Alternation Elimination for Automata over Nested Words

Abstract

Abstract. This paper presents constructions for translating alternating automata into nondeterministic nested-word automata (NWAs). With these alternation-elimination constructions at hand, we straightforwardly obtain translations from various temporal logics over nested words from the literature like CaRet and μNWTL, and extensions thereof to NWAs, which correct, simplify, improve, and generalize the previously given translations. Our alternation-elimination constructions are instances of an alternation-elimination scheme for automata that operate over the tree unfolding of graphs. We obtain these instances by providing constructions for complementing restricted classes of automata with respect to the graphs given by nested words. The scheme generalizes our alternation-elimination scheme for word automata and the presented complementation constructions generalize existing complementation constructions for word automata.

Temporal Logics for Concurrent Recursive Programs: Satisfiability and Model Checking

“…In addition, it provides path expressions similar to those from PDL [11] or XPath [17], which are orthogonal to the modalities. This general framework captures temporal logics considered in [2,1,8] when we restrict to one process, and it captures those considered in [9,12,13] when we go without recursion. Our decision procedures for the (bounded phase) satisfiability problem are optimal in all these special cases, but provide a unifying proof.…”