Two-way finite automata with quantum and classical states (2qcfa’s) were introduced by Ambainis and Watrous. Though this computing model is more restricted than the usual two-way quantum finite automata (2qfa’s) first proposed by Kondacs and Watrous, it is still more powerful than the classical counterpart. In this note, we focus on dealing with the operation properties of 2qcfa’s. We prove tha...

We study the following decision problem: is the language recognized by a quantum finite automaton empty or nonempty? We prove that this problem is decidable or undecidable depending on whether recognition is defined by strict or nonstrict thresholds. This result is in contrast with the corresponding situation for probabilistic finite automata, for which it is known that strict and nonstrict thr...

Some of the most interesting and important results concerning quantum finite automata are those showing that they can recognize certain languages with (much) less resources than corresponding classical finite automata. This paper shows three results of such a type that are stronger in some sense than other ones because (a) they deal with models of quantum finite automata with very little quantu...

In this note, we present an infinite family of promise problems which can be solved exactly by just tuning transition amplitudes of a two-state quantum finite automata operating in realtime mode, whereas the size of the corresponding classical automata grow without bound.

This note revisits the equivalence of languages recognized by measure many one way quantum finite automata with non/strict cutpoint. The main contributions are as follows: (1) We provide an additional proof of the undecidability of non/strict emptiness of measure many one way quantum finite automata; (2) By the undecidability of non/strict emptiness of measure many one way quantum finite automa...

We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the hierarchy. These probabilities converge to 1 2 . Supported by Berkeley Fellowship for Graduate Studies. Research supported by Grant No.96.0282 from the Latvia...

Two quantum finite automata are equivalent if for all input string ω over the input alphabet the two automata accept ω with equal probability. In [Theoret. Comput. Sci. 410 (2009) 3006-3017], it was shown that a k1-letter QFA A1 and a k2-letter QFA A2 over Σ = {σ}, are equivalent if and only if they are (n1 + n2) 4 + k − 1-equivalent where ni is the number of states of Ai, i = 1, 2, and k = max...

Urn automata are a new class of automata consisting of an input tape, a finite-state controller, and an urn containing tokens with a finite set of colors, where the finite-state controller can sample and replace tokens in the urn but cannot control which tokens it receives. We consider the computational power of urn automata, showing that an urn automaton with O(f(n)) tokens can, with high prob...

It is an open problem to characterize the class of languages recognized by quantum finite automata (QFA). We examine some necessary and some sufficient conditions for a (regular) language to be recognizable by a QFA. For a subclass of regular languages we get a condition which is necessary and sufficient. Also, we prove that the class of languages recognizable by a QFA is not closed under union...

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...