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Decision problems on unary probabilistic and quantum automata [article]

Mika Hirvensalo, Abuzer Yakaryılmaz
2016 arXiv   pre-print
We present the current status of the emptiness problems for unary probabilistic and quantum automata with connections with Skolem's and positivity problems.  ...  It is well known that the emptiness problem for binary probabilistic automata and so for quantum automata is undecidable.  ...  On unary alphabets, on the other hand, these problems are still open and they are known to be decidable only for some small automata.  ... 
arXiv:1610.01397v1 fatcat:ewpowktn7zhjdcqlrq5t2in6v4

Decision Problems on Unary Probabilistic and Quantum Automata

Mika Hirvensalo, Abuzer Yakaryilmaz
2016 Baltic Journal of Modern Computing  
We present the current status of the emptiness problems for unary probabilistic and quantum automata with connections with Skolem's and positivity problems.  ...  It is well known that the emptiness problem for binary probabilistic automata and so for quantum automata is undecidable.  ...  On unary alphabets, on the other hand, these problems are still open and they are known to be decidable only for some small automata.  ... 
doi:10.22364/bjmc.2016.4.4.22 fatcat:zxoa7izs6jgj7j6m6x6vgrnkiy

Page 2872 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
These results are settled within a survey on unary automata aiming to compare the descriptional power of determin- istic, nondeterministic, probabilistic and quantum paradigms.” 2003d:68068 68Q05 68Q10  ...  the succinctness of deterministic, nondeterministic, probabilistic and quantum finite automata.  ... 

Unary probabilistic and quantum automata on promise problems [article]

Aida Gainutdinova, Abuzer Yakaryilmaz
2015 arXiv   pre-print
We continue the systematic investigation of probabilistic and quantum finite automata (PFAs and QFAs) on promise problems by focusing on unary languages.  ...  Lastly, we present a new family of unary promise problems with two parameters such that when fixing one parameter QFAs can be exponentially more succinct than PFAs and when fixing the other parameter PFAs  ...  In this paper, we provide some new results regarding probabilistic and quantum automata on unary promise problems. We show that bounded-error QFAs are more powerful than PFAs.  ... 
arXiv:1502.01462v2 fatcat:mufsstagobendgoq4xconk2xfq

Unary Probabilistic and Quantum Automata on Promise Problems [chapter]

Aida Gainutdinova, Abuzer Yakaryılmaz
2015 Lecture Notes in Computer Science  
We continue the systematic investigation of probabilistic and quantum finite automata (PFAs and QFAs) on promise problems by focusing on unary languages.  ...  Lastly, we present a new family of unary promise problems with two parameters such that when fixing one parameter QFAs can be exponentially more succinct than PFAs and when fixing the other parameter PFAs  ...  In this paper, we provide some new results regarding probabilistic and quantum automata on unary promise problems. We show that bounded-error QFAs are more powerful than PFAs.  ... 
doi:10.1007/978-3-319-21500-6_20 fatcat:ass5dzddyvap3ilx2bakmryelq

Unary languages recognized by two-way one-counter automata [article]

Marzio De Biasi, Abuzer Yakaryilmaz
2014 arXiv   pre-print
By using the input head as a second counter, we present simulations of two-way deterministic finite automata with linearly bounded counters and linear--space Turing machines.  ...  Finally, we compare unary 2D1CAs with two--counter machines and provide some insights about the limits of their computational power.  ...  We thank Alexander Okhotin, Holger Petersen, and Klaus Reinhardt for their answers to our questions on the subject matter of this paper.  ... 
arXiv:1311.0849v2 fatcat:4mmokdl2prej3h4g2xwo23uy5q

Unary Languages Recognized by Two-Way One-Counter Automata [chapter]

Marzio De Biasi, Abuzer Yakaryılmaz
2014 Lecture Notes in Computer Science  
By using the input head as a second counter, we present simulations of two-way deterministic finite automata with linearly bounded counters and linear-space Turing machines.  ...  Finally, we compare unary 2D1CAs with two-counter machines and provide some insights about the limits of their computational power.  ...  We thank Alexander Okhotin, Holger Petersen, and Klaus Reinhardt for their answers to our questions on the subject matter of this paper.  ... 
doi:10.1007/978-3-319-08846-4_11 fatcat:xk7qy27eorf7jlsh5tlu5nba3m

Alternating, private alternating, and quantum alternating realtime automata [article]

Gökalp Demirci and Mika Hirvensalo and Klaus Reinhardt and A. C. Cem Say and Abuzer Yakaryılmaz
2019 arXiv   pre-print
Regarding quantum finite automata (QFAs), we show that the emptiness problem is undecidable both for universal QFAs on general alphabets, and for alternating QFAs with two alternations on unary alphabets  ...  Firstly, we show that the emptiness problem for alternating one-counter automata on unary alphabets is undecidable.  ...  Quantum alternation We refer the reader to [21, 31, 2] for the basics of quantum computation and quantum automata.  ... 
arXiv:1407.0334v4 fatcat:7ex2kzyb35atdicov25gejjmvm

