2021-12-08: Clemens Kupke (MSP)

Tue, 14 Oct 2025 16:51:42 +0000

Clemens Kupke (MSP)

Constructing disjunctive formulas in the modal mu-calculus

Abstract

The modal mu-calculus is a general modal fixpoint logic that allows to reason about the ongoing, possibly infinite behaviour of a transition system. For example, the temporal logics from Sean's 101 talk a few weeks ago can be seen as fragments of the mu-calculus.

In this talk I am planning to give a brief introduction to the mu-calculus and then focus on a key result about the logic: every formula is equivalent to a so-called disjunctive formula. Constructing a disjunctive formula of "small" size is important e.g. for satisfiability checking. I am going to sketch a construction that yields a disjunctive formula that is single-exponential in the closure size of the input formula. The construction will highlight a few subtleties that arise when thinking about the size of a mu-calculus formula.

Based on joint work with Johannes Marti and Yde Venema.

2021-12-08 15:00:00 UTC
Online