Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Exact Affine OBDDs.

Rishat Ibrahimov, Kamil Ravilevich Khadiev, Abuzer Yakaryılmaz

Published Mar 21, 2017• 2 citations
OpenAlex

Abstract

We introduce affine OBDD model and we show that exact affine OBDDs can be exponentially narrower than bounded-error quantum and classical OBDDs on some certain problems. Moreover, we consider Las-Vegas quantum and classical automata models and improve the previous gap between deterministic and probabilistic models by a factor of 2 and then follow the same gap for the known most restricted quantum model. Lastly, we follow an exponential gap between exact affine finite automata and Las-Vegas classical and quantum models.

Related papers

Affine counter automata

Masaki Nakanishi, Abuzer Yakaryılmaz

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 promise problem that can be solved by exact affine counter automata but cannot be solved by deterministic counter automata. We also show that a certain promise problem, which is conjectured not to be solved by two-way quantum finite automata in polynomial time, can be solved by Las-Vegas affine finite automata in linear time. Lastly, we show that how a counter helps for affine finite automata by showing that the language $ \mathtt{MANYTWINS} $, which is conjectured not to be recognized by affine, quantum or classical finite state models in polynomial time, can be recognized by affine counter automata with one-sided bounded-error in realtime.

arXiv:1703.04281•Jan 1, 2017•0 citations

Very narrow quantum OBDDs and width hierarchies for classical OBDDs

Farid Mansurovich Ablayev, Aida Gainutdinova, Kamil Ravilevich Khadiev +1 more

We present several results on comparative complexity for different variants of OBDD models. - We present some results on comparative complexity of classical and quantum OBDDs. We consider a partial function depending on parameter k such that for any k > 0 this function is computed by an exact quantum OBDD of width 2 but any classical OBDD (deterministic or stable bounded error probabilistic) needs width 2k+1. - We consider quantum and classical nondeterminism. We show that quantum nondeterminism can be more efficient than classical one. In particular, an explicit function is presented which is computed by a quantum nondeterministic OBDD with constant width but any classical nondeterministic OBDD for this function needs non-constant width. - We also present new hierarchies on widths of deterministic and non-deterministic OBDDs. We focus both on small and large widths.

arXiv:1405.7849•May 30, 2014•0 citations

Automata and Quantum Computing

Andris Ambainis, Abuzer Yakaryılmaz

Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted models such as quantum versions of finite automata have been studied. In this paper, we survey various models of quantum finite automata and their properties. We also provide some open questions and new directions for researchers. Keywords: quantum finite automata, probabilistic finite automata, nondeterminism, bounded error, unbounded error, state complexity, decidability and undecidability, computational complexity

arXiv:1507.01988•Jul 7, 2015•16 citations

Automata and quantum computing

Andris Ambainis, Abuzer Yakaryılmaz

Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted models such as quantum versions of finite automata have been studied. In this paper, we survey various models of quantum finite automata and their properties. We also provide some open questions and new directions for researchers. Keywords: quantum finite automata, probabilistic finite automata, nondeterminism, bounded error, unbounded error, state complexity, decidability and undecidability, computational complexity

EMS Press eBooks•Sep 13, 2021•33 citations

Comparative complexity of quantum and classical OBDDs for total and partial functions

Aida Gainutdinova

We consider a model of computation for discrete functions—Ordered Binary Decision Diagrams (OBDD).We investigate comparative complexity of quantum, deterministic, probabilistic and nondeterministic (quantum and classical) OBDDs for total and partial functions. The measure of complexity is a width of OBDD. It is known that for total functions bounded error quantum OBDDs can be exponentially more effective than deterministic and bounded error probabilistic OBDDs. We show that such quantum OBDDs also can be exponentially more effective than nondeterministic OBDDs (both quantum and classical). For partial functions the gap can be more significant. For partial function depending on a parameter k exact quantum OBDD has the width two. Deterministic and bounded error probabilistic OBDD for this function must have a width exponentially depending on k .

