The Horn Mu-calculus

The Horn -calculus is a logic programming language allowing arbitrary nesting of least and greatest fixed points. The Horn -programs can naturally expresses safety and liveness properties for reactive systems. We extend the setbased analysis of classical logic programs by mapping arbitrary -programs into “uniform” -programs. Our two main results are that uniform -programs express regular sets of trees and that emptiness for uniform -programs is EXPTIME-complete. Hence we have a nontrivial decidable relaxation for the Horn -calculus. In a different reading, the results express a kind of robustness of the notion of regularity: alternating Rabin tree automata preserve the same expressiveness and algorithmic complexity if we extend them with pushdown transition rules (in the same way Büchi extended word automata to canonical systems).