Formalising the pi-calculus using nominal logic

We formalise the pi-calculus using the nominal datatype package, based on ideas from the nominal logic by Pitts et al., and demonstrate an implementation in Isabelle/HOL. The purpose is to derive powerful induction rules for the semantics in order to conduct machine checkable proofs, closely following the intuitive arguments found in manual proofs. In this way we have covered many of the standard theorems of bisimulation equivalence and congruence, both late and early, and both strong and weak in a uniform manner. We thus provide one of the most extensive formalisations of a process calculus ever done inside a theorem prover. A significant gain in our formulation is that agents are identified up to alpha-equivalence, thereby greatly reducing the arguments about bound names. This is a normal strategy for manual proofs about the pi-calculus, but that kind of hand waving has previously been difficult to incorporate smoothly in an interactive theorem prover. We show how the nominal logic formalism and its support in Isabelle accomplishes this and thus significantly reduces the tedium of conducting completely formal proofs. This improves on previous work using weak higher order abstract syntax since we do not need extra assumptions to filter out exotic terms and can keep all arguments within a familiar first-order logic.Comment: 36 pages, 3 figure

A static analysis framework for security properties in mobile and cryptographic systems

We introduce a static analysis framework for detecting instances of security breaches in infinite mobile and cryptographic systems specified using the languages of the 7r-calculus and its cryptographic extension, the spi calculus. The framework is composed from three components: First, standard denotational semantics of the 7r-calculus and the spi calculus are constructed based on domain theory. The resulting model is sound and adequate with respect to transitions in the operational semantics. The standard semantics is then extended correctly to non-uniformly capture the property of term substitution, which occurs as a result of communications and successful cryptographic operations. Finally, the non-standard semantics is abstracted to operate over finite domains so as to ensure the termination of the static analysis. The safety of the abstract semantics is proven with respect to the nonstandard semantics. The results of the abstract interpretation are then used to capture breaches of the secrecy and authenticity properties in the analysed systems. Two initial prototype implementations of the security analysis for the 7r-calculus and the spi calculus are also included in the thesis. The main contributions of this thesis are summarised by the following. In the area of denotational semantics, the thesis introduces a domain-theoretic model for the spi calculus that is sound and adequate with respect to transitions in the structural operational semantics. In the area of static program analysis, the thesis utilises the denotational approach as the basis for the construction of abstract interpretations for infinite systems modelled by the 7r-calculus and the spi calculus. This facilitates the use of computationally significant mathematical concepts like least fixed points and results in an analysis that is fully compositional. Also, the thesis demonstrates that the choice of the term-substitution property in mobile and cryptographic programs is rich enough to capture breaches of security properties, like process secrecy and authenticity. These properties are used to analyse a number of mobile and cryptographic protocols, like the file transfer protocol and the Needham-Schroeder, SPLICE/AS, Otway-Rees, Kerberos, Yahalom and Woo Lam authentication protocols

