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Watson–Crick quantum finite automata

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Abstract

One-way quantum finite automata are reversible in nature, which greatly reduces its accepting property. In fact, the set of languages accepted by one-way quantum finite automata is a proper subset of regular languages. In this paper, we replace the tape head of one-way quantum finite automata with DNA double strand and name the model Watson–Crick quantum finite automata. The non-injective complementarity relation of Watson–Crick automata introduces non-determinism in the quantum model. We show that this introduction of non-determinism increases the computational power of one-way quantum finite automata significantly. Watson–Crick quantum finite automata can accept all regular languages and also accepts some languages which are not accepted by any multi-head deterministic finite automata. Exploiting the superposition property of quantum finite automata, we show that Watson–Crick quantum finite automata accept the language L = {ww|w ∈ {a, b}*}.

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References

  1. 1.

    Kondacs, A., Watrous, J.: On the power of quantum finite state automata. In: Proceedings of the 38th IEEE Conference on Foundations of Computer Science, pp. 66–75 (1997)

  2. 2.

    Moore, C., Crutchfield, J.P.: Quantum automata and quantum grammars. Theor. Comput. Sci. 237(1–2), 275–306 (2000)

  3. 3.

    Ambainis, A., Freivalds, R.: One-way quantum finite automata: strengths, weaknesses and generalizations. In: IEEE 39th Annual Symposium on Foundations of Computer Science, pp. 332–342 (1998)

  4. 4.

    Freund, R., Păun, G., Rozenberg, G., Salomaa, A.: Watson–Crick finite automata. In: Proceedings 3rd DIMACS workshop on DNA based computers, Philadelphia, pp. 297–328 (1997)

  5. 5.

    Păun, G., Rozenberg, G., Salomaa, A., Computing, D.N.A.: New Computing Paradigms. Springer, Berlin (1998)

  6. 6.

    Czeizler, E., Czeizler, E., Kari, L., Salomaa, K.: On the descriptional complexity of Watson–Crick automata. Theor. Comput. Sci. 410(35), 3250–3260 (2009)

  7. 7.

    Chatterjee, K., Ray, K.S.: Reversible Watson–Crick automata. Acta Informatica 54(5), 487–499 (2017)

  8. 8.

    Kutrib, M., Malcher, A.: One-way reversible multi-head finite automata, reversible computation. Lect. Notes Comput. Sci. 7581, 14–28 (2013)

  9. 9.

    Yao, A.C., Rivest, R.L.: k + 1 heads are better than k. J. ACM (JACM) 25(2), 337–340 (1978)

  10. 10.

    Nagy, B., Kovacs, Z.: On simple 5′ → 3′ sensing Watson–Crick finite-state transducers. NCMA 2019, 155–170 (2019)

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Correspondence to Debayan Ganguly.

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Ganguly, D., Chatterjee, K. & Ray, K.S. Watson–Crick quantum finite automata. Acta Informatica (2020). https://doi.org/10.1007/s00236-020-00370-x

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