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Proof search specifications of bisimulation and modal logics for the πcalculus
 ACM Trans. on Computational Logic
"... We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allo ..."
Abstract

Cited by 7 (5 self)
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We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allows this logic to be complete for both the inductive nature of operational semantics and the coinductive nature of bisimulation. The ∇ quantifier helps with the delicate issues surrounding the scope of variables within πcalculus expressions and their executions (proofs). We shall illustrate several merits of the logical specifications permitted by this logic: they are natural and declarative; they contain no sideconditions concerning names of variables while maintaining a completely formal treatment of such variables; differences between late and open bisimulation relations arise from familar logic distinctions; the interplay between the three quantifiers (∀, ∃, and ∇) and their scopes can explain the differences between early and late bisimulation and between various modal operators based on bound input and output actions; and proof search involving the application of inference rules, unification, and backtracking can provide complete proof systems for onestep transitions, bisimulation, and satisfaction in modal logic. We also illustrate how one can encode the πcalculus with replications, in an extended logic with induction and coinduction.
Implementing spi calculus using nominal techniques
 In CiE, volume 5028 of LNCS
, 2008
"... Abstract. The aim of this work is to obtain an interactive proof environment based on Isabelle/HOL for reasoning formally about cryptographic protocols, expressed as processes of the spi calculus (a πcalculus with cryptographic primitives). To this end, we formalise syntax, semantics, and hedged bi ..."
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Cited by 2 (0 self)
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Abstract. The aim of this work is to obtain an interactive proof environment based on Isabelle/HOL for reasoning formally about cryptographic protocols, expressed as processes of the spi calculus (a πcalculus with cryptographic primitives). To this end, we formalise syntax, semantics, and hedged bisimulation, an environmentsensitive bisimulation which can be used for proving security properties of protocols. In order to deal smoothly with binding operators and reason upto αequivalence of bound names, we adopt the new Nominal datatype package. This simplifies both the encoding, and the formal proofs, which turn out to correspond closely to “manual proofs”. 1
The Australian National University
"... We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allo ..."
Abstract
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We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allows this logic to be complete for both the inductive nature of operational semantics and the coinductive nature of bisimulation. The ∇ quantifier helps with the delicate issues surrounding the scope of variables within πcalculus expressions and their executions (proofs). We illustrate several merits of the logical specifications permitted by this logic: they are natural and declarative; they contain no sideconditions concerning names of variables while maintaining a completely formal treatment of such variables; differences between late and open bisimulation relations arise from familar logic distinctions; the interplay between the three quantifiers (∀, ∃, and ∇) and their scopes can explain the differences between early and late bisimulation and between various modal operators based on bound input and output actions; and proof search involving the application of inference rules, unification, and backtracking can provide complete proof systems for onestep transitions, bisimulation, and satisfaction in modal logic. We also illustrate how one can encode