Extensions of nominal terms

This thesis studies two major extensions of nominal terms. In particular, we study an extension with -abstraction over nominal unknowns and atoms, and an extension with an arguably better theory of freshness and -equivalence. Nominal terms possess two levels of variable: atoms a represent variable symbols, and unknowns X are `real' variables. As a syntax, they are designed to facilitate metaprogramming; unknowns are used to program on syntax with variable symbols. Originally, the role of nominal terms was interpreted narrowly. That is, they were seen solely as a syntax for representing partially-speci ed abstract syntax with binding. The main motivation of this thesis is to extend nominal terms so that they can be used for metaprogramming on proofs, programs, etc. and not just for metaprogramming on abstract syntax with binding. We therefore extend nominal terms in two signi cant ways: adding -abstraction over nominal unknowns and atoms| facilitating functional programing|and improving the theory of -equivalence that nominal terms possesses. Neither of the two extensions considered are trivial. The capturing substitution action of nominal unknowns implies that our notions of scope, intuited from working with syntax possessing a non-capturing substitution, such as the -calculus, is no longer applicable. As a result, notions of -abstraction and -equivalence must be carefully reconsidered. In particular, the rst research contribution of this thesis is the two-level - calculus, intuitively an intertwined pair of -calculi. As the name suggests, the two-level -calculus has two level of variable, modelled by nominal atoms and unknowns, respectively. Both levels of variable can be -abstracted, and requisite notions of -reduction are provided. The result is an expressive context-calculus. The traditional problems of handling -equivalence and the failure of commutation between instantiation and -reduction in context-calculi are handled through the use of two distinct levels of variable, swappings, and freshness side-conditions on unknowns, i.e. `nominal technology'. The second research contribution of this thesis is permissive nominal terms, an alternative form of nominal term. They retain the `nominal' rst-order avour of nominal terms (in fact, their grammars are almost identical) but forego the use of explicit freshness contexts. Instead, permissive nominal terms label unknowns with a permission sort, where permission sorts are in nite and coin nite sets of atoms. This in nite-coin nite nature means that permissive nominal terms recover two properties|we call them the `always-fresh' and `always-rename' properties that nominal terms lack. We argue that these two properties bring the theory of -equivalence on permissive nominal terms closer to `informal practice'. The reader may consider -abstraction and -equivalence so familiar as to be `solved problems'. The work embodied in this thesis stands testament to the fact that this isn't the case. Considering -abstraction and -equivalence in the context of two levels of variable poses some new and interesting problems and throws light on some deep questions related to scope and binding

Unique Solutions of Contractions, CCS, and their HOL Formalisation

The unique solution of contractions is a proof technique for bisimilarity that overcomes certain syntactic constraints of Milner's "unique solution of equations" technique. The paper presents an overview of a rather comprehensive formalisation of the core of the theory of CCS in the HOL theorem prover (HOL4), with a focus towards the theory of unique solutions of contractions. (The formalisation consists of about 20,000 lines of proof scripts in Standard ML.) Some refinements of the theory itself are obtained. In particular we remove the constraints on summation, which must be weakly-guarded, by moving to rooted contraction, that is, the coarsest precongruence contained in the contraction preorder.Comment: In Proceedings EXPRESS/SOS 2018, arXiv:1808.0807

A Concurrent Pattern Calculus

International audienceConcurrent pattern calculus (CPC) drives interaction between processes by comparing data structures, just as sequential pattern calculus drives computation. By generalising from pattern matching to pattern unification, interaction becomes symmetrical, with information flowing in both directions. CPC provides a natural language to express trade where information exchange is pivotal to interaction. The unification allows some patterns to be more discriminating than others; hence, the behavioural theory must take this aspect into account, so that bisimulation becomes subject to compatibility of patterns. Many popular process calculi can be encoded in CPC; this allows for a gain in expressiveness, formalised through encodings

Analysis and implementation of fractional-order chaotic system with standard components

This paper is devoted to the problem of uncertainty in fractional-order Chaotic systems implemented by means of standard electronic components. The fractional order element (FOE) is typically substituted by one complex impedance network containing a huge number of discrete resistors and capacitors. In order to balance the complexity and accuracy of the circuit, a sparse optimization based parameter selection method is proposed. The random error and the uncertainty of system implementation are analyzed through numerical simulations. The effectiveness of the method is verified by numerical and circuit simulations, tested experimentally with electronic circuit implementations. The simulations and experiments show that the proposed method reduces the order of circuit systems and finds a minimum number for the combination of commercially available standard components.This work was supported in part by the National Natural Science Foundation of China under Grant 61501385, in part by the National Nuclear Energy Development Project of State Administration for Science, Technology and Industry for National Defense, PRC under Grant 18zg6103, and in part by Sichuan Science and Technology Program under Grant 2018JY0522. We would like to thank Xinghua Feng for meaningful discussion.info:eu-repo/semantics/publishedVersio