Flow-preserving ZX-calculus Rewrite Rules for Optimisation and Obfuscation

Categorifying the zx-calculus

This paper presents a symmetric monoidal and compact closed bicategory that categorifies the zx-calculus developed by Coecke and Duncan. The 1-cells in this bicategory are certain graph morphisms that correspond to the string diagrams of the zx-calculus, while the 2-cells are rewrite rules.

Towards explicit rewrite rules in the λΠ-calculus modulo

This paper provides a new presentation of the λΠ-calculus modulo where the addition of rewrite rules is made explicit. The λΠ-calculus modulo is a variant of the λ-calculus with dependent types where β-reduction is extended with user-defined rewrite rules. Its expressiveness makes it suitable to serve as an output language for theorem provers, certified development tools or proof assistants. Ad...

A Simplified Stabilizer ZX-calculus

The stabilizer ZX-calculus is a rigorous graphical language for reasoning about quantum mechanics. The language is sound and complete: a stabilizer ZX-diagram can be transformed into another one if and only if these two diagrams represent the same quantum evolution or quantum state. We show that the stabilizer ZX-calculus can be simplified, removing unnecessary equations while keeping only the ...

Preserving Rewrite Proofs ?

Rewrite Rules and Strategies for Molecular Graphs

In this paper, we present a rewriting framework for modeling molecular complexes, biochemical reaction rules and generation of biochemical networks based on the representation of molecular complexes as a particular type of multigraphs with ports called molecular graphs. The advantage of this approach is to obtain for free a rewriting calculus which allows defining at the same level transformati...