On the power of two-way multihead quantum finite automata

This paper introduces a variant of two-way quantum finite automata named two-way multihead quantum finite automata. A two-way quantum finite automaton is more powerful than classical two-way finite automata. However, the generalizations of two-way quantum finite automata have not been defined so far as compared to one-way quantum finite automata model. We have investigated the newly introduced automata from two aspects: the language recognition capability and its comparison with classical and quantum counterparts. It has been proved that a language which cannot be recognized by any one-way and multi-letter quantum finite automata can be recognized by two-way quantum finite automata. Further, it has been shown that a language which cannot be recognized by two-way quantum finite automata can be recognized by two-way multihead quantum finite automata with two heads. Furthermore, it has been investigated that quantum variant of two-way deterministic multihead finite automata takes less number of heads to recognize a language containing of all words whose length is a prime number.

[1]  Shenggen Zheng,et al.  On the state complexity of semi-quantum finite automata , 2014, RAIRO Theor. Informatics Appl..

[2]  Pedram Khalili Amiri,et al.  Quantum computers , 2003 .

[3]  Ajay Kumar,et al.  Modeling of RNA secondary structures using two-way quantum finite automata , 2018 .

[4]  Martin Kutrib,et al.  Multi-Head Finite Automata: Characterizations, Concepts and Open Problems , 2009, CSP.

[5]  R. Feynman.  Simulating physics with computers , 1999 .

[6]  Arnold L. Rosenberg.  On multi-head finite automata , 1965, SWCT.

[7]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[8]  Andris Ambainis,et al.  Two-way finite automata with quantum and classical state , 1999, Theor. Comput. Sci..

[9]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[10]  Lihua Wu,et al.  Characterizations of one-way general quantum finite automata , 2009, Theor. Comput. Sci..

[11]  Kazuo Iwama,et al.  Undecidability on quantum finite automata , 1999, STOC '99.

[12]  Ajay Kumar,et al.  Quantifying matrix product state , 2018, Quantum Inf. Process..

[13]  Shenggen Zheng,et al.  Promise problems solved by quantum and classical finite automata , 2014, Theor. Comput. Sci..

[14]  Kumar S. Ray,et al.  1-Way Multihead Quantum Finite State Automata , 2016 .

[15]  Shenggen Zheng,et al.  State succinctness of two-way finite automata with quantum and classical states , 2012, Theor. Comput. Sci..

[16]  Daowen Qiu,et al.  Determining the equivalence for one-way quantum finite automata , 2007, Theor. Comput. Sci..

[17]  John Watrous,et al.  On the power of quantum finite state automata , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[18]  Kenichi Morita,et al.  Two-Way Reversible Multi-Head Finite Automata , 2011, Fundam. Informaticae.

[19]  Shenggen Zheng,et al.  Two-Tape Finite Automata with Quantum and Classical States , 2011, 1104.3634.

[20]  Paulo Mateus,et al.  Exponentially more concise quantum recognition of non-RMM regular languages , 2015, J. Comput. Syst. Sci..

[21]  Paulo Mateus,et al.  On the complexity of minimizing probabilistic and quantum automata , 2012, Inf. Comput..

[22]  Burkhard Monien.  Two-Way Multihead Automata Over a One-Letter Alphabet , 1980, RAIRO Theor. Informatics Appl..

[23]  Daowen Qiu,et al.  Characterization of Sequential Quantum Machines , 2002 .

[24]  Kumar Sankar Ray,et al.  2-tape 1-way Quantum Finite State Automata , 2016, ArXiv.

[25]  Martin Kutrib,et al.  Complexity of multi-head finite automata: Origins and directions , 2011, Theor. Comput. Sci..

[26]  Lov K. Grover.  A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[27]  Pierre McKenzie,et al.  Reversible Space Equals Deterministic Space , 2000, J. Comput. Syst. Sci..

[28]  Ansis Rosmanis,et al.  Multi-letter Reversible and Quantum Finite Automata , 2007, Developments in Language Theory.

[29]  James P. Crutchfield,et al.  Quantum automata and quantum grammars , 2000, Theor. Comput. Sci..

[30]  Jozef Gruska,et al.  Multi-letter quantum finite automata: decidability of the equivalence and minimization of states , 2011, Acta Informatica.

[31]  Ivan Hal Sudborough,et al.  Bounded-Reversal Multihead Finite Automata Languages , 1974, Inf. Control..

[32]  Daowen Qiu,et al.  Determination of equivalence between quantum sequential machines , 2006, Theor. Comput. Sci..

[33]  Jiacun Wang,et al.  Handbook of Finite State Based Models and Applications , 2012 .

[34]  Oscar H. Ibarra,et al.  On Two-way Multihead Automata , 1973, J. Comput. Syst. Sci..

[35]  Dana S. Scott,et al.  Finite Automata and Their Decision Problems , 1959, IBM J. Res. Dev..

[36]  Martin Kutrib,et al.  One-way reversible multi-head finite automata , 2012, Theor. Comput. Sci..

[37]  I. Chuang,et al.  Quantum Computation and Quantum Information: Introduction to the Tenth Anniversary Edition , 2010 .

[38]  Shenggen Zheng,et al.  Power of the interactive proof systems with verifiers modeled by semi-quantum two-way finite automata , 2013, Inf. Comput..

[39]  Sheng Yu,et al.  Hierarchy and equivalence of multi-letter quantum finite automata , 2008, Theor. Comput. Sci..

[40]  Daowen Qiu,et al.  Characterizations of quantum automata , 2004, Theor. Comput. Sci..

[41]  Kenichi Morita.  A Deterministic Two-Way Multi-head Finite Automaton Can Be Converted into a Reversible One with the Same Number of Heads , 2012, RC.

[42]  Shenggen Zheng,et al.  Some Languages Recognized by Two-Way Finite Automata with Quantum and Classical States , 2011, Int. J. Found. Comput. Sci..