For a givenweighted finite automaton over a strong bimonoid we construct its reducedNerode automaton, which is crisp-deterministic and equivalent to the original weighted automaton with respect to the initial algebra semantics.We show that the reducedNerode automaton is even smaller than theNerode automaton, which was previously used in determinization related to this semantics. We determine ne...

In [Saf88] an exponential determinization procedure for Büchi automata was shown, yielding tight bounds for decision procedures of some logics ([EJ88, Saf88, SV89, KT89]). In [SV89] the complexity of determinization and complementation of ω-automata was further investigated, leaving as an open question the complexity of the determinization of a single class of ω-automata. For this class of ω-au...

In this paper we combine determinization and state reduction methods into two-in-one algorithms that simultaneously perform determinization and state reduction. These algorithms perform better than all previous determinization algorithms for fuzzy finite automata, developed by Bělohlávek [Inform Sciences 143 (2002) 205–209], Li and Pedrycz [Fuzzy Set Syst 156 (2005) 68–92], Ignjatović et al. [I...

Quantitative automata are nondeterministic finite automata with edge weights. They value a run by some function from the sequence of visited weights to the reals, and value a word by its minimal/maximal run. They generalize boolean automata, and have gained much attention in recent years. Unfortunately, important automaton classes, such as sum, discounted-sum, and limit-average automata, cannot...

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...

The classic approaches to synthesize a reactive system from a linear temporal logic (LTL) specification first translate the given LTL formula to an equivalent ω-automaton and then compute a winning strategy for the corresponding ω-regular game. To this end, the obtained ω-automata have to be (pseudo)-determinized where typically a variant of Safra’s determinization procedure is used. In this pa...

We present a general algorithm, pre-determinization, that makes an arbitrary weighted transducer over the tropical semiring or an arbitrary unambiguous weighted transducer over a cancellative commutative semiring determinizable by inserting in it transitions labeled with special symbols. After determinization, the special symbols can be removed or replaced with -transitions. The resulting trans...

We present a novel approach to solve quantified boolean formulas with one quantifier alternation (2QBF). The algorithm incrementally adds new constraints to the formula until the constraints describe a unique Skolem function or until the absence of a Skolem function is detected. Backtracking is required if the absence of Skolem functions depends on the newly introduced constraints. We present t...