Related papers: Can one quantum bit separate any pair of words wit…
State reduction of finite automata plays a significant role in improving efficiency in formal verification, pattern recognition, and machine learning, where automata-based models are widely used. While deterministic automata have…
The quantum discrimination of two non-coherent states draws much attention recently. In this letter, we first consider the quantum discrimination of two noiseless displaced number states. Then we derive the Fock representation of noisy…
We explore bounds of {\em time-space tradeoffs} in language recognition on {\em two-way finite automata} for some special languages. We prove: (1) a time-space tradeoff upper bound for recognition of the languages $L_{EQ}(n)$ on {\em…
We revisit the complexity of procedures on SFAs (such as intersection, emptiness, etc.) and analyze them according to the measures we find suitable for symbolic automata: the number of states, the maximal number of transitions exiting a…
The problem of quantum state filtering consists of determining whether an unknown quantum state, which is chosen from a known set of states, is either a particular, specified state, or not. We consider this problem for the case that the…
A core principle of quantum theory is that non-orthogonal quantum states cannot be perfectly distinguished with single-shot measurements. However, it is possible to exclude a subset of non-orthogonal states without error in certain…
Given two languages, a separator is a third language that contains the first one and is disjoint from the second one. We investigate the following decision problem: given two regular input languages of finite words, decide whether there…
We study an optimum measurement for quantum state discrimination, which maximizes the probability of correct results when the probability of inconclusive results is fixed at a given value. The measurement describes minimum-error…
We describe a class of programmable devices that can discriminate between two quantum states. We consider two cases. In the first, both states are unknown. One copy of each of the unknown states is provided as input, or program, for the two…
We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the state-complexity of representing sub- or superword closures of context-free grammars (CFGs): (1) We prove a (tight) upper bound of $2^{\mathcal{O}(n)}$ on the size of…
Given a finite set of linearly independent quantum states, an observer who examines a single quantum system may sometimes identify its state with certainty. However, unless these quantum states are orthogonal, there is a finite probability…
We give an unique string representation, up to isomorphism, for initially connected deterministic finite automata (ICDFAs) with n states over an alphabet of k symbols. We show how to generate all these strings for each n and k, and how its…
We observe that the classical Cartesian product construction for the intersection of (languages of) nondeterministic finite automata (NFA) is non-optimal in the worst case, if the automata have many transitions. For a fixed alphabet, the…
In the task of discriminating between nonorthogonal quantum states from multiple copies, the key parameters are the error probability and the resources (number of copies) used. Previous studies have considered the task of minimizing the…
There are two common settings in a quantum-state discrimination problem. One is minimum-error discrimination where a wrong guess (error) is allowed and the discrimination success probability is maximized. The other is unambiguous…
So-called separation automata are in the core of several recently invented quasi-polynomial time algorithms for parity games. An explicit $q$-state separation automaton implies an algorithm for parity games with running time polynomial in…
Deterministic automata have been traditionally studied through the point of view of language equivalence, but another perspective is given by the canonical notion of shortest-distinguishing-word distance quantifying the of states.…
We introduce an affine generalization of counter automata, and analyze their ability as well as affine finite automata. Our contributions are as follows. We show that there is a language that can be recognized by exact realtime affine…
The potential of the exact quantum information processing is an interesting, important and intriguing issue. For examples, it has been believed that quantum tools can provide significant, that is larger than polynomial, advantages in the…
We investigate how to determine whether the states of a set of quantum systems are identical or not. This paper treats both error-free comparison, and comparison where errors in the result are allowed. Error-free comparison means that we…