This chapter presents several fundamental algorithms for weighted automata and transducers. While the mathematical counterparts of weighted transducers, rational power series , have been extensively studied in the past [22, 54, 13, 36], several essential weighted transducer algorithms, e.g., composition, determinization, minimization, have been devised only in the last decade [38, 43], in part ...

We give the quantum subset construction of orthomodular lattice-valued finite automata, then we show the equivalence between orthomodular lattice-valued finite automata, orthomodular lattice-valued deterministic finite automata and orthomodular lattice-valued finite automata with empty string-moves. Based on these equivalences, we study the algebraic operations on orthomodular lattice-valued re...

Markov decision processes (MDP) (Puterman 1994) offer a rich model that has been extensively used by the AI community for planning and learning under uncertainty. Some applications include planning for mobile robots, network management, optimizing software on mobile phones, and managing water levels of river reservoirs. MDPs have polynomial complexity in the size of the state space, but the sta...

Visibly pushdown automata (VPAs), introduced by Alur and Madhusudan in 2004, are a useful formalism in various contexts, such as expressing and checking properties on control flows of programs, or on XML documents. In this context, we propose efficient antichain-based algorithms to check universality and inclusion of VPAs. Whereas the computation complexity is known to be ExpTime-complete for b...

We study capacitated automata (CAs), where transitions correspond to resources and may have bounded capacities. Each transition in a CA is associated with a (possibly infinite) bound on the number of times it may be traversed. We study CAs from two points of view. The first is that of traditional automata theory, where we view CAs as recognizers of formal languages and examine their expressive ...

We present a new algorithm to construct a (generalized) deterministic Rabin automaton for an LTL formula φ. The automaton is the product of a co-Büchi automaton for φ and an array of Rabin automata, one for each G-subformula of φ. The Rabin automaton for Gψ is in charge of recognizing whether FGψ holds. This information is passed to the co-Büchi automaton that decides on acceptance. As opposed ...

This paper is a survey on logical aspects of nite automata Central points are the connection between nite automata and monadic second order logic the Ehrenfeucht Fra ss e technique in the context of formal language theory nite automata on words and their determinization and a self contained proof of the Rabin Tree Theorem Sections and contain material presented in a lecture series to the Final ...

This paper gives a concise introduction into the basic theory of ω-automata (as of March 2014). The starting point are the different types of recurrence conditions, modes of operation (deterministic, nondeterministic, alternating automata), and directions (forward or backward automata). The main focus is on fundamental automata constructions, for instance, for boolean operations, determinizatio...

Much attention has been brought to determinization and ε-removal in previous work. This article describes an algorithm for extracting all ε-cycles, which are a special type of non-determinism, from an arbitrary finite-state transducer (FST). The algorithm factorizes (decomposes) the FST, T , into two FSTs, T1 and T2, such that T1 contains no ε-cycles and T2 contains all ε-cycles of T . Since ε-...