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Constructing weak simulations from linear implications for processes with private names

Published online by Cambridge University Press:  29 March 2019

Ross Horne Open the ORCID record for Ross Horne [Opens in a new window]  and
Alwen Tiu
Ross Horne*
Affiliation:
Computer Science and Communications Research School, Université du Luxembourg, Esch-sur-Alzette, Luxembourg School of Computer Science and Engineering, Nanyang Technological University, Singapore, Singapore
Alwen Tiu
Affiliation:
Research School of Computer Science, Australian National University, Canberra, ACT, Australia
*
*Corresponding author. Email: ross.horne@uni.lu
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Abstract

This paper clarifies that linear implication defines a branching-time preorder, preserved in all contexts, when used to compare embeddings of process in non-commutative logic. The logic considered is a first-order extension of the proof system BV featuring a de Morgan dual pair of nominal quantifiers, called BV1. An embedding of π-calculus processes as formulae in BV1 is defined, and the soundness of linear implication in BV1 with respect to a notion of weak simulation in the π -calculus is established. A novel contribution of this work is that we generalise the notion of a ‘left proof’ to a class of formulae sufficiently large to compare embeddings of processes, from which simulating execution steps are extracted. We illustrate the expressive power of BV1 by demonstrating that results extend to the internal π -calculus, where privacy of inputs is guaranteed. We also remark that linear implication is strictly finer than any interleaving preorder.

Keywords

process calculisimulationproof theorycalculus of structures

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