Russian Mathematics•Oct 14, 2015•15 citations

New results on classical and quantum counter automata

Masaki Nakanishi, Abuzer Yakaryılmaz, Aida Gainutdinova

We show that one-way quantum one-counter automaton with zero-error is more powerful than its probabilistic counterpart on promise problems. Then, we obtain a similar separation result between Las Vegas one-way probabilistic one-counter automaton and one-way deterministic one-counter automaton. We also obtain new results on classical counter automata regarding language recognition. It was conjectured that one-way probabilistic one blind-counter automata cannot recognize Kleene closure of equality language [A. Yakaryilmaz: Superiority of one-way and realtime quantum machines. RAIRO - Theor. Inf. and Applic. 46(4): 615-641 (2012)]. We show that this conjecture is false, and also show several separation results for blind/non-blind counter automata.

Discrete Mathematics & Theoretical Computer Science•Jul 13, 2016•1 citation
We introduce affine OBDD model and we show that exact affine OBDDs can be exponentially narrower than bounded-error quantum and classical OBDDs on some certain problems. Moreover, we consider Las-Vegas quantum and classical automata models and improve the previous gap between deterministic and probabilistic models by a factor of 2 and then follow the same gap for the known most restricted quantum model. Lastly, we follow an exponential gap between exact affine finite automata and Las-Vegas classical and quantum models.
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 promise problem that can be solved by exact affine counter automata but cannot be solved by deterministic counter automata. We also show that a certain promise problem, which is conjectured not to be solved by two-way quantum finite automata in polynomial time, can be solved by Las-Vegas affine finite automata in linear time. Lastly, we show that how a counter helps for affine finite automata by showing that the language $ \mathtt{MANYTWINS} $, which is conjectured not to be recognized by affine, quantum or classical finite state models in polynomial time, can be recognized by affine counter automata with one-sided bounded-error in realtime.
We present several results on comparative complexity for different variants of OBDD models. - We present some results on comparative complexity of classical and quantum OBDDs. We consider a partial function depending on parameter k such that for any k > 0 this function is computed by an exact quantum OBDD of width 2 but any classical OBDD (deterministic or stable bounded error probabilistic) needs width 2k+1. - We consider quantum and classical nondeterminism. We show that quantum nondeterminism can be more efficient than classical one. In particular, an explicit function is presented which is computed by a quantum nondeterministic OBDD with constant width but any classical nondeterministic OBDD for this function needs non-constant width. - We also present new hierarchies on widths of deterministic and non-deterministic OBDDs. We focus both on small and large widths.
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted models such as quantum versions of finite automata have been studied. In this paper, we survey various models of quantum finite automata and their properties. We also provide some open questions and new directions for researchers. Keywords: quantum finite automata, probabilistic finite automata, nondeterminism, bounded error, unbounded error, state complexity, decidability and undecidability, computational complexity
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted models such as quantum versions of finite automata have been studied. In this paper, we survey various models of quantum finite automata and their properties. We also provide some open questions and new directions for researchers. Keywords: quantum finite automata, probabilistic finite automata, nondeterminism, bounded error, unbounded error, state complexity, decidability and undecidability, computational complexity
We consider a model of computation for discrete functions—Ordered Binary Decision Diagrams (OBDD).We investigate comparative complexity of quantum, deterministic, probabilistic and nondeterministic (quantum and classical) OBDDs for total and partial functions. The measure of complexity is a width of OBDD. It is known that for total functions bounded error quantum OBDDs can be exponentially more effective than deterministic and bounded error probabilistic OBDDs. We show that such quantum OBDDs also can be exponentially more effective than nondeterministic OBDDs (both quantum and classical). For partial functions the gap can be more significant. For partial function depending on a parameter k exact quantum OBDD has the width two. Deterministic and bounded error probabilistic OBDD for this function must have a width exponentially depending on k .
We show that one-way quantum one-counter automaton with zero-error is more powerful than its probabilistic counterpart on promise problems. Then, we obtain a similar separation result between Las Vegas one-way probabilistic one-counter automaton and one-way deterministic one-counter automaton. We also obtain new results on classical counter automata regarding language recognition. It was conjectured that one-way probabilistic one blind-counter automata cannot recognize Kleene closure of equality language [A. Yakaryilmaz: Superiority of one-way and realtime quantum machines. RAIRO - Theor. Inf. and Applic. 46(4): 615-641 (2012)]. We show that this conjecture is false, and also show several separation results for blind/non-blind counter automata.