Abstract
Iterative arrays are one-dimensional arrays of interconnected interacting finite automata. The cell at the origin is equipped with a one-way read-only input tape. We investigate iterative arrays as acceptors for formal languages. In particular, we consider real-time devices which are reversible on the core of computation, i.e., from initial configuration to the configuration given by the time complexity. This property is called real-time reversibility. It is shown that real-time reversible iterative arrays can simulate restricted variants of stacks and queues. It turns out that real-time reversible iterative arrays are strictly weaker than real-time reversible cellular automata. On the other hand, a non-semilinear language is accepted. We show that real-time reversibility itself is not even semidecidable, which extends the undecidability for cellular automata and contrasts the general case, where reversibility is decidable for one-dimensional devices. Moreover, we prove the non-semidecidability of several other properties. The closure under Boolean operations is also derived.
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References
Amoroso, S., Patt, Y.N.: Decision procedures for surjectivity and injectivity of parallel maps for tesselation structures. J. Comput. System Sci. 6, 448–464 (1972)
Angluin, D.: Inference of reversible languages. J. ACM 29, 741–765 (1982)
Bennet, C.H.: Logical reversibility of computation. IBM Journal of Research and Development 17, 525–532 (1973)
Buchholz, Th., Kutrib, M.: Some relations between massively parallel arrays. Parallel Comput. 23, 1643–1662 (1997)
Buchholz, T., Klein, A., Kutrib, M.: Iterative arrays with limited nondeterministic communication cell. In: Words, Languages and Combinatorics III, pp. 73–87. World Scientific Publishing, Singapore (2003)
Buchholz, Th., Klein, A., Kutrib, M.: Iterative arrays with small time bounds. In: Nielsen, M., Rovan, B. (eds.) MFCS 2000. LNCS, vol. 1893, pp. 243–252. Springer, Heidelberg (2000)
Cole, S.N.: Real-time computation by n-dimensional iterative arrays of finite-state machines, pp. 349–365. IEEE Computer Society Press, Los Alamitos (1969)
Czeizler, E., Kari, J.: A tight linear bound on the neighborhood of inverse cellular automata. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 410–420. Springer, Heidelberg (2005)
Fischer, P.C.: Generation of primes by a one-dimensional real-time iterative array. J. ACM 12, 388–394 (1965)
Hartmanis, J.: Context-free languages and Turing machine computations. In: Proc. Symposia in Applied Mathematics, vol. 19, pp. 42–51 (1967)
Ibarra, O.H., Palis, M.A.: Some results concerning linear iterative (systolic) arrays. J. Parallel Distributed Comput. 2, 182–218 (1985)
Imai, K., Morita, K.: Firing squad synchronization problem in reversible cellular automata. Theoret. Comput. Sci. 165, 475–482 (1996)
Iwamoto, C., Hatsuyama, T., Morita, K., Imai, K.: Constructible functions in cellular automata and their applications to hierarchy results. Theoret. Comput. Sci. 270, 797–809 (2002)
Kari, J.: Reversibility and surjectivity problems of cellular automata. J. Comput. System Sci. 48, 149–182 (1994)
Kari, J.: Theory of cellular automata: a survey. Theoret. Comput. Sci. 334, 3–33 (2005)
Kutrib, M.: Automata arrays and context-free languages. In: Where Mathematics, Computer Science and Biology Meet, pp. 139–148. Kluwer Academic Publishers, Dordrecht (2001)
Kutrib, M., Malcher, A.: Fast reversible language recognition using cellular automata. In: Language and Automata Theory and Applications (LATA 2007). LNCS, Springer, Heidelberg ( to appear, 2007)
Malcher, A.: On the descriptional complexity of iterative arrays. IEICE Trans. Inf. Syst. E87-D, 721–725 (2004)
Morita, K., Harao, M.: Computation universality of one dimensional reversible injective cellular automata. Trans. IEICE E72, 758–762 (1989)
Morita, K., Shirasaki, A., Gono, Y.: A 1-tape 2-symbol reversible Turing machine. Trans. of the IEICE E72, 223–228 (1989)
Morita, K.: Computation-universality of one-dimensional one-way reversible cellular automata. Inform. Process. Lett. 42, 325–329 (1992)
Morita, K., Ueno, S.: Parallel generation and parsing of array languages using reversible cellular automata. Int. J. Pattern Recog. and Artificial Intelligence 8, 543–561 (1994)
Morita, K.: Reversible simulation of one-dimensional irreversible cellular automata. Theoret. Comput. Sci. 148, 157–163 (1995)
Morita, K., Ueno, S., Imai, K.: Characterizing the ability of parallel array generators on reversible partitioned cellular automata. Int. J. Pattern Recog. and Artificial Intelligence 13, 523–538 (1999)
Pin, J.E.: On reversible automata. In: Simon, I. (ed.) LATIN 1992. LNCS, vol. 583, pp. 401–416. Springer, Heidelberg (1992)
Toffoli, T.: Computation and construction universality of reversible cellular automata. J. Comput. System Sci. 15, 213–231 (1977)
Smith III, A.R.: Real-time language recognition by one-dimensional cellular automata. J. Comput. System Sci. 6, 233–253 (1972)
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Kutrib, M., Malcher, A. (2007). Real-Time Reversible Iterative Arrays. In: Csuhaj-Varjú, E., Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 2007. Lecture Notes in Computer Science, vol 4639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74240-1_33
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DOI: https://doi.org/10.1007/978-3-540-74240-1_33
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