Automata on Infinite Words. Automata running on infinite words (such as non-deterministic Büchi automata) provide an established framework for the specification and verification of nonterminating programs (in particular via the model checking technique). However, some of their basic properties are known to require non-trivial reasoning principles. This is most notably the case of closure under ...

The determinization of Büchi automata is a celebrated problem, with applications in synthesis, probabilistic verification, and multi-agent systems. Since the 1960s, there has been a steady progress of constructions: by McNaughton, Safra, Piterman, Schewe, and others. Despite the proliferation of solutions, they are all essentially ad-hoc constructions, with little theory behind them other than ...

The problem of Büchi determinization is a fundamental problem with important applications in reactive synthesis, multi-agent systems and probabilistic verification. The first asymptotically optimal Büchi determinization (a.k.a the Safra construction), was published in 1988. While asymptotically optimal, the Safra construction is notorious for its technical complexity and opaqueness in terms of ...

Recently, ‘determinization in hindsight’ has enjoyed surprising success in on-line probabilistic planning. This technique evaluates the actions available in the current state by using non-probabilistic planning in deterministic approximations of the original domain. Although the approach has proven itself effective in many challenging domains, it is computationally very expensive. In this paper...

Controller synthesis techniques based on symbolic abstractions appeal by producing correct-by-design controllers, under intricate behavioural constraints. Yet, being relations between abstract states and inputs, such controllers are immense in size, which makes them futile for embedded platforms. Control-synthesis tools such as PESSOA, SCOTS, and CoSyMA tackle the problem by storing controllers...

The inversion method proposed by Glück and Kawabe uses grammar programs as intermediate results that comprise sequences of operations (data generation, matching, etc.). The determinization method used in the inversion method fails for a grammar program of which the collection of item sets causes a conflict even if there exists a deterministic program equivalent to the grammar program. In this p...

We study determinization of weighted finite-state automata (WFAs), which has important applications in automatic speech recognition (ASR). We provide the first polynomial-time algorithm to test for the twins property, which determines if a WFA admits a deterministic equivalent. We also provide a rigorous analysis of a determinization algorithm of Mohri, with tight bounds for acyclic WFAs. Given...

In the paper, we generalize an algorithm and some related results by Mohri [25] for determinization of weighted finite automata (WFA) over the tropical semiring. We present the underlying mathematical concepts of his algorithm in a precise way for arbitrary semirings. We define a class of semirings in which we can show that the twins property is sufficient for the termination of the algorithm. ...

2 Automata over forests 4 2.1 Forest automata . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Bottom-up deterministic forest automata . . . . . . . . . . 5 2.3 Minimization of BUDFA . . . . . . . . . . . . . . . . . . . 8 2.4 BUNFA and determinization . . . . . . . . . . . . . . . . . 14 2.5 Computing the syntactic forest algebra of a language . . . 16 2.6 Logical characterization . . . ....