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Providing a Formal Linkage between MDG and HOL
, 2002
"... We describe an approach for formally verifying the linkage between a symbolic state enumeration system and a theorem proving system. This involves the following three stages of proof. Firstly we prove theorems about the correctness of the translation part of the symbolic state system. It interface ..."
Abstract

Cited by 2 (2 self)
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We describe an approach for formally verifying the linkage between a symbolic state enumeration system and a theorem proving system. This involves the following three stages of proof. Firstly we prove theorems about the correctness of the translation part of the symbolic state system. It interfaces between low level decision diagrams and high level description languages. We ensure that the semantics of a program is preserved in those of its translated form. Secondly we prove linkage theorems: theorems that justify introducing a result from a state enumeration system into a proof system. Finally we combine the translator correctness and linkage theorems. The resulting new linkage theorems convert results to a high level language from the low level decision diagrams that the result was actually proved about in the state enumeration system.They justify importing lowlevel external verification results into a theorem prover. We use a linkage between the HOL system and a simplified version of the MDG system to illustrate the ideas and consider a small example that integrates two applications from MDG and HOL to illustrate the linkage theorems.
Formally Linking MDG and HOL Based on a Verified MDG System
"... We describe an approach for formally linking a symbolic state enumeration system and a theorem proving system based on a veri ed version of the former. It has been realized using a simpli ed version of the MDG system and the HOL system. Firstly, we have veri ed aspects of correctness of a simp ..."
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We describe an approach for formally linking a symbolic state enumeration system and a theorem proving system based on a veri ed version of the former. It has been realized using a simpli ed version of the MDG system and the HOL system. Firstly, we have veri ed aspects of correctness of a simpli ed version 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 veri cation results can be formally imported into HOL to form a HOL theorem. Thirdly, we have combined the translator correctness theorems and importing theorems. This allows the MDG veri cation results to be imported in terms of a high level language (MDGHDL) rather than a low level language. We also summarize a general method to prove existential theorems for the design. The feasibility of this approach is demonstrated in a case study that integrates two applications: hardware veri cation (in MDG) and usability veri cation (in HOL). A single HOL theorem is proved that integrates the two results.
Providing a Formal Linkage between MDG Verification System and HOL Proof System
, 2003
"... We describe an approach for formally linking a symbolic state enumeration system and a theorem proving system based on a verified version of the former. It has been realized using the HOL system and a simplified version of the MDG system. It involves the following three steps. Firstly, wehave verifi ..."
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We describe an approach for formally linking a symbolic state enumeration system and a theorem proving system based on a verified version of the former. It has been realized using the HOL system and a simplified version of the MDG system. It involves the following three steps. Firstly, wehave verified aspects of correctness of a simplified version 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 a set of theorems, which formally import MDG verification results into HOL theorems. Thirdly, wehave combined the translator correctness and importation theorems to allow MDG verification results to be imported in terms of a high level language (MDGHDL) rather than low level decision diagrams. We also summarize a general method of the stronger consistency theorem to prove design implementations against respective specifications. The feasibility of this approach is demonstrated in a case study that integrates two applications: hardware verification (in MDG) and usability verification (in HOL). A single HOL theorem is proved that integrates the two results.
LCFstyle for Secure Verification Platform based on Multiway Decision Graphs
"... Abstract. 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 reasoni ..."
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Abstract. 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. A comparison between both categories is discussed in details. In this paper, we are interested in presenting as an example a platform for Multiway Decision Graphs (MDGs) in LCFstyle theorem prover. Based on this platform, many conversions such as the reachability analysis and reduction techniques can be implemented that uses the MDG theory within the HOL theorem prover. The paper also questions the best formalization principle of decision graphs to build such a platform in theorem proving since a set of basic operations are used to efficiently manipulate the decision graphs which constitute the kernel of the model checking algorithms, by describing two alternatives to formalize these decision graphs. Then we contrast between them according to their efficiency, complexity and feasibility. Finally, we hope this paper to serve as an adequate introduction to the concepts involved in formalization and a survey of relevant work. 1