2017-10-27: Johannes Marti (Universität Bremen)

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

Johannes Marti (Universität Bremen)

Size-Matters in the Modal mu-Calculus

Abstract

I talk about three methods for measuring the size of formulas in the modal mu-calculus and explore how the choice between them influences the complexity of computations on formulas. Especially, I focus on the guarded transformation, which is a simple syntactic transformation on formulas that is commonly assumed to be polynomial but has recently been shown to require exponential time.

I will complain about the mess in the literature and present two of our (Clemens, Yde and me) own preliminary results:

1) There is a polynomial guarded transformation if we measure the input formula in the number of its subformulas and measure the output formula in the size of its closure.

2) If there is a polynomial guarded transformation where we measure the input formula in the size of its closure then there is a polynomial algorithm for solving parity games. Hence finding such a transformation is at least as hard as solving parity games, which is commonly believed to be quite hard.

We employ an automata-theoretic approach that relates the different measures for the size of a formula to different constraints on the transition structure of an automaton corresponding to the formula.

This is a very technical talk but there will be many pictures!

2017-10-27 16:00:00 UTC
LT1310