The Minimum Amount of Useful Space: New Results and New Directions [chapter]

Klaus Reinhardt, Abuzer Yakaryılmaz
2014 Lecture Notes in Computer Science  
CAs with quantum and classical states within middle log n space and bounded error. ⋆ A preliminary report on some contents of this paper is arXiv:1309.4767. ⋆⋆ Yakaryılmaz was partially supported by CAPES  ...  We consider minimal space requirements when using memory with restricted access policy (pushdown -hence giving pushdown automata (PDAs), and counter -hence giving counter automata (CAs)) in connection  ...  our questions on the subject matter of this paper, and, the anonymous reviewers for their very helpful comments (based on which we rewrote the abstract and made many corrections within the text).  ... 
doi:10.1007/978-3-319-09698-8_28 fatcat:ht5j2x4qrjamrba4nrct4fi7dq

Classical Automata on Promise Problems

Viliam Geffert, Abuzer Yakaryilmaz
2015 Discrete Mathematics & Theoretical Computer Science  
First, it was known that there is a family of unary promise problems solvable by quantum automata by using a single qubit, but the number of states required by corresponding one-way deterministic automata  ...  International audience Promise problems were mainly studied in quantum automata theory. Here we focus on state complexity of classical automata for promise problems.  ...  Then, in Section 4, we consider a family of unary promise problems given by Ambainis and Yakaryılmaz in [2] , solvable by only two-state one-way quantum finite automata.  ... 
doi:10.46298/dmtcs.2138 fatcat:u6wynlc34nbp3dxyjchyarxw5i

Quantum finite automata: survey, status and research directions [article]

Amandeep Singh Bhatia, Ajay Kumar
2019 arXiv   pre-print
The statistics of quantum finite automata related papers are shown and open problems are identified for more advanced research.  ...  Quantum automata can be classified thusly: quantum finite automata, quantum sequential machine, quantum pushdown automata, quantum Turing machine and orthomodular lattice-valued automata.  ...  Recent results Gainutdinova and Abuzer Yakarylmaz 2015 [77] • Investigated the power of QFA and PFA on unary promise problems.  ... 
arXiv:1901.07992v1 fatcat:yoxwrd6e55gh3heapwy3w5uuhm

Classical Automata on Promise Problems [chapter]

Viliam Geffert, Abuzer Yakaryılmaz
2014 Lecture Notes in Computer Science  
Promise problems were mainly studied in quantum automata theory. Here we focus on state complexity of classical automata for promise problems.  ...  First, it was known that there is a family of unary promise problems solvable by quantum automata by using a single qubit, but the number of states required by corresponding one-way deterministic automata  ...  First, we present a probabilistically very easy family of unary promise problems, i.e., solvable by one-way two-state automata with bounded-error.  ... 
doi:10.1007/978-3-319-09704-6_12 fatcat:n6tnt6spl5fwfabiih5i5hp454

Automata and Quantum Computing [article]

Andris Ambainis, Abuzer Yakaryılmaz
2018 arXiv   pre-print
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.  ...  Keywords: quantum finite automata, probabilistic finite automata, nondeterminism, bounded error, unbounded error, state complexity, decidability and undecidability, computational complexity  ...  Cem Say and John Watrous for their helpful comments on the subject matter of this chapter.  ... 
arXiv:1507.01988v2 fatcat:ww2rhgjp6bfevcgasu4e4xant4

Classical automata on promise problems [article]

Viliam Geffert, Abuzer Yakaryilmaz
2014 arXiv   pre-print
Promise problems were mainly studied in quantum automata theory. Here we focus on state complexity of classical automata for promise problems.  ...  First, it was known that there is a family of unary promise problems solvable by quantum automata by using a single qubit, but the number of states required by corresponding one-way deterministic automata  ...  First, we present a probabilistically very easy family of unary promise problems, i.e., solvable by one-way two-state automata with bounded-error.  ... 
arXiv:1405.6671v2 fatcat:oiezwypghrcgvavjhshmgatkea

New results on classical and quantum counter automata [article]

Masaki Nakanishi, Abuzer Yakaryılmaz, Aida Gainutdinova
2019 arXiv   pre-print
We show that one-way quantum one-counter automaton with zero-error is more powerful than its probabilistic counterpart on promise problems.  ...  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.  ...  Masaki was partially supported by JSPS KAKENHI Grant Numbers 16K00007, 24500003 and 24106009, and also by the Asahi Glass Foundation.  ... 
arXiv:1412.6761v4 fatcat:sdeiezshnzdv7efns5nouueeau
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