Weak Automata for the Linear Time μ-Calculus [chapter]

Martin Lange
2005 Lecture Notes in Computer Science  
This paper presents translations forth and back between formulas of the linear time µ-calculus and finite automata with a weak parity acceptance condition. This yields a normal form for these formulas, in fact showing that the linear time alternation hierarchy collapses at level 0 and not just at level 1 as known so far. The translation from formulas to automata can be optimised yielding automata whose size is only exponential in the alternation depth of the formula. describing, resp. the
more » ... ge containing just the empty word, all words beginning with the letter a, the union and the concatenation of two languages, finite and infinite iteration of a language. We write [[α]] for the language defined by α.
doi:10.1007/978-3-540-30579-8_18 fatcat:ixe5hogilnhq5fjy7iskzhuvjm