We consider a deterministic finite automaton which accepts all subsequences of a set of texts, called subsequence automaton. We show an online algorithm for constructing subsequence automaton for a set of texts. It runs in O(|Σ|m) time using O(|Σ|m) space, where m is the number of states of the subsequence automaton, and |Σ| is the size of alphabet. For k texts of length n, since m = O(n), it r...

The factor automaton of a finite word w is the minimal deterministic automaton recognizing the set of factors of w. It is a data structure allowing the search of a pattern in a text in time and space proportional to the length of the pattern. In this paper we link classical combinatorial parameters on words to the size and the structure of the factor automaton. As a main result, we give a chara...

Visibly pushdown automata are special pushdown automata whose stack behavior is driven by the input symbols according to a partition of the alphabet. We show that it is decidable for a given visibly pushdown automaton whether it is equivalent to a visibly counter automaton, i.e. an automaton that uses its stack only as counter. In particular, this allows to decide whether a given visibly pushdo...

We consider the representational state complexity of unranked tree automata. The bottom-up computation of an unranked tree automaton may be either deterministic or nondeterministic, and further variants arise depending on whether the horizontal string languages defining the transitions are represented by a DFA or an NFA. Also, we consider for unranked tree automata the alternative syntactic def...

There are several types of finite automata on infinite words, differing in their acceptance conditions. As each type has its own advantages, there is an extensive research on the size blowup involved in translating one automaton type to another. Of special interest is the Muller type, providing the most detailed acceptance condition. It turns out that there is inconsistency and incompleteness i...

The state complexity of a finite(-state) automaton intuitively measures the size description automaton. Sakoda and Sipser [STOC 1972, pp. 275–286] were concerned with nonuniform families finite automata they discussed behaviors classes defined by such having polynomial-size complexity. In similar fashion, we introduce using quantum empowered flexible use garbage tapes. We first present general ...

Complementation and determinization are two fundamental notions in automata theory. The close relationship between the two has been well observed in the literature. In the case of nondeterministic finite automata on finite words (NFA), complementation and determinization have the same state complexity, namely Θ(2n) where n is the state size. The same similarity between determinization and compl...

Of special interest in formal verification are safety properties, which assert that the system always stays within some allowed region. Each safety property ψ can be associated with a set of bad prefixes: a set of finite computations such that an infinite computation violates ψ iff it has a prefix in the set. By translating a safety property to an automaton for its set of bad prefixes, verifica...

Since Edward Moore, finite automata theory has been inspired by physics, in particular by quantum complementarity. We review automaton complementarity, reversible automata and the connections to generalized urn models. Recent developments in quantum information theory may have appropriate formalizations in the automaton context. 1 Physical connections Physics and computer science share common i...