Proof Systems for the Modal μ-Calculus Obtained by Determinizing Automata

07/13/2023
by   Maurice Dekker, et al.
0

Automata operating on infinite objects feature prominently in the theory of the modal μ-calculus. One such application concerns the tableau games introduced by Niwiński Walukiewicz, of which the winning condition for infinite plays can be naturally checked by a nondeterministic parity stream automaton. Inspired by work of Jungteerapanich and Stirling we show how determinization constructions of this automaton may be used to directly obtain proof systems for the μ-calculus. More concretely, we introduce a binary tree construction for determinizing nondeterministic parity stream automata. Using this construction we define the annotated cyclic proof system 𝖡𝖳, where formulas are annotated by tuples of binary strings. Soundness and Completeness of this system follow almost immediately from the correctness of the determinization method.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/01/2022

A Survey on Satisfiability Checking for the μ-Calculus through Tree Automata

Algorithms for model checking and satisfiability of the modal μ-calculus...
research
10/24/2017

Permutation Games for the Weakly Aconjunctive mu-Calculus

We introduce a natural notion of limit-deterministic parity automata and...
research
06/13/2022

Introducing Proof Tree Automata and Proof Tree Graphs

In structural proof theory, designing and working on large calculi make ...
research
07/31/2022

Countdown μ-calculus

We introduce the countdown μ-calculus, an extension of the modal μ-calcu...
research
07/26/2022

Extensible Proof Systems for Infinite-State Systems

This paper revisits soundness and completeness of proof systems for prov...
research
10/27/2020

Size matters in the modal μ-calculus

We discuss and compare complexity measures for the modal μ-calculus, foc...
research
07/04/2023

Focus-style proofs for the two-way alternation-free μ-calculus

We introduce a cyclic proof system for the two-way alternation-free moda...

Please sign up or login with your details

Forgot password? Click here to reset