
A Complete Proof System for 1Free Regular Expressions Modulo Bisimilarity
Robin Milner (1984) gave a sound proof system for bisimilarity of regula...
read it

A Coinductive Version of Milner's Proof System for Regular Expressions Modulo Bisimilarity
By adapting Salomaa's complete proof system for equality of regular expr...
read it

Completeness Theorems for FirstOrder Logic Analysed in Constructive Type Theory (Extended Version)
We study various formulations of the completeness of firstorder logic p...
read it

Normalizing Casts and Coercions
This system description introduces norm_cast, a toolbox of tactics for t...
read it

A formal proof of modal completeness for provability logic
This work presents a formalized proof of modal completeness for GödelLö...
read it

Countdown games, and simulation on (succinct) onecounter nets
We answer an open complexity question by Hofman, Lasota, Mayr, Totzke (L...
read it

Completeness and Performance Of The APO Algorithm
Asynchronous Partial Overlay (APO) is a search algorithm that uses coope...
read it
On Star Expressions and Coalgebraic Completeness Theorems
An open problem posed by Milner asks for a proof that a certain axiomatisation, which Milner showed is sound with respect to bisimilarity for regular expressions, is also complete. One of the main difficulties of the problem is the lack of a full Kleene theorem, since there are automata that can not be specified, up to bisimilarity, by an expression. Grabmayer and Fokkink (2020) characterise those automata that can be expressed by regular expressions without the constant 1, and use this characterisation to give a positive answer to Milner's question for this subset of expressions. In this paper, we analyse Grabmayer and Fokkink's proof of completeness from the perspective of universal coalgebra, and thereby give an abstract account of their proof method. We then compare this proof method to another approach to completeness proofs from coalgebraic language theory. This culminates in two abstract proof methods for completeness, what we call the local and global approaches, and a description of when one method can be used in place of the other.
READ FULL TEXT
Comments
There are no comments yet.