Affine Computation and Affine Automaton

We introduce a quantum-like classical computational concept, called affine computation, as a generalization of probabilistic computation. After giving the basics of affine computation, we define affine finite automata AfA and compare it with quantum and probabilistic finite automata QFA and PFA, respectively with respect to three basic language recognition modes. We show that, in the cases of bounded and unbounded error, AfAs are more powerful than QFAs and PFAs, and, in the case of nondeterministic computation, AfAs are more powerful than PFAs but equivalent to QFAs.

[1]  A. C. Cem Say,et al.  Quantum Finite Automata: A Modern Introduction , 2014, Computing with New Resources.

[2]  A. C. Cem Say,et al.  Languages recognized by nondeterministic quantum finite automata , 2009, Quantum Inf. Comput..

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

[4]  Azaria Paz,et al.  Introduction to probabilistic automata (Computer science and applied mathematics) , 1971 .

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

[6]  Andris Ambainis,et al.  Automata and Quantum Computing , 2015, Handbook of Automata Theory.

[7]  Abuzer Yakaryilmaz,et al.  Can one quantum bit separate any pair of words with zero-error? , 2016, ArXiv.

[8]  Mariëlle Stoelinga,et al.  An Introduction to Probabilistic Automata , 2002, Bull. EATCS.

[9]  Marcos Villagra,et al.  Language recognition power and succinctness of affine automata , 2016, Natural Computing.

[10]  Abuzer Yakaryilmaz,et al.  Superiority of one-way and realtime quantum machines , 2011, RAIRO Theor. Informatics Appl..

[11]  Sheila A. Greibach.  Remarks on Blind and Partially Blind One-Way Multicounter Machines , 1978, Theor. Comput. Sci..

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

[13]  Azaria Paz,et al.  Probabilistic automata , 2003 .

[14]  A. C. Cem Say,et al.  Unbounded-error quantum computation with small space bounds , 2010, Inf. Comput..

[15]  Scott Aaronson,et al.  Quantum computing, postselection, and probabilistic polynomial-time , 2004, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[16]  John Watrous,et al.  Quantum Computational Complexity , 2008, Encyclopedia of Complexity and Systems Science.

[17]  A. C. Cem Say,et al.  Languages Recognized with Unbounded Error by Quantum Finite Automata , 2008, CSR.

[18]  Christel Baier,et al.  Probabilistic ω-automata , 2012, JACM.