition are: the two well-formed equations and the LHS of each equation should not be equal. We prove a HOL theorem (WF Conj) that states the correctness of the inference rule related to this condition is included in [40].…”

Section: Well-formedness Conditionsmentioning

confidence: 99%

See 4 more Smart Citations

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: Df In Holmentioning

confidence: 99%

“…(Note that there is no need of an equation v = a for every concrete variable v ∈ V .) Please note that all the embedding details can be reached at [40]. …”

Section: Well-formedness Conditionsmentioning

confidence: 99%

Section: Well-formedness Conditionsmentioning

confidence: 99%

Section: Well-formedness Conditionsmentioning

confidence: 99%

Section: Well-formedness Conditionsmentioning

confidence: 99%

See 3 more Smart Citations

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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Automatic verification of reduction techniques in Higher Order Logic

2013

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In this paper we propose an automatic methodology to verify the soundness of model checking reduction techniques. The idea is to use the consistency of the specifications to verify if the reduced model is faithful to the original one. The user provides the reduction technique, the specification and the system under verification. Then, using Higher Order Logic he verifies automatically if the reduction technique is soundly applied. The method is completely defined in an MDG–HOL special integration platform that combines an automatic high level model checking tool Multiway Decision Graphs (MDGs) within the HOL theorem prover. 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 offer a considerable gain in terms of the correctness of heuristics and reduction techniques as applied to commercial model checking, however a small penalty is paid in terms of CPU time and memory usage.

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The performance of combining multiway decision graphs and HOL theorem prover

Cited by 2 publications

References 14 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

Automatic verification of reduction techniques in Higher Order Logic

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