Abstract
Reversible computational models with discrete internal states are said to be time-symmetric, if they can go back and forth in time by applying the same transition function. The direction in time is adjusted by a weak transformation of the phase-space, that is, an involution. So, these machines themselves cannot distinguish whether they run forward or backward in time. From this viewpoint, finite state machines and pushdown machines are studied in detail. In essence, it turns out that there are reversible machines which are not time-symmetric, but equivalent time-symmetric machines can effectively be constructed. The notion of time-symmetry is discussed, several examples are given, and further results concerning unary inputs and descriptional complexity issues are shown.
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
Aho, A.V., Ullman, J.D.: The theory of parsing, translation, and compiling Parsing vol. I. Prentice-Hall Inc. (1972)
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)
Axelsen, H.B.: Reversible multi-head finite automata characterize reversible logarithmic space. In: Dediu, A.-H., Martín-Vide, C. (eds.) LATA 2012. LNCS, vol. 7183, pp. 95–105. Springer, Heidelberg (2012)
Axelsen, H.B., Glück, R.: A simple and efficient universal reversible Turing machine. In: Language and Automata Theory and Applications (LATA 2011). LNCS, vol. 6638, pp. 117–128. Springer (2011)
Bennet, C.H.: Logical reversibility of computation. IBM J. Res. Dev. 17, 525–532 (1973)
Frank, M.P.: Introduction to reversible computing: motivation, progress, and challenges. In: Computing Frontiers 2005, pp. 385–390. ACM (2005)
Gajardo, A., Kari, J., Moreira, A.: On time-symmetry in cellular automata. J. Comput. System Sci. 78, 1115–1126 (2012)
García, P., Vázquez de Parga, M., Cano, A., López, D.: On locally reversible languages. Theoret. Comput. Sci. 410, 4961–4974 (2009)
García, P., Vázquez de Parga, M., López, D.: On the efficient construction of quasi-reversible automata for reversible languages. Inform. Process. Lett. 107, 13–17 (2008)
Ginsburg, S., Rice, H.G.: Two families of languages related to ALGOL. J. ACM 9, 350–371 (1962)
Gruska, J.: Quantum Computing. McGraw-Hill (1999)
Gudder, S., Ball, R.: Properties of quantum languages. Int. J. Theoret. Phys. 41, 569–591 (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., Malcher, A.: Fast reversible language recognition using cellular automata. Inform. Comput. 206, 1142–1151 (2008)
Kutrib, M., Malcher, A.: Real-time reversible iterative arrays. Theoret. Comput. Sci. 411, 812–822 (2010)
Kutrib, M., Malcher, A.: Reversible pushdown automata. In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 368–379. Springer, Heidelberg (2010)
Kutrib, M., Malcher, A.: Reversible pushdown automata. J. Comput. System Sci. 78, 1814–1827 (2012)
Kutrib, M., Malcher, A.: One-way reversible multi-head finite automata. In: Glück, R., Yokoyama, T. (eds.) RC 2012. LNCS, vol. 7581, pp. 14–28. Springer, Heidelberg (2013)
Lamb, J.S., Roberts, J.A.: Time-reversal symmetry in dynamical systems: A survey. Phys. D 112, 1–39 (1998)
Landauer, R.: Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183–191 (1961)
Lombardy, S.: On the construction of reversible automata for reversible languages. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 170–182. Springer, Heidelberg (2002)
Morita, K.: Reversible computing and cellular automata – A survey. Theoret. Comput. Sci. 395, 101–131 (2008)
Morita, K.: Two-way reversible multi-head finite automata. Fund. Inform. 110, 241–254 (2011)
Morita, K.: A deterministic two-way multi-head finite automaton can be converted into a reversible one with the same number of heads. In: Glück, R., Yokoyama, T. (eds.) RC 2012. LNCS, vol. 7581, pp. 29–43. Springer, Heidelberg (2013)
Morita, K., Shirasaki, A., Gono, Y.: A 1-tape 2-symbol reversible Turing machine. Trans. IEICE E72, 223–228 (1989)
Phillips, I.C.C., Ulidowski, I.: Reversing algebraic process calculi. J. Log. Algebr. Program. 73, 70–96 (2007)
Pin, J.E.: On reversible automata. In: Simon, I. (ed.) LATIN 1992. LNCS, vol. 583, pp. 401–416. Springer, Heidelberg (1992)
Yokoyama, T.: Reversible computation and reversible programming languages. Electron. Notes Theor. Comput. Sci. 253, 71–81 (2010)
Yokoyama, T., Axelsen, H.B., Glück, R.: Reversible flowchart languages and the structured reversible program theorem. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 258–270. Springer, Heidelberg (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kutrib, M., Worsch, T. (2013). Time-Symmetric Machines. In: Dueck, G.W., Miller, D.M. (eds) Reversible Computation. RC 2013. Lecture Notes in Computer Science, vol 7948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38986-3_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-38986-3_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38985-6
Online ISBN: 978-3-642-38986-3
eBook Packages: Computer ScienceComputer Science (R0)