On the complexity of minimizing probabilistic and quantum automata

  title={On the complexity of minimizing probabilistic and quantum automata},
  author={Paulo Mateus and Daowen Qiu and Lvzhou Li},
  journal={Inf. Comput.},

Figures from this paper

On the state complexity of semi-quantum finite automata
Three results of such a type that are stronger in some sense than other ones because they deal with models of quantum finite automata with very little quantumness so-called semi-quantum one- and two-way finite Automata.
Multi-letter quantum finite automata: decidability of the equivalence and minimization of states
It is shown that the states minimization problem of multi-letter QFAs is solvable in EXPSPACE and the decidability of the equivalence and minimization problems ofMulti-letter quantum finite automata is studied.
Quantum machines with classical control
The concept of quantum Turing machine with classical control introduced in [25] is revised and the result that such machines fulfil the s-m-n property, while keeping the expressivity of a quantum model for computation is revisited.
Quantum finite automata: survey, status and research directions
This article seeks to provide a comprehensive and systematic analysis of quantum finite automata models, quantum finite Automata models with density operators and quantum finite automakers with classical states, interactive proof systems, quantum communication complexity and query complexity as described in the literature.
Decidability of minimization of fuzzy automata
This paper gives the concept of systems of fuzzy polynomial equations and then presents a procedure to solve these systems, and proves for the first time that the state minimization problem is decidable for fuzzy automata over totally ordered lattices.
On the State Minimization of Fuzzy Automata
This paper investigates the minimization problem of fuzzy automata, aiming to obtain a procedure for finding a minimal state fuzzy automaton equivalent to a given one, and reduces the above decision problem to finding a solution of a system of fuzzy polynomial equations.
On equivalence, languages equivalence and minimization of multi-letter and multi-letter measure-many quantum automata
This paper shows that for k-letter quantum finite automata, the non-strict cut-point language equivalence problem is undecidable, and comments on existing proofs about the minimization problem of one way quantum finiteAutomata not only because they have been showing great interest in this kind of problem, but also due to that the problem itself is a challenge.
Classical and quantum realtime alternating automata
Realtime private alternating finite automata (PAFAs) are defined and they can recognize some non-regular unary languages, and the emptiness problem is undecidable for them, and PAFAs augmented with a counter can recognize the unary squares language.
On hybrid models of quantum finite automata


Probabilistic ω-automata
This paper addresses closure properties under the Boolean operators union, intersection and complementation and algorithmic aspects, such as checking emptiness or language containment, and provides a comparison of probabilistic ω-automata concerning expressiveness and efficiency.
Characterizations of 1-Way Quantum Finite Automata
This paper characterize the measure-once model when it is restricted to accepting with bounded error and show that, without that restriction, it can solve the word problem over the free group and shows that piecewise testable sets can be accepted with boundederror by a measure-many quantum finite automaton, introducing new construction techniques for quantum automata in the process.
On the power of quantum finite state automata
It is proved that the class of languages recognizing by linear time, bounded error 2qfa's properly includes the regular languages, and 1-way and 2-way quantum finite state automata are introduced, which are the quantum analogues of deterministic, nondeterministic and probabilistic 1- way and2-way finite state Automata.
A Polynomial-Time Algorithm for the Equivalence of Probabilistic Automata
The algorithm used to determine the equivalence of probabilistic automata can also solve the path equivalence problem for nondeterministic finite automata without $\lambda $-transitions and the equivalences problem for unambiguous finite automATA in polynomial time.
Characterizations of one-way general quantum finite automata
1-way quantum finite automata: strengths, weaknesses and generalizations
  • A. Ambainis, R. Freivalds
  • Computer Science
    Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
  • 1998
This work constructs a 1-way QFA that is exponentially smaller than any equivalent classical (even randomized) finite automaton, and thinks that this construction may be useful for design of other space-efficient quantum algorithms.
Languages Recognized with Unbounded Error by Quantum Finite Automata
The conclusion that quantum Turing machines are more powerful than probabilistic Turing machines when restricted to constant space bounds is made.
Quantum automata and quantum grammars