Crisp-determinization of weighted tree automata over strong bimonoids

Weighted Tree Automata over Strong Bimonoids

We consider weighted tree automata over strong bimonoids which are, roughly speaking, semirings without distributivity. We prove sufficient and necessary conditions under which the initial algebra semantics and the run semantics of these automata coincide. We prove closure properties of the class of recognizable tree series, a determinization result, and a characterization of recognizable step ...

Determinization of weighted finite automata over strong bimonoids

We consider weighted finite automata over strong bimonoids, where these weight structures can be considered as semirings which might lack distributivity. Then, in general, the well-known run semantics, initial algebra semantics, and transition semantics of an automaton are different. We prove an algebraic characterization for the initial algebra semantics in terms of stable finitely generated s...

Weighted finite automata over strong bimonoids

We investigate weighted finite automata over strings and strong bimonoids. Such algebraic structures satisfy the same laws as semirings except that no distributivity laws need to hold. We define two different behaviors and prove precise characterizations for them if the underlying strong bimonoid satisfies local finiteness conditions. Moreover, we show that in this case the given weighted autom...

Determinization of Weighted Tree Automata Using Factorizations

We present a determinization construction for weighted tree automata using factorizations. Among others, this result subsumes a previous result for determinization of weighted string automata using factorizations (Kirsten and Mäurer, 2005) and two previous results for weighted tree automata, one of them not using factorizations (Borchardt, 2004) and one of them restricted to nonrecursive automa...

Determinization of Finite State Weighted Tree Automata