A Complexity Measure on Büchi Automata
نویسنده
چکیده
We define a complexity measure on non-deterministic Büchi automata, based on the notion of the width of the skeleton tree introduced by Kähler and Wilke. We show that the induced hierarchy tightly correlates to the Wagner Hierarchy, a corner stone in the theory of regular ω-languages that is derived from a complexity measure on deterministic Muller automata. The relation between the hierarchies entails, for instance, that a nondeterministic Büchi automaton of width k can be translated to a deterministic parity automaton of degree at most 2k + 1.
منابع مشابه
On-the-fly Emptiness Check of Transition-Based Streett Automata
In the automata theoretic approach to model checking, checking a state-space S against a linear-time property φ can be done in O(|S| × 2) time. When model checking under n strong fairness hypotheses expressed as a Generalized Büchi automaton, this complexity becomes O(|S| × 2). Here we describe an algorithm to check the emptiness of Streett automata, which allows model checking under n strong f...
متن کاملRecurrence and Transience for Probabilistic Automata
In a context of ω-regular specifications for infinite execution sequences, the classical Büchi condition, or repeated liveness condition, asks that an accepting state is visited infinitely often. In this paper, we show that in a probabilistic context it is relevant to strengthen this infinitely often condition. An execution path is now accepting if the proportion of time spent on an accepting s...
متن کاملImproved Upper and Lower Bounds for Büchi Disambiguation
We present a new ranking based construction for disambiguating non-deterministic Büchi automata and show that the state complexity tradeoff of the translation is in O(n · (0.76n)). This exponentially improves the best upper bound (i.e., 4 · (3n)) known earlier for Büchi disambiguation. We also show that the state complexity tradeoff of translating non-deterministic Büchi automata to strongly un...
متن کاملExponential Determinization for ω-Automata with Strong-Fairness Acceptance Condition
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...
متن کاملThree SCC-Based Emptiness Checks for Generalized Büchi Automata
The automata-theoretic approach for the verification of linear time properties involves checking the emptiness of a Büchi automaton. However generalized Büchi automata, with multiple acceptance sets, are preferred when verifying under weak fairness hypotheses. Existing emptiness checks for which the complexity is independent of the number of acceptance sets are all based on the enumeration of S...
متن کامل