Abstract
Quantum finite automata have been studied intensively since their introduction in late 1990s. This paper seeks their direct application to interactive proof systems in which a mighty quantum prover communicates with a quantum-automaton verifier through a common communication cell.
This work was supported in part by the Natural Sciences and Engineering Research Council of Canada.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ambainis, A., Beaudry, M., Golovkins, M., Ķikusts, A., Mercer, M., Thérien, D.: Algebraic results on quantum automata. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 93–104. Springer, Heidelberg (2004)
Babai, L.: Trading group theory for randomness. In: Proc. 17th STOC, pp. 421–429 (1985)
Borodin, A., Cook, S., Pippenger, N.: Parallel computation for well-endowed rings and space-bounded probabilistic machines. Inform. Control 58, 113–136 (1983)
Brodsky, A., Pippenger, N.: Characterizations of 1-way quantum finite automata. SIAM J. Comput. 31, 1456–1478 (2002)
Condon, A.: The complexity of space bounded interactive proof systems. In: Ambos-Spies, et al. (eds.) Complexity Theory: Current Research, pp. 147–189. Cambridge University Press, Cambridge (1993)
Condon, A., Hellerstein, L., Pottle, S., Wigderson, A.: On the power of finite automata with both nondeterministic and probabilistic states. SIAM J. Comput. 27, 739–762 (1998)
Dwork, C., Stockmeyer, L.: Finite state verifiers I: the power of interaction. J. ACM 39, 800–828 (1992)
Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM J. Comput. 18, 186–208 (1989)
Goldwasser, S., Sipser, M.: Private coins versus public coins in interactive proof systems. In: Proc. 18th STOC, pp. 59–68 (1986)
Gruska, J.: Quantum Computing. McGraw Hill, New York (1999)
Kitaev, A., Watrous, J.: Parallelization, amplification, and exponential time simulation of quantum interactive proof systems. In: Proc. 32nd STOC, pp. 608–617 (2000)
Kobayashi, H., Matsumoto, K.: Quantum multi-prover interactive proof systems with limited prior entanglement. J. Comput. Syst. Sci. 66, 429–450 (2003)
Kondacs, A., Watrous, J.: On the power of quantum finite state automata. In: Proc. 38th FOCS, pp. 66–75 (1997)
Moore, C., Crutchfield, J.: Quantum automata and quantum grammars. Theor. Comput. Sci. 237, 275–306 (2000)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Nishimura, H., Yamakami, T.: Polynomial time quantum computation with advice. Inform. Process. Lett. 90, 195–204 (2004)
Shamir, A.: IP=PSPACE. J. ACM 39, 869–877 (1992)
Watrous, J.: On quantum and classical space-bounded processes with algebraic transition amplitudes. In: Proc. 40th FOCS, pp. 341–351 (1999)
Watrous, J.: PSPACE has constant-round quantum interactive proof systems. Theor. Comput. Sci. 292, 575–588 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nishimura, H., Yamakami, T. (2005). An Application of Quantum Finite Automata to Interactive Proof Systems (Extended Abstract). In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds) Implementation and Application of Automata. CIAA 2004. Lecture Notes in Computer Science, vol 3317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30500-2_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-30500-2_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24318-2
Online ISBN: 978-3-540-30500-2
eBook Packages: Computer ScienceComputer Science (R0)