Abstract
We study the computational power of real-time finite automata that have been augmented with a vector of dimension k, and programmed to multiply this vector at each step by an appropriately selected k×k matrix. Only one entry of the vector can be tested for equality to 1 at any time. Classes of languages recognized by deterministic, nondeterministic, and “blind” versions of these machines are studied and compared with each other, and the associated classes for multicounter automata, automata with multiplication, and generalized finite automata.
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References
Fischer, P.C., Meyer, A.R., Rosenberg, A.L.: Counter machines and counter languages. Mathematical Systems Theory 2(3), 265–283 (1968)
Greibach, S.A.: Remarks on blind and partially blind one-way multicounter machines. Theoretical Computer Science 7, 311–324 (1978)
Ibarra, O.H., Sahni, S.K., Kim, C.E.: Finite automata with multiplication. Theoretical Computer Science 2(3), 271 (1976)
Turakainen, P.: Generalized automata and stochastic languages. Proceedings of the American Mathematical Society 21, 303–309 (1969)
Yakaryılmaz, A.: Superiority of one-way and realtime quantum machines. RAIRO - Theoretical Informatics and Applications 46(4), 615–641 (2012)
Laing, R.: Realization and complexity of commutative events. Technical report, University of Michigan (1967)
Fischer, P.C., Meyer, A.R., Rosenberg, A.L.: Real time counter machines. In: Proceedings of the 8th Annual Symposium on Switching and Automata Theory (SWAT 1967). FOCS 1967, pp. 148–154. IEEE Computer Society, Washington, DC (1967)
Diêu, P.D.: Criteria of representability of languages in probabilistic automata. Cybernetics and Systems Analysis 13(3), 352–364 (1977); Translated from Kibernetika (3), 39–50, (May-June 1977)
Freivalds, R.: Probabilistic two-way machines. In: Proceedings of the International Symposium on Mathematical Foundations of Computer Science, pp. 33–45 (1981)
Dwork, C., Stockmeyer, L.: Finite state verifiers I: The power of interaction. Journal of the ACM 39(4), 800–828 (1992)
Ravikumar, B.: Some observations on 2-way probabilistic finite automata. In: Shyamasundar, R.K. (ed.) FSTTCS 1992. LNCS, vol. 652, pp. 392–403. Springer, Heidelberg (1992)
Diêu, P.D.: On a class of stochastic languages. Mathematical Logic Quarterly 17(1), 421–425 (1971)
Yakaryilmaz, A.: Quantum Alternation. In: Bulatov, A.A., Shur, A.M. (eds.) CSR 2013. LNCS, vol. 7913, pp. 334–346. Springer, Heidelberg (2013)
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Salehi, Ö., Yakaryılmaz, A., Say, A.C.C. (2013). Real-Time Vector Automata. In: Gąsieniec, L., Wolter, F. (eds) Fundamentals of Computation Theory. FCT 2013. Lecture Notes in Computer Science, vol 8070. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40164-0_28
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DOI: https://doi.org/10.1007/978-3-642-40164-0_28
Publisher Name: Springer, Berlin, Heidelberg
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