Rewriting semantics of production rule sets

Abstract

This paper is about the semantics of production rule sets, a language used to model asynchronous digital circuits. Two formal semantics are developed and proved equivalent: a settheoretic semantics that improves upon an earlier effort of ours, and an executable semantics in rewriting logic. The set-theoretic semantics is especially suited to meta-level proofs about production rule sets, whereas the executable semantics can be used with existing tools to establish, automatically, desirable properties of individual circuits. Experiments involving several small circuits are detailed wherein the executable semantics and the rewriting logic tool Maude are used to automatically check two important properties: hazard and deadlock freedom. In doing so, we derive several useful optimizations that make automatic checking of these properties more tractable.

Modelling and verification of post-quantum key encapsulation mechanisms using Maude

“…Maude ( Clavel et al, 2007 ; Durán et al, 2020 ) is based on rewriting logic ( Meseguer, 1992 ), a logic ideally suited to specify and execute computational systems in a simple and natural way. Since nowadays most computational systems are concurrent, rewriting logic is particularly well suited to specify concurrent systems without making any early commitments about the model of concurrency in question, which can be synchronous or asynchronous, and can vary widely in shape and nature: from a Petri net ( Stehr, Meseguer & Ölveczky, 2001 ) to a process calculus ( Martí-Oliet & Verdejo-López, 2000 ), from an object-based system ( Meseguer, 1993 ) to asynchronous hardware ( Katelman, Keller & Meseguer, 2012 ), from a mobile ad hoc network protocol ( Liu, Ölveczky & Meseguer, 2015 ) to a cloud-based storage system ( Bobba et al, 2018 ), from a web browser ( Chen et al, 2007 ) to a programming language with threads ( Meseguer & Roşu, 2007 ), or from a distributed control system ( Bae, Meseguer & Ölveczky, 2014 ) to a model of mammalian cell pathways ( Eker et al, 2001 ; Talcott et al, 2003 ). And all without any encoding : You see and get a direct system definition without any artificial encoding.…”

Twenty years of rewriting logic

“…Asynchronous designs can be specified with the notation of production rules, which roughly speaking describe how each gate behaves when inputs to its wires are available. In [252] a rewriting logic semantics of asynchronous digital devices specified as sets of production rules is given and is realized in Maude (see also the longer paper [253] in this issue). This is the first executable formal semantics of such devices I am aware of.…”

Programming and symbolic computation in Maude

“…It is a logic ideally suited to specify and execute computational systems in a simple and natural way. Since nowadays most computational systems are concurrent, rewriting logic is particularly well suited to specify concurrent systems without making any a priori commitments about the model of concurrency in question, which can be synchronous or asynchronous, and can vary widely in its shape and nature: from a Petri net [128] to a process calculus [134,126], from an object-based system [92] to asynchronous hardware [75], from a mobile ad hoc network protocol [79] to a cloud-based storage system [14], from a web browser [21,122] to a programming language with threads [107,108], from a distributed control system [105,11] to a model of mammalian cell pathways [54,130], and so on. And all without any encoding: what you see and get is a direct definition of the system itself, not some crazy Turing machine or Petri net encoding of it.…”