On the size of disjunctive formulas in the μ-calculus

  title={On the size of disjunctive formulas in the $\mu$-calculus},
  author={Clemens Kupke and Johannes Marti and Yde Venema},
A key result in the theory of the modal μ-calculus is the disjunctive normal form theorem by Janin & Walukiewicz, stating that every μ-calculus formula is semantically equivalent to a so-called disjunctive formula. These disjunctive formulas have good computational properties and play a pivotal role in the theory of the modal μ-calculus. It is therefore an interesting question what the best normalisation procedure is for rewriting a formula into an equivalent disjunctive formula of minimal size… 

Tables from this paper



Some model theory for the modal μ-calculus: syntactic characterisations of semantic properties

This paper discusses a number of semantic properties pertaining to formulas of the modal $\mu$-calculus, and proves that it is decidable in elementary time whether a given $\mu $-Calculus formula has the property or not.

Size matters in the modal μ-calculus

Size notions that are completely invariant under alpha equivalence are introduced, showing how to rename bound variables so that alpha-equivalence becomes syntactic identity on the closure set and reviewing the complexity of guarded transformations.

Deciding the unguarded modal -calculus

A tableau calculus for deciding satisfiability of arbitrary formulas, i.e., not necessarily guarded -calculus formulas is presented, based on a new unfolding rule for greatest fixpoint formulas which allows unguarded formulas to be handled without an explicit transformation into guarded form, thus avoiding a (seemingly) exponential blow-up in formula size.

On modal mu-calculus with explicit interpolants

Alternating tree automata, parity games, and modal {$\mu$}-calculus

The automaton model proposed is really equivalent to the modal μ-calculus with respect to expressive power, just as the one proposed by Janin and Walukiewicz, but simpler.

Tighter Bounds for the Determinisation of Büchi Automata

This paper proposes a determinisation technique that is simpler than the constructions of Safra, Piterman, and Muller and Schupp, because it separates the principle acceptance mechanism from the concrete acceptance condition.

Reasoning about The Past with Two-Way Automata

The main result in this paper is an exponential time upper bound for the satisfiability problem of the Μ-calculus with both forward and backward modalities, developed a theory of two-way alternating automata on infinite trees.

Coalgebraic Automata Theory: Basic Results

The main technical result concerns an explicit construction which transforms a given alternating F-automaton into an equivalent nondeterministic one, whose size is exponentially bound by the size of the original automaton.